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12.3.cpp
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75 lines (67 loc) · 1.92 KB
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/*
* 题目名称：最大子矩阵
* 题目来源：北京大学复试上机题
* 题目链接：http://t.cn/AiYSemJz
* 代码作者：杨泽邦(炉灰)
*/
#include <iostream>
#include <cstdio>
#include <climits>
using namespace std;
const int maxn = 100 + 10;
const int INF = INT_MAX;
int matrix[maxn][maxn]; //原矩阵
int total[maxn][maxn]; //辅助矩阵
int arr[maxn]; //一维数组
int dp[maxn];
int MaxSubsequence(int n) {
int maximum = -INF;
for (int i = 0; i < n; ++i) {
if (i == 0) {
dp[i] = arr[i];
} else {
dp[i] = max(arr[i], dp[i - 1] + arr[i]);
}
maximum = max(maximum, dp[i]);
}
return maximum;
}
int MaxSubmatrix(int n) {
int maximal = -INF;
for (int i = 0; i < n; ++i) {
for (int j = i; j < n; ++j) {
for (int k = 0; k < n; ++k) { //获得一维数组
if (i == 0) {
arr[k] = total[j][k];
} else {
arr[k] = total[j][k] - total[i - 1][k];
}
}
int current = MaxSubsequence(n);
maximal = max(maximal, current);
}
}
return maximal;
}
int main() {
int n;
while (scanf("%d", &n) != EOF) {
for (int i = 0; i < n; ++i) {
for (int j = 0; j < n; ++j) {
scanf("%d", &matrix[i][j]);
}
}
for (int i = 0; i < n; ++i) { //初始化辅助函数
for (int j = 0; j < n; ++j) {
if (i == 0) {
total[i][j] = matrix[i][j];
} else {
total[i][j] = total[i - 1][j] + matrix[i][j];
}
}
}
int answer = MaxSubmatrix(n);
printf("%d\n", answer);
}
return 0;
}