LeetCode 85. 最大矩形 python

85. 最大矩形

给定一个仅包含 0 和 1 的二维二进制矩阵，找出只包含 1 的最大矩形，并返回其面积。

示例:

输入:
[
[“1”,“0”,“1”,“0”,“0”],
[“1”,“0”,“1”,“1”,“1”],
[“1”,“1”,“1”,“1”,“1”],
[“1”,“0”,“0”,“1”,“0”]
]
输出: 6

动态规划 - 使用柱状图的优化暴力方法:

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


作者：LeetCode
链接：https://leetcode-cn.com/problems/maximal-rectangle/solution/zui-da-ju-xing-by-leetcode/

使用柱状图 - 栈:

class Solution:

    # Get the maximum area in a histogram given its heights
    def leetcode84(self, heights):
        stack = [-1]

        maxarea = 0
        for i in range(len(heights)):

            while stack[-1] != -1 and heights[stack[-1]] >= heights[i]:
                maxarea = max(maxarea, heights[stack.pop()] * (i - stack[-1] - 1))
            stack.append(i)

        while stack[-1] != -1:
            maxarea = max(maxarea, heights[stack.pop()] * (len(heights) - stack[-1] - 1))
        return maxarea


    def maximalRectangle(self, matrix: List[List[str]]) -> int:

        if not matrix: return 0

        maxarea = 0
        dp = [0] * len(matrix[0])
        for i in range(len(matrix)):
            for j in range(len(matrix[0])):

                # update the state of this row's histogram using the last row's histogram
                # by keeping track of the number of consecutive ones

                dp[j] = dp[j] + 1 if matrix[i][j] == '1' else 0

            # update maxarea with the maximum area from this row's histogram
            maxarea = max(maxarea, self.leetcode84(dp))
        return maxarea

作者：LeetCode
链接：https://leetcode-cn.com/problems/maximal-rectangle/solution/zui-da-ju-xing-by-leetcode/

动态规划 - 每个点的最大高度:

class Solution:

    def maximalRectangle(self, matrix: List[List[str]]) -> int:
        if not matrix: return 0

        m = len(matrix)
        n = len(matrix[0])

        left = [0] * n # initialize left as the leftmost boundary possible
        right = [n] * n # initialize right as the rightmost boundary possible
        height = [0] * n

        maxarea = 0

        for i in range(m):

            cur_left, cur_right = 0, n
            # update height
            for j in range(n):
                if matrix[i][j] == '1': height[j] += 1
                else: height[j] = 0
            # update left
            for j in range(n):
                if matrix[i][j] == '1': left[j] = max(left[j], cur_left)
                else:
                    left[j] = 0
                    cur_left = j + 1
            # update right
            for j in range(n-1, -1, -1):
                if matrix[i][j] == '1': right[j] = min(right[j], cur_right)
                else:
                    right[j] = n
                    cur_right = j
            # update the area
            for j in range(n):
                maxarea = max(maxarea, height[j] * (right[j] - left[j]))

        return maxarea


作者：LeetCode
链接：https://leetcode-cn.com/problems/maximal-rectangle/solution/zui-da-ju-xing-by-leetcode/