"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
nCr = 1
res = 1
for r in range(1, n + 1):
nCr = (nCr * (n + 1 - r)) / r
res += nCr * nCr
return res
[[1], [2], [3]] [[4], [5], [6], [10], [15], [20], [50], [100], [75], [200], [150], [1000], [1000000], [151], [1000001], [101], [102], [True], [51], [14], [9], [1001], [49], [13], [999], [21], [199], [22], [201], [999999], [24], [53], [1002], [999998], [52], [74], [16], [202], [17], [1000002], [18], [1000003], [203], [103], [998], [25], [23], [1004], [999997], [8], [19], [68], [198], [67], [197], [48], [204], [152], [1003], [11], [997], [12], [206], [73], [72], [196], [999996], [195], [205], [1005], [194], [54], [148], [996], [55], [1000004], [56], [66], [26], [76], [999995], [1000005], [3], [149], [96], [71], [7], [207], [2], [95], [64], [57], [58], [995], [63], [208], [97], [69], [153], [104], [94], [154], [90], [77], [994], [91], [79], [27], [1000006], [70], [98], [41], [88]] code-llama-multi-7b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
"""
:param n: int
:return: float
"""
if n == 1:
return 2.0
return 2.0 * count_binary_seq(n - 1) + 2.0 * math.factorial(n)
if __name__ == '__main__':
print(count_binary_seq(1))
print(count_binary_seq(2))
print(count_binary_seq(3))
print(count_binary_seq(4))
print(count_binary_seq(5))
print(count_binary_seq(6))
print(count_binary_seq(7))
print(count_binary_seq(8))
print(count_binary_seq(9))
print(count_binary_seq(10))
print(count_binary_seq(11))
print(count_binary_seq(12))
print(count_binary_seq(13))
print(count_binary_seq(14))
print(count_binary_seq(15))
print(count_binary_seq(16))
print(count_binary_seq(17))
print(count_binary_seq(18))
print(count_binary_seq(19))
print(count_binary_seq(20))
print(count_binary_seq(21))
print(count_binary_seq(22))
print(count_binary_seq(23))
print(count_binary_seq(24))
print(count_binary_seq(25))
print(count_binary_seq(26))
print(count_binary_seq(27))
print(count_binary_seq(28))
print(count_binary_seq(29))
print(count_binary_seq(30))
print(count_binary_seq(31))
print(count_binary_seq(32))
print(count_binary_seq(3databricks--dbrx-instruct. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
"""
This function calculates the count of all binary sequences of length 2n such that the sum of first n bits is same as the sum of last n bits.
"""
if n == 0:
return 1
elif n == 1:
return 2
else:
return (4 ** (n - 1)) * (2 * n - 1)
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)CohereForAI--c4ai-command-r-plus. fail_base: False, fail_plus: True
def count_binary_seq(n: int) -> int:
"""
Write a function to find the count of all binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits.
Args:
n (int): The length of the first half of the binary sequence.
Returns:
int: The count of valid binary sequences.
"""
from math import comb
total_length = 2 * n
choose = comb(total_length, n)
return choose
```claude-3-haiku-20240307. fail_base: True, fail_plus: True
Here's the solution wrapped in a Python markdown block:
```python
import math
def count_binary_seq(n):
"""
Find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
"""
if n == 0:
return 1.0
total = 0
for i in range(2**n):
first_half = bin(i)[2:].zfill(n)
second_half = bin(i ^ (2**n - 1))[2:].zfill(n)
if sum(map(int, first_half)) == sum(map(int, second_half)):
total += 1
return total
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)code-millenials-34b. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n <= 0:
return 0
elif n == 1:
return 2
else:
return 2 * (2 ** (2 * n - 1))
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)dolphin-2.6. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
# Calculate the number of binary sequences of length 2n
num_binary_seq = 2 ** (2 * n)
# Calculate the number of binary sequences of length n
num_binary_seq_n = 2 ** n
# Calculate the number of binary sequences of length n with the same sum of first n bits and last n bits
num_binary_seq_same_sum = num_binary_seq_n
# Calculate the number of binary sequences of length n with different sums of first n bits and last n bits
num_binary_seq_diff_sum = num_binary_seq_n * num_binary_seq_n - num_binary_seq_same_sum
# Calculate the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits
count_binary_seq = num_binary_seq_same_sum / num_binary_seq
return count_binary_seq
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)claude-3-opus-20240229. fail_base: True, fail_plus: True
Here's the code to solve the problem, wrapped in a markdown block:
```python
def count_binary_seq(n):
def count_sequences(n, diff):
if n == 0:
return 1 if diff == 0 else 0
return count_sequences(n - 1, diff + 1) + count_sequences(n - 1, diff - 1)
return count_sequences(n, 0) * 2 ** nmixtral-8x7b-instruct. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
# Calculate the sum of the first n bits
first_n_sum = (1 + 2**n - 1) * n
# Calculate the total number of binary sequences of length 2n
total_seq = 2**(2*n)
# Calculate the number of binary sequences with sum of first n bits not equal to sum of last n bits
unequal_sum_seq = 2 * (2**n - 1) * 2**n
# Calculate the number of binary sequences with sum of first n bits equal to sum of last n bits
equal_sum_seq = total_seq - unequal_sum_seq
# Return the count of binary sequences with equal sum of first n bits and last n bits
return equal_sum_seq
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 12.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 192.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(4), 3840.0, rel_tol=0.001)wizardcoder-34b. fail_base: False, fail_plus: True
Here's a Python function that finds the count of all binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits:
```python
import math
def count_binary_seq(n):
"""
Returns the count of all binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits.
"""
count = 0
for i in range(2**(2*n)):
binary = bin(i)[2:].zfill(2*n)
if sum(int(bit) for bit in binary[:n]) == sum(int(bit) for bit in binary[n:]):
count += 1
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
Explanation:
- We start by initializing a count variable to 0.
- We loop through all the integers from 0 to 2^(2n-1) using the `range()` function.
- We convert each integer to its binary representation using the `bin()` function and remove the '0b' prefix using slicing.
- We check if the sum of the first n bits is equal to the sum of the last n bits by slicing the binary string and using a generator expression to convert each bit to an integer and summing them up.
- If the condition is true, we increment the count variable.
- Finally, we return the count.
Note that we use the `math.isclose()` function to compare the result with the expected value of 2.0 since the output is a float. The `rel_tol` parameter specifies the relative tolerance, which means that the two values are considered equal if the difference between them is less than or equal to the given tolerance multiplied by the larger value. In this case, we set it to 0.001, which means that the two values are considered equal if they differ by no more than 1%. mixtral-8x22b-instruct-v0.1. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
# Calculate the total number of binary sequences of length 2n
total_sequences = 2 ** (2 * n)
# Calculate the number of binary sequences of length n
n_sequences = 2 ** n
# Calculate the number of binary sequences of length n with the same sum of bits
same_sum_sequences = 0
for i in range(n + 1):
# Calculate the number of binary sequences of length n with i bits set to 1
num_sequences = binomial_coefficient(n, i)
# If n is even, the number of sequences with the same sum of bits is the same for i and n - i
if n % 2 == 0:
same_sum_sequences += num_sequences ** 2
# If n is odd, the number of sequences with the same sum of bits is the same for i and n - i, except for i = n/2
else:
if i == n // 2:
same_sum_sequences += num_sequences * (num_sequences - 1) // 2
else:
same_sum_sequences += num_sequences ** 2
# Calculate the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits
count = same_sum_sequences / total_sequences
return count
def binomial_coefficient(n, k):
# Calculate the binomial coefficient using the formula n! / (k! * (n - k)!)
if k > n - k:
k = n - k
result = 1
for i in range(k):
result *= (n - i)
result //= (i + 1)
return result
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)code-llama-multi-34b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n: int
:return: float
"""
if n == 1:
return 2.0
else:
return 2 * count_binary_seq(n - 1)
if __name__ == '__main__':
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 8.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 32.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(4), 128.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(5), 512.0, rel_tol=0.001)
Qwen--Qwen1.5-72B-Chat. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n == 0:
return 1
else:
# The count of binary sequences of length 2n with equal sums of first and last n bits
# can be calculated as the sum of count of binary sequences of length 2n-2 with equal sums
# of first and last n-1 bits (prefix and suffix match) multiplied by 2 (for 0 and 1 as middle bit),
# and count of binary sequences of length 2n-2 with different sums of first and last n-1 bits
# (prefix and suffix don't match) which is just count_binary_seq(n-1) * count_binary_seq(n-1)
return 2 * count_binary_seq(n-1) + count_binary_seq(n-1) ** 2
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)mistral-large-latest. fail_base: True, fail_plus: True
Sure, I can help with that. Here's a Python function that uses dynamic programming to solve the problem:
```python
import math
def count_binary_seq(n):
# Create a 2D table to store the count of sequences
dp = [[0 for _ in range(n + 1)] for _ in range(n + 1)]
# Base case: There is only one sequence of length 0 with sum 0
dp[0][0] = 1
# Fill the table using dynamic programming
for i in range(1, 2 * n + 1):
for j in range(min(i, n) + 1):
# A bit can be either 0 or 1
dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j]
# The result is the number of sequences with sum n for the first n bits and the last n bits
return dp[2 * n][n]
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
This function works by creating a 2D table where `dp[i][j]` is the number of binary sequences of length `i` where the sum of the bits is `j`. It then fills this table using dynamic programming, with the result being the value of `dp[2 * n][n]`.codegen-2b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
"""
>>> count_binary_seq(1)
2.0
>>> count_binary_seq(2)
3.0
>>> count_binary_seq(3)
4.0
>>> count_binary_seq(4)
5.0
>>> count_binary_seq(5)
6.0
>>> count_binary_seq(6)
7.0
>>> count_binary_seq(7)
8.0
>>> count_binary_seq(8)
9.0
>>> count_binary_seq(9)
10.0
>>> count_binary_seq(10)
11.0
>>> count_binary_seq(11)
12.0
>>> count_binary_seq(12)
13.0
>>> count_binary_seq(13)
14.0
>>> count_binary_seq(14)
15.0
>>> count_binary_seq(15)
16.0
>>> count_binary_seq(16)
17.0
>>> count_binary_seq(17)
18.0
>>> count_binary_seq(18)
19.0
>>> count_binary_seq(19)
20.0
>>> count_binary_seq(20)
21.0
>>> count_binary_seq(21)
22.0
>>> count_binary_seq(22)
23.0
>>> count_binary_seq(23)
24.0
>>> count_binary_seq(24)
25.0
>>> count_binary_seq(25)
26.0
>>> count_binary_seq(26)
27.0
>>> count_binary_seq(27)
28.0
>>> count_binary_seq(28)
29.0
>>> count_binary_seq(29)
30.0
>>> count_binary_seq(30)
31.0
>>> count_binary_seq(31)
32.HuggingFaceH4--starchat2-15b-v0.1. fail_base: True, fail_plus: True
import math
from itertools import product
def count_binary_seq(n):
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
# Generate all possible binary sequences of length n
sequences = product([0, 1], repeat=n)
count = 0
for seq in sequences:
# Calculate the sum of first n bits
sum_first_n = sum(seq)
# Calculate the sum of last n bits
sum_last_n = sum(seq[n:])
# If the sums are equal, increment the count
if sum_first_n == sum_last_n:
count += 1
# Multiply the count by 2 to account for the symmetry in the sequences
return count * 2
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)codegemma-7b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
import sys
import time
import cProfile
import pstats
import io
import os
import re
import random
import string
import copy
import collections
import itertools
import functools
import operator
import heapq
import bisect
import array
import math
import fractions
import decimal
import cmath
import numbers
import struct
import pickle
import base64
import hashlib
import hmac
import zlib
import gzip
import bz2
import lzma
import re
import shlex
import stringprep
import unicodedata
import ipaddress
import email
import email.message
import email.header
import email.headerregistry
import email.utils
import email.contentmanager
import email.iterators
import email.policy
import email.errors
import email.charset
import email.base64mime
import email.encoders
import email.quoprimime
import email.iterators
import email.message
import email.parser
import email.policy
import email.utils
import email.contentmanager
import email.contentmanager
import email.iterators
import email.message
import email.header
import email.headerregistry
import email.utils
import email.errors
import email.charset
import email.base64mime
import email.encoders
import email.quoprimime
import email.iterators
import email.message
import email.parser
import email.policy
import email.utils
import email.contentmanager
import email.contentmanager
import email.iterators
import email.message
import email.header
import email.headerregistry
import email.utils
import email.errors
import email.charset
import email.base64mime
import email.encoders
import email.quoprimime
import email.iterators
import email.message
import email.parser
import email.policy
import email.utils
import email.contentmanager
import email.contentmanager
import email.iterators
import email.message
import email.header
import email.headerregistry
import email.utils
import email.errors
import email.charset
import email.base64mime
import email.encoders
import email.quoprimime
import email.iterators
import email.message
import email.parser
import email.policy
importcode-llama-multi-13b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n:
:return:
"""
if n == 1:
return 2
elif n == 2:
return 4
elif n == 3:
return 8
elif n == 4:
return 16
elif n == 5:
return 32
elif n == 6:
return 64
elif n == 7:
return 128
elif n == 8:
return 256
elif n == 9:
return 512
elif n == 10:
return 1024
elif n == 11:
return 2048
elif n == 12:
return 4096
elif n == 13:
return 8192
elif n == 14:
return 16384
elif n == 15:
return 32768
elif n == 16:
return 65536
elif n == 17:
return 131072
elif n == 18:
return 262144
elif n == 19:
return 524288
elif n == 20:
return 1048576
elif n == 21:
return 2097152
elif n == 22:
return 4194304
elif n == 23:
return 8388608
elif n == 24:
return 16777216
elif n == 25:
return 33554432
elif n == 26:
return 67108864
elif n == 27:
return 134217728
elif n == 28:
return 2deepseek-coder-6.7b-instruct. fail_base: True, fail_plus: True
Here is the Python function in a markdown style code block:
```python
def count_binary_seq(n):
# Initialize the count of binary sequences
count = [0] * (2*n + 1)
# Initialize the first count value
count[0] = 1
# Iterate through the range of 1 to 2n
for i in range(1, 2*n + 1):
# Update the count value
count[i] = 2 * count[i-1]
# If i is greater than or equal to n, subtract the count value of i-n
if i >= n:
count[i] -= count[i-n]
# Return the count value of 2n
return count[2*n]
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
This function uses dynamic programming to solve the problem. It initializes an array `count` to store the count of binary sequences of length `i` for `i` in the range from `0` to `2n`. It then iterates through the range from `1` to `2n`, updating the count value for each `i`. If `i` is greater than or equal to `n`, it subtracts the count value of `i-n` from the count value of `i`. Finally, it returns the count value of `2n`.
The function is tested with an assertion that checks if the count of binary sequences of length `1` is approximately `2.0`. The `math.isclose` function is used to compare the count value with `2.0`, with a relative tolerance of `0.001`.
open-hermes-2.5-code-290k-13b. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
total_combinations = 2 ** n
half_combinations = total_combinations // 2
return math.isclose(half_combinations, 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)codet5p-6b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
return math.factorial(2*n) // (math.factorial(n) * math.factorial(2*n-n))
print(count_binary_seq(1))
print(count_binary_seq(2))
print(count_binary_seq(3))
print(count_binary_seq(4))
print(count_binary_seq(5))
print(count_binary_seq(6))
print(count_binary_seq(7))
print(count_binary_seq(8))
print(count_binary_seq(9))
print(count_binary_seq(10))
print(count_binary_seq(11))
print(count_binary_seq(12))
print(count_binary_seq(13))
print(count_binary_seq(14))
print(count_binary_seq(15))
print(count_binary_seq(16))
print(count_binary_seq(17))
print(count_binary_seq(18))
print(count_binary_seq(19))
print(count_binary_seq(20))
print(count_binary_seq(21))
print(count_binary_seq(22))
print(count_binary_seq(23))
print(count_binary_seq(24))
print(count_binary_seq(25))
print(count_binary_seq(26))
print(count_binary_seq(27))
print(count_binary_seq(28))
print(count_binary_seq(29))
print(count_binary_seq(30))
print(count_binary_seq(31))
print(count_binary_seq(32))
print(count_binary_seq(33))
print(count_binary_seq(34))
print(count_binary_seq(35))
print(count_binary_seq(36))
print(count_binary_seq(37))
print(count_binary_seq(38))
print(count_binary_seq(39))
print(count_binary_seq(40))
print(count_binary_seq(41))
print(count_binary_seq(42))
print(count_binarycodegemma-7b-it. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n == 0:
return 1
return 2 * count_binary_seq(n - 1)
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)mistralai--Mistral-7B-Instruct-v0.2. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
# Calculate the number of binary digits in a sequence of length 2n
num_bits = 2 * n
# Create a binary number with n leading zeros and fill the rest with ones
# This number will be used as a mask for checking the condition
mask = (1 << (num_bits - n)) - 1
# Calculate the number of sequences having the same sum of first and last n bits
count = 0
for i in range(0, (1 << num_bits)):
if (i & mask) == ((i >> n) & mask):
count += 1
return count
# Test the function with n = 1
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)xwincoder-34b. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n == 1:
return 2
else:
return 2 * count_binary_seq(n - 1)
def main():
n = 1
assert math.isclose(count_binary_seq(n), 2.0, rel_tol=0.001)
print("All tests passed.")
wizardcoder-15b. fail_base: True, fail_plus: True
Here's the Python script for the problem:
```python
import math
def count_binary_seq(n):
count = 0
for i in range(2**n):
binary = bin(i)[2:].zfill(n)
if int(binary[:n], 2) == int(binary[n:], 2):
count += 1
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
The `count_binary_seq` function takes an integer `n` as input and returns the count of all binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits.
The function first initializes a count variable to 0. It then loops through all possible binary numbers of length n using a for loop and the `bin` and `zfill` functions. The `bin` function converts an integer to its binary representation and the `zfill` function pads the binary string with leading zeros to make it of length n.
For each binary number, the function checks if the sum of the first n bits is the same as the sum of the last n bits using the `int` function to convert the binary strings to integers and the `==` operator. If the condition is true, the count variable is incremented by 1.
Finally, the function returns the count of all binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits.
The `assert` statement checks if the function returns the correct count for the given input. The `math.isclose` function is used to compare floating point numbers with a relative tolerance of 0.001.code-llama-34b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param: - n - number of bits
return - float
"""
if n == 1:
return 2
elif n == 2:
return 5
else:
return 2 * count_binary_seq(n-1) + count_binary_seq(n-2)
def count_binary_seq_memo(n, memo=None):
if memo is None:
memo = {}
if n == 1:
return 2
elif n == 2:
return 5
elif n in memo:
return memo[n]
else:
memo[n] = 2 * count_binary_seq_memo(n-1, memo) + count_binary_seq_memo(n-2, memo)
return memo[n]
def count_binary_seq_dp(n):
if n == 1:
return 2
elif n == 2:
return 5
dp = [0] * (n+1)
dp[1] = 2
dp[2] = 5
for i in range(3, n+1):
dp[i] = 2 * dp[i-1] + dp[i-2]
return dp[n]
deepseek-coder-33b-instruct. fail_base: False, fail_plus: True
Here is the Python function to solve the problem:
```python
def count_binary_seq(n):
# Initialize the count to 0
count = 0
# Iterate over all possible binary sequences of length 2n
for i in range(2**(2*n)):
# Convert the number to binary and pad it with zeros to make it 2n bits
binary = bin(i)[2:].zfill(2*n)
# Check if the sum of the first n bits is equal to the sum of the last n bits
if binary[:n].count('1') == binary[n:].count('1'):
count += 1
return count
```
This function works by iterating over all possible binary sequences of length 2n, converting each number to binary, and then checking if the sum of the first n bits is equal to the sum of the last n bits. If it is, it increments the count.
Please note that this function will not work for large values of n due to the time complexity of the function. For large values of n, you may need to use a more efficient algorithm or data structure.
phi-2. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
if n == 0:
return 1
if n == 1:
return 2
return count_binary_seq(n-1) + count_binary_seq(n-2)
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 3.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 5.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(4), 8.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(5), 13.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(6), 21.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(7), 34.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(8), 55.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(9), 89.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(10), 144.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(11), 233.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(12), 377.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(13), 610.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(14), 987.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(15), 1597.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(16), 2584.0, rel_tol=0.001)
assert math.codet5p-2b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
return math.factorial(2*n) / (math.factorial(n) * math.factorial(n+1))
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(4), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(5), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(6), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(7), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(8), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(9), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(10), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(11), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(12), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(13), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(14), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(15), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(16), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(17), 2.0, rel_tbigcode--starcoder2-15b-instruct-v0.1. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
"""
Returns the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
"""
if n == 0:
return 1
count = 0
for i in range(2):
count += count_binary_seq(n - 1)
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```codegemma-2b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
if n == 0:
return 1
else:
return 2 * count_binary_seq(n - 1)white-rabbit-neo-33b-v1. fail_base: True, fail_plus: True
def count_binary_seq(n):
# Base case: if n is 0, there is only one binary sequence of length 0
if n == 0:
return 1
# Recursive case: count the number of binary sequences of length 2(n-1)
# and then add the sequences that satisfy the condition
count = count_binary_seq(n - 1)
# Add the sequences that satisfy the condition
for i in range(n):
count += 2 ** (2 * i)
return count
# Test the function
import math
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)microsoft--Phi-3-mini-4k-instruct. fail_base: False, fail_plus: True
import math
from itertools import product
def count_binary_seq(n):
"""
Counts the number of binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits.
"""
count = 0
for seq in product('01', repeat=2*n):
if sum(int(bit) for bit in seq[:n]) == sum(int(bit) for bit in seq[n:]):
count += 1
return count
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)speechless-codellama-34b. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n == 0:
return 1
else:
return 2 * count_binary_seq(n-1)
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
Explanation:
The function `count_binary_seq` takes an integer `n` as input and returns the count of all binary sequences of length `2n` such that the sum of the first `n` bits is the same as the sum of the last `n` bits. The function uses recursion to calculate the count. If `n` is 0, there is only one binary sequence of length 0, which is an empty string. Otherwise, the count is doubled for each increment of `n`.
meta-llama-3-70b-instruct. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
total = 2 ** (2 * n)
half = 2 ** n
result = 0
for i in range(n + 1):
result += math.comb(half, i) ** 2
return result / total
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)stable-code-3b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
return 2 ** (2 * n)
def count_binary_seq_recursive(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive(n - 1)
def count_binary_seq_recursive_2(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_2(n - 1)
def count_binary_seq_recursive_3(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_3(n - 1)
def count_binary_seq_recursive_4(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_4(n - 1)
def count_binary_seq_recursive_5(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_5(n - 1)
def count_binary_seq_recursive_6(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_6(n - 1)
def count_binary_seq_recursive_7(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_7(n - 1)
def count_binary_seq_recursive_8(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_8(n - 1)
def count_binary_seq_recursive_9(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_9(n - 1)
def count_binary_seq_recursive_10(n):
if n == 0:
return 1
return 2 * count_binary_seq_recursive_10(n - 1)
def count_binary_seq_recursive_11(n):
if n == 0codegen-6b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
>>> count_binary_seq(1)
2.0
>>> count_binary_seq(2)
4.0
>>> count_binary_seq(3)
6.0
>>> count_binary_seq(4)
8.0
>>> count_binary_seq(5)
10.0
>>> count_binary_seq(6)
12.0
>>> count_binary_seq(7)
14.0
>>> count_binary_seq(8)
16.0
>>> count_binary_seq(9)
18.0
>>> count_binary_seq(10)
20.0
>>> count_binary_seq(11)
22.0
>>> count_binary_seq(12)
24.0
>>> count_binary_seq(13)
26.0
>>> count_binary_seq(14)
28.0
>>> count_binary_seq(15)
30.0
>>> count_binary_seq(16)
32.0
>>> count_binary_seq(17)
34.0
>>> count_binary_seq(18)
36.0
>>> count_binary_seq(19)
38.0
>>> count_binary_seq(20)
40.0
>>> count_binary_seq(21)
42.0
>>> count_binary_seq(22)
44.0
>>> count_binary_seq(23)
46.0
>>> count_binary_seq(24)
48.0
>>> count_binary_seq(25)
50.0
>>> count_binary_seq(26)
52.0
>>> count_binary_seq(27)
54.0
>>> count_binary_seq(28)
56.0
>>> count_binary_seq(29)
58.0
>>> count_binary_seq(30)
60.0
>>> count_binary_seq(31)
62.0
>>>gpt-4-1106-preview. fail_base: False, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
# Calculate the binomial coefficient
def binomial_coeff(n, k):
if k == 0 or k == n:
return 1
return binomial_coeff(n-1, k-1) + binomial_coeff(n-1, k)
# Calculate the count of binary sequences
count = 0
for i in range(n+1):
count += binomial_coeff(n, i) ** 2
return count
# Example usage
# count_binary_seq(1) should return 2
gemma-7b-it. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
# The number of ways to have a sum of k bits in the first n bits is given by the binomial coefficient
# C(n, k) = n choose k = n! / (k! * (n-k)!).
# So, the total number of sequences is the sum of C(n, k) for k = 0 to n.
# Use a memoization table to avoid repeated calculations.
memo = {}
def count(n, k):
if n == 0:
return 1 if k == 0 else 0
if n not in memo:
memo[n] = count(n-1, k-1) + count(n-1, k)
return memo[n]
return count(n, n)opencodeinterpreter-ds-33b. fail_base: True, fail_plus: True
```python
def count_binary_seq(n):
if n == 0:
return 1
else:
return 2 * count_binary_seq(n - 1)
print(count_binary_seq(1))openchat. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
# Initialize the count to 0
count = 0
# Calculate the total number of binary sequences of length 2n
total_sequences = 2 ** (2 * n)
# Calculate the number of binary sequences with sum of first n bits equal to sum of last n bits
# This can be done by considering the number of ways to distribute n '1's among the first n bits
# and the number of ways to distribute n '1's among the last n bits
# The total number of ways to distribute n '1's among 2n bits is given by the binomial coefficient C(2n, n)
# The number of ways to distribute n '1's among the first n bits is given by the binomial coefficient C(n, n/2)
# The number of ways to distribute n '1's among the last n bits is given by the binomial coefficient C(n, n/2)
# Therefore, the total number of binary sequences with sum of first n bits equal to sum of last n bits is given by C(2n, n) - 2 * C(n, n/2)
count = math.comb(2 * n, n) - 2 * math.comb(n, n // 2)
return count
# Test the function
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)speechless-starcoder2-7b. fail_base: False, fail_plus: True
def count_binary_seq(n):
# Total number of binary sequences of length 2n
total = 2 ** (2 * n)
# Number of binary sequences where sum of first n bits is same as sum of last n bits
same_sum = 0
# Iterate over all binary sequences
for i in range(total):
# Convert binary to string
binary = bin(i)[2:].zfill(2 * n)
# Split the binary string into two halves
first_half = binary[:n]
second_half = binary[n:]
# Calculate the sum of first n bits
first_sum = sum(int(bit) for bit in first_half)
# Calculate the sum of last n bits
second_sum = sum(int(bit) for bit in second_half)
# If the sum of first n bits is same as sum of last n bits, increment the count
if first_sum == second_sum:
same_sum += 1
return same_sum
# Test the function
assert count_binary_seq(1) == 2wizardcoder-7b. fail_base: True, fail_plus: True
Here's a Python function that finds the count of all binary sequences of length 2n such that the sum of the first n bits is equal to the sum of the last n bits:
```python
import math
def count_binary_seq(n):
# Initialize variables
count = 0
total_sum = 2**n
# Iterate through all possible binary sequences of length 2n
for i in range(2**(2*n):
# Check if the sum of the first n bits is equal to the sum of the last n bits
if sum(int(bit) for bit in bin(i)[:n]) == sum(int(bit) for bit in bin(i)[-n:]):
count += 1
# Return the count
return count
```
To test the function, we can call it with n=1 and check if the output is close to 2.0:
```python
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
This should return True, since there are two binary sequences of length 2 with the same sum of the first and last bits: 00 and 11. octocoder. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
if n == 0:
return 1
else:
return 2 * count_binary_seq(n-1) + count_binary_seq(n-1)
gemma-1.1-7b-it. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n == 0:
return 1
count = 0
for i in range(2**n):
if sum(list(bin(i)[2:])) % 2 == sum(list(bin(i)[2:])[-n:]) % 2:
count += 1
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)deepseek-coder-6.7b-base. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n:
:return:
"""
dp = [[0 for _ in range(2 * n + 1)] for _ in range(n + 1)]
dp[0][0] = 1
for i in range(1, n + 1):
for j in range(2 * n + 1):
dp[i][j] = dp[i - 1][j - 1] + dp[i][j - 1]
return dp[n][n]
if __name__ == '__main__':
print(count_binary_seq(1))codegen-16b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
>>> count_binary_seq(1)
2.0
>>> count_binary_seq(2)
4.0
>>> count_binary_seq(3)
6.0
>>> count_binary_seq(4)
8.0
>>> count_binary_seq(5)
10.0
>>> count_binary_seq(6)
12.0
>>> count_binary_seq(7)
14.0
>>> count_binary_seq(8)
16.0
>>> count_binary_seq(9)
18.0
>>> count_binary_seq(10)
20.0
>>> count_binary_seq(11)
22.0
>>> count_binary_seq(12)
24.0
>>> count_binary_seq(13)
26.0
>>> count_binary_seq(14)
28.0
>>> count_binary_seq(15)
30.0
>>> count_binary_seq(16)
32.0
>>> count_binary_seq(17)
34.0
>>> count_binary_seq(18)
36.0
>>> count_binary_seq(19)
38.0
>>> count_binary_seq(20)
40.0
>>> count_binary_seq(21)
42.0
>>> count_binary_seq(22)
44.0
>>> count_binary_seq(23)
46.0
>>> count_binary_seq(24)
48.0
>>> count_binary_seq(25)
50.0
>>> count_binary_seq(26)
52.0
>>> count_binary_seq(27)
54.0
>>> count_binary_seq(28)
56.0
>>> count_binary_seq(29)
58.0
>>> count_binary_seq(30)
60.0
>>> count_binary_seq(31)
62.0
>>>mistral-7b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n:
:return:
"""
if n == 0:
return 1
if n == 1:
return 2
return count_binary_seq(n - 1) * 2 + count_binary_seq(n - 2)
if __name__ == '__main__':
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 5.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 14.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(4), 42.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(5), 132.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(6), 429.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(7), 1430.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(8), 4862.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(9), 16796.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(10), 58786.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(11), 206934.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(12), 747762.0, rel_tol=0.001)
assert math.isclose(count_binaryspeechless-mistral-7b. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
count = 0
for i in range(2**n):
bin_str = bin(i)[2:]
if len(bin_str) != 2*n:
continue
if sum(bin_str[:n]) == sum(bin_str[n:]):
count += 1
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
```
This Python script defines a function `count_binary_seq` that takes an integer `n` as input and returns the count of all binary sequences of length `2n` such that the sum of the first `n` bits is the same as the sum of the last `n` bits. The function uses a for loop to iterate over all binary sequences of length `2n`, checks if the sum of the first `n` bits is equal to the sum of the last `n` bits, and increments the count if it is. The function returns the final count.
The assert statement at the end checks if the function returns the correct result for the input `n=1`. The `math.isclose` function is used to compare the result with the expected value (2.0) within a certain tolerance (0.001). If the result is not close enough to the expected value, the assert statement will raise an AssertionError.
codet5p-16b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
if n == 0:
return 1
if n == 1:
return 2
return 2 * count_binary_seq(n - 1) + count_binary_seq(n - 2)
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 5.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 14.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(4), 42.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(5), 132.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(6), 429.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(7), 1430.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(8), 48620.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(9), 1767650.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(10), 4782969.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(11), 8589869.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(12), 17179869.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(13), 34359738.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(14), 687194767.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(15), 1374389534.0, rel_tol=0.001)
assert math.isclose(countcode-llama-13b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n: int) -> float:
"""
Counts the number of binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
:param n: length of binary sequence
:return: number of binary sequences
"""
if n == 0:
return 0
if n == 1:
return 2
return 2 * count_binary_seq(n - 1)
if __name__ == "__main__":
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(2), 6.0, rel_tol=0.001)
assert math.isclose(count_binary_seq(3), 20.0, rel_tol=0.001)
xdan-l1-chat. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
if n == 0:
return 1
total_bits = 2 * n
sum_of_n_bits = n * (n + 1)
def is_valid(seq):
left_sum = sum(seq[:n])
right_sum = sum(seq[n:])
return left_sum == right_sum and left_sum == sum_of_n_bits
count = 0
for i in range(2 ** total_bits):
seq = [int(d) for d in bin(i)[2:].zfill(total_bits)]
if is_valid(seq):
count += 1
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)solar-10.7b-instruct. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
from math import isclose
def count_binary_seq(n: int) -> float:
count = 0
for i in range(2**n):
binary = bin(i)[2:].zfill(n*2)
first_sum = sum(map(int, binary[0:n]))
last_sum = sum(map(int, binary[n:]))
if first_sum == last_sum:
count += 1
return count
assert isclose(count_binary_seq(1), 2.0, rel_tol=0.001)gemma-2b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
count = 0
for i in range(2**n):
if i & (i>>1) == 0:
count += 1
return count
claude-3-sonnet-20240229. fail_base: True, fail_plus: True
Here's the Python code to solve the problem, wrapped in a markdown block:
```python
import math
def count_binary_seq(n):
"""
Finds the count of all binary sequences of length 2n such that the sum of the first n bits is the same as the sum of the last n bits.
Args:
n (int): The length of each half of the binary sequence.
Returns:
float: The count of valid binary sequences.
"""
# Base case: when n is 0, there is only one sequence (empty string)
if n == 0:
return 1.0
# Initialize the count to 0
count = 0.0
# Iterate over all possible sums of the first n bits (from 0 to n)
for first_sum in range(n + 1):
# Calculate the count of sequences with the given sum for the first n bits
first_count = math.comb(n, first_sum)
# If the sum of the first n bits is the same as the sum of the last n bits,
# add the count to the total count
if first_sum <= n:
count += first_count * first_count
# Multiply the count by 2 to account for the sequences where the first n bits
# are different from the last n bits
count *= 2
return count
# Test case
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
print("Test case passed!")starcoder2-15b-oci. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
if n == 1:
return 2
else:
return 2 * count_binary_seq(n-1)
starcoder2-3b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n: length of binary sequence
:return: count of binary sequences
"""
return 2 ** n
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(2), 8.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n: length of binary sequence
:return: count of binary sequences
"""
return 2 ** n
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(3), 32.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n: length of binary sequence
:return: count of binary sequences
"""
return 2 ** n
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(4), 128.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n: length of binary sequence
:return: count of binary sequences
"""
return 2 ** n
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(5), 512.0, rel_tol=0.001)
"""
def count_binary_seq(n):
"""
:param n: length of binary sequence
:return: count of binary sequences
"""
return 2 ** n
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binaryspeechless-starcoder2-15b. fail_base: True, fail_plus: True
import math
def count_binary_seq(n):
# The total number of binary sequences of length 2n is 2^(2n)
total_sequences = 2 ** (2 * n)
# The number of sequences where the sum of the first n bits is not equal to the sum of the last n bits is 2^(n) * 2^(n)
# This is because there are 2^(n) ways to choose the first n bits and 2^(n) ways to choose the last n bits.
# However, we need to subtract the sequences where the sum of the first n bits is equal to the sum of the last n bits.
# These are the sequences where the first n bits are all 0s or all 1s, and the last n bits are the same as the first n bits.
# There are 2^(n) such sequences.
sequences_to_subtract = 2 ** n
# The final count is the total number of sequences minus the sequences to subtract.
count = total_sequences - sequences_to_subtract
return count
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)gemma-7b. fail_base: True, fail_plus: True
"""
Write a function to find the count of all binary sequences of length 2n such that sum of first n bits is same as sum of last n bits.
assert math.isclose(count_binary_seq(1), 2.0, rel_tol=0.001)
"""
import math
def count_binary_seq(n):
if n == 1:
return 2
else:
return 2 * count_binary_seq(n - 1)
opencodeinterpreter-ds-6.7b. fail_base: True, fail_plus: True
```python
def count_binary_seq(n):
if n == 1:
return 2
else:
return 2 * count_binary_seq(n - 1)
# Test the function
print(count_binary_seq(1))