363. Max Sum of Rectangle No Larger Than K

363. Max Sum of Rectangle No Larger Than K

题目链接：https://leetcode.com/problems...

参考discussion里的解释：
https://discuss.leetcode.com/...

先是如何在2d矩阵里找max sum的问题，参考视频：
https://www.youtube.com/watch...

然后就是一个array里面找不大于k的最大值问题了:
https://www.quora.com/Given-a...

要找到最大的sum <= k, 用cumulative sum就是cum[j] - k <= cum[i]，upper_bound就是TreeSet来做了。
行和列哪个打就用另一个扫。

public class Solution {
    public int maxSumSubmatrix(int[][] matrix, int k) {
        if(matrix.length == 0 || matrix.length == 0) return 0;
        
        int m = matrix.length, n = matrix[0].length;
        int global = Integer.MIN_VALUE;
        // m >> n
        for(int j = 0; j < n; j++) {
            int[] col = new int[m];
            for(int p = j; p < n; p++) {
                // cumulative sum
                for(int i = 0; i < m; i++) col[i] += matrix[i][p];
                // maximum array sum < k
                TreeSet<Integer> set = new TreeSet();
                // include 1 line
                set.add(0);
                int prefixSum = 0, local = Integer.MIN_VALUE;
                for(int sum : col) {
                    prefixSum += sum;
                    // upper_bound
                    Integer cum = set.ceiling(prefixSum - k);
                    if(cum != null) local = Math.max(local, prefixSum - cum);
                    set.add(prefixSum);
                }
                global = Math.max(global, local);
            }
        }
        
        return global;
    }
}

另外找最大不超过k的range sum还可以用merge sort，参考discussion：
https://discuss.leetcode.com/...