题解 | 最大子矩阵

#include <iostream>
#include <vector>
#include <climits>
using namespace std;

int kadane(vector<int>& arr) {
    int maxSoFar = arr[0], maxEndingHere = arr[0];
    for(int i = 1; i < arr.size(); i++) {
        maxEndingHere = max(arr[i], maxEndingHere + arr[i]);
        maxSoFar = max(maxSoFar, maxEndingHere);
    }
    return maxSoFar;
}

int maxSubmatrixSum(vector<vector<int>>& matrix) {
    int n = matrix.size();
    int maxSum = INT_MIN;
    
    // 遍历所有可能的行对
    for(int i = 0; i < n; i++) {
        vector<int> colSum(n, 0);
        for(int j = i; j < n; j++) {
            // 计算i到j行之间每列的和
            for(int k = 0; k < n; k++) {
                colSum[k] += matrix[j][k];
            }
            // 对colSum使用Kadane算法
            maxSum = max(maxSum, kadane(colSum));
        }
    }
    return maxSum;
}

int main() {
    int n;
    cin >> n;
    vector<vector<int>> matrix(n, vector<int>(n));
    
    for(int i = 0; i < n; i++) {
        for(int j = 0; j < n; j++) {
            cin >> matrix[i][j];
        }
    }
    
    cout << maxSubmatrixSum(matrix) << endl;
    return 0;
}

import java.util.Scanner;

public class Main {
    public static int kadane(int[] arr) {
        int maxSoFar = arr[0], maxEndingHere = arr[0];
        for(int i = 1; i < arr.length; i++) {
            maxEndingHere = Math.max(arr[i], maxEndingHere + arr[i]);
            maxSoFar = Math.max(maxSoFar, maxEndingHere);
        }
        return maxSoFar;
    }
    
    public static int maxSubmatrixSum(int[][] matrix) {
        int n = matrix.length;
        int maxSum = Integer.MIN_VALUE;
        
        for(int i = 0; i < n; i++) {
            int[] colSum = new int[n];
            for(int j = i; j < n; j++) {
                for(int k = 0; k < n; k++) {
                    colSum[k] += matrix[j][k];
                }
                maxSum = Math.max(maxSum, kadane(colSum));
            }
        }
        return maxSum;
    }
    
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[][] matrix = new int[n][n];
        
        for(int i = 0; i < n; i++) {
            for(int j = 0; j < n; j++) {
                matrix[i][j] = sc.nextInt();
            }
        }
        
        System.out.println(maxSubmatrixSum(matrix));
        sc.close();
    }
}

def kadane(arr):
    max_so_far = max_ending_here = arr[0]
    for x in arr[1:]:
        max_ending_here = max(x, max_ending_here + x)
        max_so_far = max(max_so_far, max_ending_here)
    return max_so_far

def max_submatrix_sum(matrix):
    n = len(matrix)
    max_sum = float('-inf')
    
    for i in range(n):
        col_sum = [0] * n
        for j in range(i, n):
            for k in range(n):
                col_sum[k] += matrix[j][k]
            max_sum = max(max_sum, kadane(col_sum))
    
    return max_sum

n = int(input())
matrix = []
for _ in range(n):
    row = list(map(int, input().split()))
    matrix.append(row)

print(max_submatrix_sum(matrix))