UVa LA 2965

题目

https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=966

题意

n个大写字母串(n <= 24)，问最多取多少个，使得所有字符出现的次数都是偶数。

思路

如刘书

1. 由于最多出现26个字母，而且字母在字符串中出现的次数本身不重要，只要记录奇偶性，所以可以将这些字符串转化为01串便于存储。

2. 问题转化为最多取多少个01串，使得其异或结果为0

3. 这样就可以用2^24来枚举，但这样状态还是太多了

4. 问题可以转化为前n/2个字符串子集组成的异或结果与后n/2个字符串子集组成的异或结果相同的情况下，最多取多少个字符串。

感想

1. 一开始忘了字符串本身可能存在重复的字符串

2. 之后忘了程序会修改pos

代码

#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <map>
#include <queue>
#include <set>
#include <string>
#include <tuple>
#define LOCAL_DEBUG
using namespace std;
const int MAXN = 24;
int n;
int a[MAXN];
int staStack[1 << MAXN];
int posStack[1 << MAXN];

int bone2sta(char * str) {
    int sta = 0;
    for (char * p = str; *p != 0; p++) {
        sta ^= 1 << (*p - 'A');
    }
    return sta;
}

int getDigitCnt(int x) {
    int ans = 0;
    while (x > 0) {
        x -= (x & -x);
        ans++;
    }
    return ans;
}

int main() {
#ifdef LOCAL_DEBUG
    freopen("C:\Users\Iris\source\repos\ACM\ACM\input.txt", "r", stdin);
    freopen("C:\Users\Iris\source\repos\ACM\ACM\output.txt", "w", stdout);
#endif // LOCAL_DEBUG
    //int T;
//    scanf("%d", &T);

    for (int ti = 1;scanf("%d", &n) == 1 && n; ti++) {
        for (int i = 0; i < n; i++) {
            char buff[27];
            scanf("%s", buff);
            a[i] = bone2sta(buff);
        }
        int half_n = n / 2;
        map<int, int> sta2pos;
        sta2pos[0] = 0;
        int staCnt = 0;
        staStack[staCnt++] = 0;
        for (int i = 0; i < half_n; i++) {
            for (int j = staCnt - 1; j >= 0; j--) {
                posStack[j] = sta2pos[staStack[j]];
            }
            for (int j = staCnt - 1; j >= 0; j--) {
                int sta = staStack[j];
                int pos = posStack[j];
                int newSta = sta ^ a[i];
                int newPos = pos | (1 << i);
                if (sta2pos.count(newSta) == 0) {
                    sta2pos[newSta] = newPos;
                    staStack[staCnt++] = newSta;
                    
                }
                else {
                    int oldDigitCnt = getDigitCnt(sta2pos[newSta]);
                    int newDigitCnt = getDigitCnt(pos) + 1;
                    if(newDigitCnt > oldDigitCnt)sta2pos[newSta] = newPos;
                }
            }
        }
        map<int, int> othersta2pos;
        othersta2pos[0] = 0;
        staCnt = 0;
        staStack[staCnt++] = 0;
        for (int i = half_n; i < n; i++) {
            for (int j = staCnt - 1; j >= 0; j--) {
                posStack[j] = othersta2pos[staStack[j]];
            }
            for (int j = staCnt - 1; j >= 0; j--) {
                int sta = staStack[j];
                int pos = posStack[j];
                int newSta = sta ^ a[i];
                int newPos = pos | (1 << i);
                if (othersta2pos.count(newSta) == 0) {
                    othersta2pos[newSta] = newPos;
                    staStack[staCnt++] = newSta;

                }
                else {
                    int oldDigitCnt = getDigitCnt(othersta2pos[newSta]);
                    int newDigitCnt = getDigitCnt(pos) + 1;
                    if (newDigitCnt > oldDigitCnt)othersta2pos[newSta] = newPos;
                }
            }
        }
        int ans = 0, ansPos = 0;
        for (int j = 0; j < staCnt; j++) {
            int sta = staStack[j];
            if (sta2pos.count(sta) != 0) {
                int digitCnt = getDigitCnt(sta2pos[sta]) + getDigitCnt(othersta2pos[sta]);
                if (digitCnt > ans) {
                    ans = digitCnt;
                    ansPos = sta2pos[sta] | othersta2pos[sta];
                }
            }
        }
        printf("%d
", ans);
        for (int i = 0; i < n; i++) {
            if (ansPos & (1 << i)) {
                printf("%d ", i + 1);
            }
        }
        puts("");
    }

    return 0;
}