Educational Codeforces Round 75 (Rated for Div. 2) B. Binary Palindromes

Posted 2020-11-21 ydddd

链接：

https://codeforces.com/contest/1251/problem/B

题意：

A palindrome is a string t which reads the same backward as forward (formally, t[i]=t[|t|+1?i] for all i∈[1,|t|]). Here |t| denotes the length of a string t. For example, the strings 010, 1001 and 0 are palindromes.

You have n binary strings s1,s2,…,sn (each si consists of zeroes and/or ones). You can swap any pair of characters any number of times (possibly, zero). Characters can be either from the same string or from different strings — there are no restrictions.

Formally, in one move you:

choose four integer numbers x,a,y,b such that 1≤x,y≤n and 1≤a≤|sx| and 1≤b≤|sy| (where x and y are string indices and a and b are positions in strings sx and sy respectively),
swap (exchange) the characters sx[a] and sy[b].
What is the maximum number of strings you can make palindromic simultaneously?

思路:

考虑所有串的长度，当有奇数长度存在时，保证可以交换出全部，当没有时， 可能存在0或1为奇数，不能配对，有奇数可以将奇数减位，同时保证剩下的偶数相等。

代码：

#include<bits/stdc++.h>
using namespace std;
typedef long long LL;

int n;
string s;

int main()
{
    int t;
    scanf("%d", &t);
    while(t--)
    {
        int one = 0, zer = 0;
        int q = 0;
        scanf("%d", &n);
        for (int i = 1;i <= n;i++)
        {
            cin >> s;
            int len = (int)s.length();
            if (len%2)
                q++;
            for (int j = 0;j < len;j++)
            {
                if (s[j] == '0')
                    zer++;
                else
                    one++;
            }
        }
        if (q > 0)
            printf("%d
", n);
        else
        {
            if (one%2 || zer%2)
                printf("%d
", n-1);
            else
                printf("%d
", n);
        }
    }
    return 0;
}