8.21 - hard - 75

363. Max Sum of Rectangle No Larger Than K

如果是求最大值，用for left in range(N): for right in range(left, N)：的双层循环来做，每外层循环的开始是直接用当前的col的值，然后每内层循环的时候把当前col的值加到前一层上，然后针对每一次形成的array做一次求最大值。

花了好长时间才做出来。。。。

class Solution(object):
    def maxSumSubmatrix(self, matrix, k):
        """
        :type matrix: List[List[int]]
        :type k: int
        :rtype: int
        """
        target = k
        if not matrix:
            return 0
        row = len(matrix)
        col = len(matrix[0])
        m = min(row,col)
        n = max(row,col)
        # indicating sum up in every row or every column
        colIsBig = col > row
        res = -sys.maxint
    
        for i in range(m): # 针对小一层的进行循环
            arr = [0]*n
            # sum from row j to row i
            for j in range(i, -1, -1):
                # traverse every column/row and sum up
                for k in range(n):
                    arr[k] = arr[k]+(matrix[j][k] if colIsBig else matrix[k][j])
                
                prefix_sum = 0
                h = [0]
                #print arr
                for k in range(n):
                    prefix_sum += arr[k]
                    # 首先找到prefix_sum插入的位置
                    index = bisect.bisect_left(h, prefix_sum-target)
                    if index < len(h):
                        res = max(res,prefix_sum-h[index])
                    # insert prefix_sum into h and keep the order
                    insert_index = bisect.bisect_left(h, prefix_sum)
                    h.insert(insert_index, prefix_sum)
        return res