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            leetcode-85-最大矩形

            题目描述:

            方法一:动态规划+使用柱状图的优化暴力方法 O(N*2M) O(NM) N为行数

            class Solution:
                def maximalRectangle(self, matrix: List[List[str]]) -> int:
                    maxarea = 0
            
                    dp = [[0] * len(matrix[0]) for _ in range(len(matrix))]
                    for i in range(len(matrix)):
                        for j in range(len(matrix[0])):
                            if matrix[i][j] == 0: continue
            
                            # compute the maximum width and update dp with it
                            width = dp[i][j] = dp[i][j-1] + 1 if j else 1
            
                            # compute the maximum area rectangle with a lower right corner at [i, j]
                            for k in range(i, -1, -1):
                                width = min(width, dp[k][j])
                                maxarea = max(maxarea, width * (i-k+1))
                    return maxarea

            方法二:栈 参考84题 O(NM) O(M)

            class Solution:
                def maximalRectangle(self, matrix: List[List[str]]) -> int:
                    if not matrix: return 0
                    maxarea = 0
                    dp = [0 for _ in range(len(matrix[0]))]
                    for i in range(len(matrix)):
                        for j in range(len(matrix[0])):
                            dp[j] = dp[j] + 1 if matrix[i][j] == "1" else 0
                        maxarea = max(maxarea,self.largestRectangleArea(dp))
                    return maxarea
            
                def largestRectangleArea(self, heights: List[int]) -> int:
                    stack = [0]
                    heights = [0] + heights + [0]
                    res = 0
                    for i in range(len(heights)):
                        while heights[stack[-1]] > heights[i]:
                            tmp = stack.pop()
                            res = max(res, (i - stack[-1] - 1) * heights[tmp])
                        stack.append(i)
                    return res

            方法三:动态规划  O(NM)

            class Solution:
                def maximalRectangle(self, matrix: List[List[str]]) -> int:
                    if not matrix or not matrix[0]: return 0
                    row = len(matrix)
                    col = len(matrix[0])
                    left_j = [-1] * col
                    right_j = [col] * col
                    height_j = [0] * col
                    res = 0
                    for i in range(row):
                        cur_left = -1
                        cur_right = col
            
                        for j in range(col):
                            if matrix[i][j] == "1":
                                height_j[j] += 1
                            else:
                                height_j[j] = 0
            
                        for j in range(col):
                            if matrix[i][j] == "1":
                                left_j[j] = max(left_j[j], cur_left)
                            else:
                                left_j[j] = -1
                                cur_left = j
            
                        for j in range(col - 1, -1, -1):
                            if matrix[i][j] == "1":
                                right_j[j] = min(right_j[j], cur_right)
                            else:
                                right_j[j] = col
                                cur_right = j
                        for j in range(col):
                            res = max(res, (right_j[j] - left_j[j] - 1) * height_j[j])
                    return res
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