Problem
Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return its area.
Example:
Input:
[
["1","0","1","0","0"],
["1","0","1","1","1"],
["1","1","1","1","1"],
["1","0","0","1","0"]
]
Output: 6
Notes
Two parts:
- generate a heights histogram for every row.
- apple “largest rectangle in histogram” on each row of histogram
Solution
class Solution:
def maximalRectangle(self, matrix):
if not matrix or not matrix[0]:
return 0
m = len(matrix)
n = len(matrix[0])
histograms = [[0] * n for i in range(m)]
res = 0
for i in range(m):
for j in range(n):
if matrix[i][j] == "1":
histograms[i][j] = histograms[i - 1][j] + 1 if i > 0 else 1
for histogram in histograms:
res = max(res, self.largestRectangleHistogram(histogram))
return res
def largestRectangleHistogram(self, histogram):
if not histogram:
return 0
stack = []
res = 0
index = 0
n = len(histogram)
while index < n:
if not stack or histogram[index] >= histogram[stack[-1]]:
stack.append(index)
index += 1
else:
res = max(
res, histogram[stack.pop()] *
((index - stack[-1] - 1) if stack else index))
while stack:
height = histogram[stack.pop()]
res = max(res, height * ((n - stack[-1] - 1) if stack else n))
return res
maxtrix = [["1","0","1","0","0"],["1","0","1","1","1"],["1","1","1","1","1"],["1","0","0","1","0"]]
print(Solution().maximalRectangle(maxtrix))