n维前缀和

n维前缀和

DP法

每一维考虑，从低维向高维转移。

#include <bits/stdc++.h>
using namespace std;
#define LL long long
#define endl '\n'
const int MAXN = 1e5;
const int MD = 7; //每维小于7
const double eps = 1e-6;
int n, t;
map<int, int> sum;
void clean()
{
    sum.clear();
}
void solve()
{
    clean();
    cin >> t >> n;
    int MA = 1; // state范围
    for (int i = 1; i <= n; ++i)
        MA *= MD;
    // input t points of n dimension
    for (int i = 1; i <= t; ++i)
    {
        int state = 0;
        for (int j = 1; j <= n; ++j)
        {
            int x;
            cin >> x;
            state = state * MD + x;
        }
        sum[state] = 1;
    }
    int now = 1;
    for (int i = 1; i <= n; ++i)
    {
        for (int j = 0; j < MA; ++j)
        {
            if (j % (now * MD) / now)
                sum[j] += sum[j - now];
        }
        now *= MD;
    }
    int q;
    cin >> q;
    while (q--)
    {
        int sta = 0;
        for (int i = 1; i <= n; ++i)
        {
            int x;
            cin >> x;
            sta = sta * MD + x;
        }
        cout << sum[sta] << endl;
    }
}
int main()
{
    ios::sync_with_stdio(false);
    cout.tie(NULL);
    int T = 1;
    cin >> T;
    while (T--)
    {
        solve();
    }
    return 0;
}

容斥原理

利用容斥原理方法