lyrB[k][j])(240)=∑k=1n(SumA[xr][k]−SumA[xl−1]k])∗(SumB[k][yr]−SumB[k][yl−1])" role="presentation"> ans====∑i=xlxr∑j=ylyr∑k=1nA[i][k]∗B[k][j]∑k=1n∑i=xlxr∑j=ylyrA[i][k]∗B[k][j]∑k=1n(∑i=xlxrA[i][k])∗(∑j=ylyrB[k][j])∑k=1n(SumA[xr][k

]−SumA[xl−1]k])∗(SumB[k][yr]−SumB[k][yl−1])(237)(238)(239)(240) $$\begin{array}{}\text{(237)}& ans& =& \underset{}{\overset{}{\sum }}\end{array}$$

i = x l x r ∑ j = y l y r ∑ k = 1 n A [ i ] [ k ] ∗ B [ k ] [ j ] (238) = ∑ k = 1 n ∑ i = x l x r ∑ j = y l y r A [ i ] [ k ] ∗ B [ k ] [ j ] (239) = ∑ k = 1 n ( ∑ i = x l x r A [ i ] [ k ] ) ∗ ( ∑ j = y l y r B [ k ] [ j ] ) (240) = ∑ k = 1 n ( S u m A [ x r ] [ k ] − S u m A [ x l − 1 ] k ] ) ∗ ( S u m B [ k ] [ y r ] − S u m B [ k ] [ y l − 1 ] ) $$\begin{eqnarray} ans &=& \sum_{i = xl}^{xr}\sum_{j = yl}^{yr}\sum_{k = 1}^{n}A[i][k]*B[k][j] \newline &=& \sum_{k = 1}^{n}\sum_{i = xl}^{xr}\sum_{j = yl}^{yr}A[i][k]*B[k][j] \newline &=& \sum_{k = 1}^{n}(\sum_{i = xl}^{xr}A[i][k]) * (\sum_{j = yl}^{yr}B[k][j]) \newline &=& \sum_{k = 1}^{n}(SumA[xr][k] - SumA[xl - 1]k]) * (SumB[k][yr] - SumB[k][yl - 1]) \end{eqnarray}$$

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程式碼：

#include<cstdio>
#include<vector>
#include<queue>
#include<ctime>
#include<algorithm>
#include<cstdlib>
#include<stack>
#include<cstring>
#include<cmath>
using namespace std;

typedef long long LL;

const int INF = 2147483647;
const int maxn = 2010;

int n,m;
int a[maxn][maxn],b[maxn][maxn];
LL ans;

inline LL getint()
{
    LL ret = 0,f = 1;
    char c = getchar();
    while (c < '0' || c > '9')
    {
        if (c == '-') f = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9') ret = ret * 10 + c - '0',c = getchar();
    return ret * f;
}

int main()
{
    #ifdef AMC
        freopen("AMC1.txt","r",stdin);
        freopen("AMC2.txt","w",stdout);
    #endif
    n = getint(); m = getint();
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            a[i][j] = getint();
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            b[i][j] = getint();

    for (int j = 1; j <= n; j++)    
        for (int i = 1; i <= n; i++)
            a[i][j] += a[i - 1][j];
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            b[i][j] += b[i][j - 1];

    for (int i = 1; i <= m; i++)
    {
        int x = getint(),y = getint();
        int z = getint(),w = getint();
        int xl = min(x,z),xr = max(x,z);
        int yl = min(y,w),yr = max(y,w);

        ans = 0;
        for (int j = 1; j <= n; j++)
            ans += 1ll * (a[xr][j] - a[xl - 1][j]) * (b[j][yr] - b[j][yl - 1]);
        printf("%lld\n",ans);
    }

    return 0;
}