Return the minimum cuts needed for a palindrome partitioning of s.
For example, given s = "aab",
Return 1 since the palindrome partitioning ["aa","b"] could be produced using 1 cut.
给定一个字符串s,用最少的次数将它拆分成多个回文子串。我们用动态规划来解决。首先我们用一个二维的布尔数组isPalin[][]记录当前子串是否是回文串,例如isPalin[i][j] = true,就代表了字符串中从字符i到字符j是回文子串。(当s.charAt(i) == s.charAt(j)并且i + 1 >= j - 1的时候,也就是对应了’aa‘和’a?a‘这两种情况,此时肯定为回文串)。用数组dp[]来记录每个阶段的最小值,如果检测到从第一个字符到当前字符为回文子串,那么dp[j] = 0, 因为不需要拆分所以为0; 如果从字符i开始到当前字符为回文子串并且i > 0,此时dp[j] = dp[i - 1] + 1。实现代码如下:
public class Solution { public int minCut(String s) { if(s == null) return 0; boolean[][] isPalin = new boolean[s.length()][s.length()]; int[] dp = new int[s.length()]; for(int i = 0; i < dp.length; i++) { int min = i; for(int j = 0; j <= i; j++) { if(s.charAt(j) == s.charAt(i) && (j + 1 >= i - 1 || isPalin[j + 1][i - 1])) { isPalin[j][i] = true; min = (j == 0) ? 0 : Math.min(min, dp[j - 1] + 1); } } dp[i] = min; } return dp[s.length() - 1]; } }