221. Maximal Square (2D-dp)
如果 matrix[i-1][j-1] == 0 ,DP[i, j] 也是 0,因為 square 不存在
如果 matrix[i-1][j-1] == 1,那麼 DP[i, j] 就有以下幾種可能
1)從DP [i-1,j] 這個形狀 加上一行
2)從DP [i, j-1] 這個形狀 加上一列
3)從DP [i-1, j-1] 這個正方形加上一行和一列


1.子問題
2. dp function:
我們能求的其實是邊長
dp[i][j]: base on right down corner i,j - the larget side length (注意是邊長
dp[i][j] = Math.min(Math.min(dp[i-1][j], dp[i][j-1]), dp[i-1][j-1]) + 1;
注意這題要求的是面積, 所以邊長*邊長
/*
time complexity: O(m*n), space complexity: O(m*n), m is matrix's width, n is matrix's height
*/
class Solution {
public int maximalSquare(char[][] matrix) {
int m = matrix.length;
if (m == 0) return 0;
int n = matrix[0].length;
int dp[][] = new int[m+1][n+1];
int maxLen = 0;
for (int i = 1 ; i <= m; i++) {
for (int j = 1; j <= n; j++) {
if (matrix[i-1][j-1] == '1') {
dp[i][j] = Math.min(Math.min(dp[i-1][j], dp[i][j-1]), dp[i-1][j-1]) + 1;
maxLen = Math.max(maxLen, dp[i][j]);
}
}
}
return maxLen*maxLen;
}
}
same idea as 1277. Count Square Submatrices with All Ones
class Solution {
public int maximalSquare(char[][] matrix) {
int m = matrix.length;
int n = matrix[0].length;
int maxLen = 0;
int dp[][] = new int[m][n];
for (int i = 0; i < m; i++) {
if (matrix[i][0] == '1') {
dp[i][0] = 1;
maxLen = 1;
}
}
for (int i = 1; i < n; i++) {
if (matrix[0][i] == '1') {
dp[0][i] = 1;
maxLen = 1;
}
}
for (int i = 1; i < m; i++) {
for (int j = 1; j < n; j++) {
if (matrix[i][j] == '1') {
dp[i][j] = Math.min(dp[i-1][j], Math.min(dp[i][j-1], dp[i-1][j-1])) + 1;
maxLen = Math.max(maxLen, dp[i][j]);
}
}
}
return maxLen*maxLen;
}
}
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