Problem:


Score : 200 points

Problem Statement

There are N bags of biscuits. The i-th bag contains A_i biscuits.

Takaki will select some of these bags and eat all of the biscuits inside.
Here, it is also possible to select all or none of the bags.

He would like to select bags so that the total number of biscuits inside is congruent to P modulo 2.
How many such ways to select bags there are?

Constraints

1 \leq N \leq 50

P = 0 or 1

1 \leq A_i \leq 100

Input

Input is given from Standard Input in the following format:

N P
A_1 A_2 ... A_N

Output

Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.

Sample Input 1

2 0
1 3

Sample Output 1

2

There are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:

Select neither bag. The total number of biscuits is 0.

Select both bags. The total number of biscuits is 4.

Sample Input 2

1 1
50

Sample Output 2

0

Sample Input 3

3 0
1 1 1

Sample Output 3

4

Two bags are distinguished even if they contain the same number of biscuits.

Sample Input 4

45 1
17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26

Sample Output 4

17592186044416



Sample input:
2 0
1 3


Sample output:
2

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-

import sys

N,P = map(int, raw_input().split())
a = map(int, raw_input().split())

count_0 = 0
count_1 = 0
number = 0

def comb(n,r):
    if n < 0 or r < 0 or n < r:
        return 0
    elif n == 0 or r == 0:
        return 1
    else:
        return comb(n-1,r-1)+comb(n-1,r)

for i in range(N):
    if a[i] % 2 == 0:
        count_0 += 1
    else:
        count_1 += 1

print "count_0 = %d" % count_0
print "count_1 = %d" % count_1

if P == 0:
    if count_1 == 0:
        number = 1
    else:
        for j in range(count_1 /2 +1):
            number += comb(count_1,2*j)
else:
    if count_1 != 0:
        if count_1 % 2 == 0:
            for j in range(1,count_1 / 2):            
                number += comb(count_1,2*j - 1)
        else:
            for j in range(1,count_1/2 + 1):
                number += comb(count_1, 2*j - 1)

if number != 0:
    print "number = %d" % number * (2**count_0)

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-

import sys
import os

input_text_path = __file__.replace('.py', '.txt')
fd = os.open(input_text_path, os.O_RDONLY)
os.dup2(fd, sys.stdin.fileno())

N, P = map(int, input().split())

A_temp = list(map(int, input().split()))
A = []

for a in A_temp:
    A.append(a % 2)

zero_num = A.count(0)
one_num = A.count(1)

def Permutation(n, m):
    ret = 1
    for i in range(m):
        ret *= (n - i)
    return ret

def Combination(n, m):
    #import itertools
    #lst = [1] * n
    #c = list(itertools.combinations(lst, m))
    #return len(c)
    return Permutation(n, m) // Permutation(m, m)

combination_for_one = 0
if P == 0:
    for i in range(2, one_num + 1, 2):
        combination_for_one += Combination(one_num, i)
    combination_for_one += 1
else:
    for i in range(0, one_num, 2):
        combination_for_one += Combination(one_num, i)

ans = combination_for_one * (2 ** zero_num)

print(ans)

Submission status: Runtime Error

Solution code:
#Biscuits

N,P = list(map(int, input().split()))
A = list(map(int, input().split()))

#奇数の数
k = 0
for a in A:
    if a%2 ==1:
        k+=1

if ( k ==0 ):
    ans = int(p==0)
else:
    ans = 2**(N-1)
print(ans)

Submission status: Runtime Error

Solution code:
#Biscuits

N,P = list(map(int, input().split()))
A = list(map(int, input().split()))

#奇数の数
k = sum([A[i]%2 for i in range(N)])

if ( k ==0 ):
    ans = int(p==0)
else:
    ans = 2**(N-1)
print(ans)

Submission status: Runtime Error

Solution code:
def nCk(n, k):
    ans = 1
    i = 0
    while i < k:
        ans *= n - i
        i += 1
    i = 1
    while i <= k:
        ans /= i
        i += 1
    return ans

def main():
    [N, P] = map(int, raw_input().split())
    even = 0
    odd = 0
    A = map(int, raw_input().split())
    i = 0
    while i < N:
        if 0 == A[i] & 1:
            even += 1
        else:
            odd += 1
        i += 1
    i = P
    k = 0
    while i <= odd:
        k += nCk(odd, i)
        i += 2
    print((2 ** even) * k)

main()

Submission status: Runtime Error

Solution code:
import numpy as np
import itertools
from scipy.special import comb

n,p =input().split()
n = int(n)
p = int(p)

a_list = input().split()
a_list = [int(x) for x in a_list]
a_array = np.array(a_list)

amari = a_array % 2

zero_count = np.sum(amari == 0)
one_count = np.sum(amari == 1)

zero_pattern = 2**zero_count

if p == 0:
    if one_count >= 2:
        i = 1
        one_pattern = 1
        while i*2 <= one_count:
            one_pattern += comb(one_count,i*2)
            i += 1
    else:
        one_pattern = 1
else:
    if one_count >= 1:
        i = 1
        one_pattern = 0
        while i*2 - 1 <= one_count:
            one_pattern += comb(one_count,i*2-1)
            i += 1
    if one_count < 1:
        one_pattern = 0
        
print(int(zero_pattern * one_pattern))

Submission status: Runtime Error

Solution code:
import numpy as np
import itertools
from scipy.special import comb

n,p =input().split()
n = int(n)
p = int(p)

a_list = input().split()
a_list = [int(x) for x in a_list]
a_array = np.array(a_list)

amari = a_array % 2

zero_count = np.sum(amari == 0)
one_count = np.sum(amari == 1)

zero_pattern = 2**zero_count

if p == 0:
    if one_count >= 2:
        i = 1
        one_pattern = 1
        while i*2 <= one_count:
#             one_pattern  += len(list(itertools.combinations(np.arange(one_count),i*2)))
            one_pattern += comb(one_count,i*2)
            i += 1
    else:
        one_pattern = 1
else:
    if one_count >= 1:
        i = 1
        one_pattern = 0
        while i*2 - 1 <= one_count:
#             one_pattern  += len(list(itertools.combinations(np.arange(one_count),i*2-1)))
            one_pattern += comb(one_count,i*2-1)
            i += 1
    if one_count < 1:
        one_pattern = 0
        
print(int(zero_pattern * one_pattern))

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python
# encoding: utf-8

n, p = map(int, raw_input().split())

o, e = 0, 0
a = map(int, raw_input().split())
for i in xrange(n):
    x = a[i]
    if x % 2 == 0:
        e += 1
    else:
        o += 1

C = [[]]
for i in xrange(1, 51):
    C.append(range(51))
    C[i][0] = C[i][i] = 1
    for j in xrange(1, i):
        C[i][j] = C[i - 1][j - 1] + C[i - 1][j]


ans = 2**e

tmp = 0
for i in xrange(p, o + 1, 2):
    tmp += C[o][i]

print ans * tmp

Submission status: Runtime Error

Solution code:
def ncr(n, r):
    ans = 1
    if r * 2 >= n:
        return ncr(n, n - r)
    for i in xrange(n - r + 1, n + 1):
        ans *= i
    for i in xrange(1, r + 1):
        ans //= i
    return ans


def main():
    n, p = [int(_) for _ in raw_input().split()]
    o = 0
    e = 0
    for ai in (int(_) for _ in raw_input().split()):
        if ai % 2 == 1:
            o += 1
        else:
            e += 1
    t = 2 ** e
    ans = 0
    for q in xrange(p, o + 1, 2):
        ans += t * ncr(o, q)
    return ans


if __name__ == '__main__':
    print(main())