LeetCode 221 Maximal Square (最大子正方形 dp)
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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 01 0 1 1 11 1 1 1 11 0 0 1 0
Return 4.Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.
题目链接:https://leetcode.com/problems/maximal-square/
public class Solution { public int maximalSquare(char[][] matrix) { int n = matrix.length; if (n == 0) { return 0; } int m = matrix[0].length; int[][] dp = new int[n + 5][m + 5]; int[][] up = new int[n + 5][m + 5]; int[][] left = new int[n + 5][m + 5]; boolean has = false; for (int j = 0; j < m; j ++) { if (matrix[0][j] == '1') { up[0][j] = 1; has = true; } dp[0][j] = up[0][j]; } for (int i = 0; i < n; i ++) { if (matrix[i][0] == '1') { left[i][0] = 1; has = true; } dp[i][0] = left[i][0]; } for (int i = 0; i < n; i ++) { for (int j = 0; j < m; j ++) { if (i > 0) { up[i][j] = (matrix[i][j] == '1') ? up[i - 1][j] + 1 : 0; } if (j > 0) { left[i][j] = (matrix[i][j] == '1') ? left[i][j - 1] + 1 : 0; } } } int ans = has ? 1 : 0; dp[0][0] = (matrix[0][0] == '1') ? 1 : 0; for (int i = 1; i < n; i ++) { for (int j = 1; j < m; j ++) { if (matrix[i][j] == '1') { dp[i][j] = Math.min(left[i][j - 1], Math.min(up[i - 1][j], dp[i - 1][j - 1])) + 1; ans = Math.max(ans, dp[i][j]); } } } return ans * ans; }}
上面的代码写得很丑。。。其实仔细观察可以发现,up和left数组是多余的,dp[i][j] = min(left[i][j - 1], up[i - 1][j], dp[i - 1][j - 1])) + 1这个状态转移方程其实等价于dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1])) + 1,原来转移方程的原理是若当前点是'1'且dp[i - 1][j - 1]已经构成了一个边长为k的正方形,若点(i, j)向上向左均可以延伸k个单位长度,那么dp[i][j]可以得到一个边长为k+1的正方形,但其实满足以上三个条件时,显然可以得出dp[i - 1][j]和dp[i][j - 1]都能得到一个边长为k的正方形的结论(画个图可以很清楚的看出),这样两个转移方程就等价了,为了方便处理,将整个矩阵向右下移动一个单位长度,所以其实这样写即可,击败了78%
public class Solution { public int maximalSquare(char[][] matrix) { int n = matrix.length; if (n == 0) { return 0; } int m = matrix[0].length; int[][] dp = new int[n + 1][m + 1]; int ans = 0; for (int i = 1; i <= n; i ++) { for (int j = 1; j <= m; j ++) { if (matrix[i - 1][j - 1] == '1') { dp[i][j] = Math.min(dp[i - 1][j - 1], Math.min(dp[i - 1][j], dp[i][j - 1])) + 1; ans = Math.max(ans, dp[i][j]); } } } return ans * ans; }}
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