221. Maximal Square

https://leetcode.com/problems/maximal-square/#/description

 

Given a 2D binary matrix filled with 0's and 1's, find the largest square containing only 1's and return its area.

For example, given the following matrix:

1 0 1 0 0
1 0 1 1 1
1 1 1 1 1
1 0 0 1 0

Return 4.

 

 

Sol 1:

 

Brute Force.

 

class Solution(object):
    def maximalSquare(self, matrix):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """
        # brute force

        if len(matrix) <= 0 :
            return 0
        
        
        rows = len(matrix) 
        cols = len(matrix[0])
        
        maxsqlen = 0
        for i in range(rows):
            for j in range(cols):
                # initilize flag to be True
                if matrix[i][j] == '1':
                    sqlen = 1
                    flag = True
                    # border limits 
                    while sqlen + i < rows and sqlen + j < cols and flag:
                        # advance square length downwords 
                        for k in range(j, sqlen + j + 1):
                            if matrix[i+sqlen][k] == '0':
                                flag = False
                                break
                        # advance square length to the right
                        for k in range(i, sqlen + i + 1):
                            if matrix[k][j+sqlen] == '0':
                                flag = False
                                break
                                
                        if flag:
                            sqlen += 1
                    
                    if maxsqlen < sqlen:
                        maxsqlen = sqlen
                        
        return maxsqlen * maxsqlen 

 

Complexity Analysis

• Time complexity : O\big((mn)^2\big)O((mn)​2​​). In worst case, we need to traverse the complete matrix for every 1.
• Space complexity : O(1)O(1). No extra space is used.

 

 

Sol 2:

 

DP.

 

（sth. wrong with initlization of DP...）

 

class Solution(object):
    def maximalSquare(self, matrix):
        """
        :type matrix: List[List[str]]
        :rtype: int
        """
        # DP
        # Time complexity : O(mn)O(mn). Single pass.
        # pace complexity : O(mn)O(mn). Another matrix of same size is used for dp.

        if len(matrix) <= 0 :
            return 0
        
        
        rows = len(matrix) 
        cols = len(matrix[0])
        
        maxsqlen = 0
        dp = ['0'] * (rows + 1) * (cols + 1)
        
        for i in range(1, rows+1):
            for j in range(1, cols+1):
                if matrix[i-1][j-1] == '1':
                    dp[i][j] = min(dp[i][j-1], dp[i-1][j], dp[i-1][j-1]) + 1
                    maxsqlen = max(maxsqlen, dp[i][j])
                    
        return maxsqlen * maxsqlen