131. 132. Palindrome Partitioning *HARD* -- 分割回文字符串

131. Palindrome Partitioning

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

Return all possible palindrome partitioning of s.

For example, given s = "aab",
Return

[
  ["aa","b"],
  ["a","a","b"]
]

class Solution {
public:
    bool isPalindrome(string s)
    {
        int l = s.length(), left, right;
        for(left = , right = l-; left < right; left++, right--)
        {
            if(s[left] != s[right])
                return false;
        }
        return true;
    }

    void partitionHelper(vector<vector<string>> &ans, string &s, int start, vector<string> &vec)
    {
        int l = s.length(), i;
        if(start == l)
        {
            ans.push_back(vec);
            return;
        }
        for(i = start; i < l; i++)
        {
            string sub = s.substr(start, i-start+);
            if(isPalindrome(sub))
            {
                vec.push_back(sub);
                partitionHelper(ans, s, i+, vec);
                vec.pop_back();
            }
        }
    }

    vector<vector<string>> partition(string s) {
        vector<vector<string>> ans;
        vector<string> vec;
        partitionHelper(ans, s, , vec);
        return ans;
    }
};

132. Palindrome Partitioning II

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.

class Solution {
public:
    int minCut(string s) {
        int l = s.length(), i, j;
        if(l <= )
            return ;

　　　　 //判断是否为回文字符串
        vector<vector<bool>> isPal(l, vector<bool>(l, false));
        for(i = l-; i >= ; i--) //HERE
        {
            isPal[i][i] = true;
            for(j = i+; j < l; j++)
            {
                if(s[i] == s[j] && (j == i+ || isPal[i+][j-]))
                    isPal[i][j] = true;
            }
        }
        vector<int> num(l);
        num[] = ;
        for(i = ; i < l; i++)
        {
            if(isPal[][i])
            {
                num[i] = ;
                continue;
            }
            num[i] = i;
            for(j = ; j <= i; j++)
            {
                if(isPal[j][i] && num[j-]+ < num[i])
                    num[i] = num[j-] + ;
            }
        }
        return num[l-];
    }
};

（1）

//construct the pailndrome checking matrix
// 1) matrix[i][j] = true; if (i==j) -- only one char
// 2) matrix[i][j] = true; if (i==j+1) && s[i]==s[j] -- only two chars
// 3) matrix[i][j] = matrix[i+1][j-1]; if s[i]==s[j] -- more than two chars

注意：

在构造矩阵时，要自下往上，否则一些位置会用到的值还没有填写。

（2）

/*
* Dynamic Programming
* -------------------
*
* Define res[i] = the minimum cut from 0 to i in the string.
* The result eventually is res[s.size()-1].
* We know res[0]=0. Next we are looking for the optimal solution function f.
*
* For example, let s = "leet".
*
* f(0) = 0; // minimum cut of str[0:0]="l", which is a palindrome, so not cut is needed.
* f(1) = 1; // str[0:1]="le" How to get 1?
* f(1) might be: (1) f(0)+1=1, the minimum cut before plus the current char.
* (2) 0, if str[0:1] is a palindrome (here "le" is not )
* f(2) = 1; // str[0:2] = "lee" How to get 2?
* f(2) might be: (1) f(1) + 1=2
* (2) 0, if str[0:2] is a palindrome (here "lee" is not)
* (3) f(0) + 1, if str[1:2] is a palindrome, yes!
* f(3) = 2; // str[0:3] = "leet" How to get 2?
* f(3) might be: (1) f(2) + 1=29
* (2) 0, if str[0:3] is a palindrome (here "leet" is not)
* (3) f(0) + 1, if str[1:3] is a palindrome (here "eet" is not)
* (4) f(1) + 1, if str[2:e] is a palindrome (here "et" is not)
* OK, output f(3) =2 as the result.
*
* So, the optimal function is:
*
* f(i) = min [ f(j)+1, j=0..i-1 and str[j:i] is palindrome
* 0, if str[0,i] is palindrome ]
*
* The above algorithm works well for the smaller test cases, however for the big cases, it still cannot pass.
* Why? The way we test the palindrome is time-consuming.
*
* Also using the similar DP idea, we can construct the look-up table before the main part above,
* so that the palindrome testing becomes the looking up operation. The way we construct the table is also the idea of DP.
*
* e.g. mp[i][j]=true if str[i:j] is palindrome.
* mp[i][i]=true;
* mp[i][j] = true if str[i]==str[j] and (mp[i+1][j-1]==true or j-i<2 ) j-i<2 ensures the array boundary.
*/