944 · 最大子矩阵（前缀和）

链接：LintCode 炼码 - 更高效的学习体验！

题解：

class Solution {
public:
    /**
     * @param matrix: the given matrix
     * @return: the largest possible sum
     */
    int maxSubmatrix(vector<vector<int>> &matrix) {
        // write your code here
        int m = matrix.size();
        if (m <= 0) {
            return 0;
        }
        int n = matrix[0].size();
        if (n <= 0) {
            return 0;
        }
        vector<vector<int>> prefix(m+1, vector<int>(n+1, 0));
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < n; ++j) {
                prefix[i+1][j+1] = prefix[i][j+1] + prefix[i+1][j] - prefix[i][j] + matrix[i][j];
            }
        }
        int result = INT_MIN;
        for (int top = 0; top < m; ++top) {
            for (int bottom = top; bottom < m; ++bottom) {
                int min_sum = 0;
                for (int i = 0; i < n; ++i) {
                   int tmp = prefix[bottom+1][i+1] - prefix[top][i+1];
                   result = max(result, tmp-min_sum);
                   min_sum = min(min_sum, tmp);
                }
            }
        }
        return result;
    }
};