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HDU - 5119 Happy Matt Friends(DP)

Go_Viola 2023-04-07 阅读 26


题目大意:给你N个数,问有多少个子集,满足子集内所有数的xor和大于等于M

解题思路:用dp[i][j]表示前i个数,xor和为j的情况有多少种
则dp[i][j] = dp[i - 1][j],表示第i个数不选
dp[i][j ^ val[i]] += dp[i][j],表示选了第i个数

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
typedef long long LL;
const int N = (1 << 20) + 10;

LL dp[41][N];
int n, m, cnt, cas = 1;
int val[41];

void init() {
    scanf("%d%d", &n, &m);

    int Max = 0;
    for (int i = 0; i < n; i++) {
        scanf("%d", &val[i]);
        Max = max(Max, val[i]);
    }

    cnt = 0;
    while (Max) {
        cnt++;
        Max /= 2;
    }
}

void solve() {
    int All = 1 << cnt;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < All; j++)
            dp[i][j] = 0;

    dp[0][0] = dp[0][val[0]] = 1;
    for (int i = 1; i < n; i++)
        for (int j = 0; j < All; j++) {
            dp[i][j] += dp[i - 1][j];
            dp[i][j ^ val[i]] += dp[i - 1][j];
        }

    LL ans = 0;
    for (int i = m; i < All; i++)
        ans += dp[n - 1][i];
    printf("Case #%d: %lld\n", cas++, ans);

}

int main() {
    int test;
    scanf("%d", &test);
    while (test--) {
        init();
        solve();
    }
    return 0;
}


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