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[LeetCode] Palindrome Partitioning II (DP)

Given a string s, partition s such that every substring of the partition is a palindrome.

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.

避免用递归产生低效的程序,用DP的方法:

class Solution {    public:        int minCut(string s) {            if(s.empty()) return 0;            int n = s.size();            vector<vector<bool>> pal(n,vector<bool>(n,false));//记录Si到Sj之间是否形成回文            vector<int> d(n);//记录Si到S末尾分割能形成回文的最小分割数            for(int i=n-1;i>=0;i--)            {                d[i]=n-i-1;                for(int j=i;j<n;j++)                {                    if(s[i]==s[j] && (j-i<2 || pal[i+1][j-1]))                    {                       pal[i][j]=true;                       if(j==n-1)                           d[i]=0;                       else if(d[j+1]+1<d[i])                           d[i]=d[j+1]+1;                    }                }            }            return d[0];        } };   

每个两两之间都考虑到,需要O(n^2)次数,然后只考虑其中能构成回文的子序列,即Si和Sj之间能构成回文的子序列pal[i][j]=true,仔细体会一下。