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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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