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085 Maximal Rectangle.py
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"""
Given a 2D binary matrix filled with 0's and 1's, find the largest rectangle containing all ones and return its area.
"""
__author__ = 'Danyang'
class Solution:
def maximalRectangle(self, matrix):
"""
Algorithm 1:
brutal force, iterate from top-left points and expand the area.
Algorithm 2:
Similar to 082 Largest Rectangle in Histogram with additional height calculation
Scanning row by row. (possible to use another dp)
Algorithm 3:
Without using stack, keep two dp arrays
https://github.com/algorhythms/LeetCode-Java/blob/master/src/MaximalRectangle/Solution.java
reference: http://shanjiaxin.blogspot.sg/2014/05/maximal-rectangle-leetcode.html
:param matrix: a list of lists of char
:return: int
"""
if not matrix or not matrix[0]:
return 0
# matrix = map(lambda x: list(x), matrix) # not necessary
global_max = -1<<32
m = len(matrix)
n = len(matrix[0])
# added dp to get heights
dp_height = [[-1 for _ in xrange(n)] for _ in xrange(m)]
dp_height[0] = map(lambda x: int(x), matrix[0])
for i in xrange(1, m):
for j in xrange(n):
if matrix[i][j] == "1":
dp_height[i][j] = 1+dp_height[i-1][j]
else:
dp_height[i][j] = 0
# end of dp
for i in xrange(m):
# Largest Rectangle in Histogram
inc_stack = []
j = 0
while j<=n:
# if not inc_stack or j+1<n and dp_height[i][j]<=dp_height[i][j+1]: # mistake
if not inc_stack or j<n and dp_height[i][j]>=dp_height[i][inc_stack[-1]]:
inc_stack.append(j)
j += 1
else:
last = inc_stack.pop()
# height = self.get_height(matrix, i, last)
height = dp_height[i][last]
if inc_stack:
global_max = max(global_max, height*(j-(inc_stack[-1]+1)))
else:
global_max = max(global_max, height*j)
return global_max
def get_height(self, matrix, row, col):
# possible replace by dp; otherwise TLE
height = 0
for i in xrange(row, -1, -1):
if matrix[row][col] == "0":
break
height += 1
return height
if __name__=="__main__":
assert Solution().maximalRectangle(["01", "01"])==2
assert Solution().maximalRectangle(["10001000001111110111111010111100111101001111001011111111101110110110011101101001110011101111001010110100110110111110101111011111110101111111111111111111111101110111111111000111100111111111011010111011","11010111100111111111111011110111111011101111111010101100110001100110101111101101111111010011111011111110111001110111010111111111011111110110011010111110101110111010101101101101110111111101111110100110","11010001100111011011111111111110111111010011011011111011111111110111111110111101111011111101101100111111001111101010111111011101110111011111001111111111111111101111110111111111111010101011111011111111","11111111011111110010110111001111111111111101111111111110100101111101110110001111100110101101111100111111110111001010110100011111111001010011100101011011011111111111110111111101001101110001110111110111","11011000010101101111011101011101101100111111101111111111111001010011011110110111110111111011100000001111111100011011101110110000000110001111111111111110111011011100000111111111110001111100111111111111","11111001101111101111111100111101111111111001011101111111111011111011110111111011110101111111111111111111010111111111111011111110110101111111111001110011010101111011111111111111011011100110111111101111","00111111011011111111100111110111011111111101101011111011110111100111111111111111111001111110000111111011011010111101110111111101111010111011011111110111101101110011111011111111110101111111011110011111","00101110111111011111110110001110111101111111111001111010010101101111010011101111111011011110110111001011001111100101110111111101000111101110111101111111100110011100111011111111011111110111111111110111","11111111011011011101111110111011110111011111111001101111111111011010111101110111111111111111111001000110111111001011011111010110111111101101100111110011110111111111011101110101111110101111111101101111","11101100010111111101111111101110110110111111101111111101111111110111001111000111110110111101111111011110111101101111101111101111010111011111011111101011101111110111111111111111110011111110111110111001","11110111111111001111111101011011101101111111100111111011111101011111111010110011111111111111111011010111111110111101110101111111011111111010011101111101011111110111100001110100111111110111011000011010","11111111101011110010101111101000111111011111101001010111111111110111010110101111101111111111111100101111111111011001101110101011001111111110011111111001111011111111011100111011111111111001110111010111","11111100101110111011110111111101111011111100111011011011111011111011111101000101101101111011111011101111011010100110011110011110011101101101110111111101101111110111110111110101111111100111111111111011","10111111011011000111111101111110001111111110111111111111111111111100111111110111011101111101101011011110010111111111111111101111101011111110111011011011111111111010001110111111110001111111111111111011","01001110100111011111001011011111111111100111110101111111111011110101111111011010110101111111110101010110011011111011100011111011111001101101011111101111011110111011101001101111111101100111111111111111","10111011111011011110111010111101111111011111111110111010011110111011111111111111111111111011111110111011110111111110110111110111011111101111111101011010001100100011101011101111111111111100110111110111","10111000101111111111111111110011010100110010101111101001111111110111111101111101100001110111111111111011110111111011111111110111111111111110111011100111110111111101111111111111111011111111011111111111","10101111111100111011111110111100111010111111110111010110111111111010001110101110111110101111111110111101011111110011000111111111111111111011101101111011011111111011111111101110111101101111111111101111","11111111111111001111111011011111111011000111111100000111101110101110011011111111110110111110101111110011111101110111111101111111110010111011111111101111110111111010011110111011111111111111111111100111","11100101111111111111110111111110111111111101101010111111011101011011111111101001111011111001100111111101011111111101111111011110111100111011111101011101111111111001010101010111111111111101111111111111","11100001111010011111110011001111011011110011110111101110101111111111011011110101111101101011011010111111111111111111111000111111110111011100111100111111101101101011111101110111111011100110110101011110","11011110110111110011011101001111111111101111000101111011111011010111111011111011111011111011111111111011110010111111111111111101111111100111111111101111111111111110111101111101011001110001010111110110","11111110110111111111110101101001111111111101110111100110110110101111110100111011101111111101111001111111110111111001111011111111101101111101111111100001110011111011011011111111111010001101110111111011","10111110111111110111111110111111111110111111011010111000011101011111111101101101111111101111111111101011111111110111111110101111111111111101111011110111111011111111110110111111011011111110110110110111","10111111001111111011110011011110101111111111111011111111111110001111111011101101111111101011001111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