Codeforces Round #513 by Barcelona Bootcamp (rated, Div. 1 + Div. 2), problem: (C) Maximum Subrectan

传送门:http://codeforces.com/contest/1060/problem/C

       我们要找到一个子矩阵元素和小于x,元素个数最多,那么我们发现,只要从a数组中取出一段连续的元素,b中取出一段连续的元素,他们组成的矩阵一定是子矩阵,而且子矩阵元素的和为

                           sum = (a[i] + a[i+1] + .... + a[j]) * (b[ii] + b[ii+1] + ... + b[jj])

       那么我们就可以先预处理出a,b数组的某段的和,然后数组记录a,b数组中长度为i的连续段的和的最小值,然后枚举a,b数组里段的长度,记录小于x的段,两段的长度乘积为元素个数,记录元素个数最多的那个即可。

代码如下:

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
inline int read(){
    int f = 1, x = 0;char ch = getchar();
    while (ch > '9' || ch < '0'){if (ch == '-')f = -f;ch = getchar();}
    while (ch >= '0' && ch <= '9'){x = x * 10 + ch - '0';ch = getchar();}
    return x * f;
}
const int maxn = 1e4 + 10;
int a[maxn],b[maxn],maxa[maxn],maxb[maxn];
int main(){
    int n = read(),m = read();
    for (int i = 1; i <= n; ++i) {
        a[i] = read();
        a[i] += a[i-1];
        maxa[i] = INT_MAX;
    }
    for (int i = 1; i <= m; ++i) {
        b[i] = read();
        b[i] += b[i-1];
        maxb[i] = INT_MAX;
    }
    int x = read(),maxx = 0;
    for (int i = 1; i <= n; ++i) {
        for (int j = i; j <= n; ++j) {
            maxa[j-i+1] = min(a[j]-a[i-1],maxa[j-i+1]);
        }
    }
    for (int i = 1; i <= m; ++i) {
        for (int j = i; j <= m; ++j) {
            maxb[j-i+1] = min(b[j]-b[i-1],maxb[j-i+1]);
        }
    }
    for (int i = 1; i <= n; ++i) {
        for (int j = 1; j <= m; ++j) {
            if ((LL)maxa[i]*maxb[j] <= x){
                maxx = max(i*j,maxx);
            }
        }
    }
    printf("%d\n",maxx);
    return 0;
}

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转载自blog.csdn.net/CCCCTong/article/details/82942748