划分型博弈型dp

划分型动态规划：

513. Perfect Squares

https://www.lintcode.com/problem/perfect-squares/description?_from=ladder&&fromId=16

public class Solution {
    /**
     * @param n: a positive integer
     * @return: An integer
     */
    public int numSquares(int n) {
        // write your code here
        if (n==0){
            return 0;
        } 
        
        int[] f = new int[n+1];
        
        for(int i=1;i<=n;i++){
            f[i] = Integer.MAX_VALUE;
            for(int j=1;j*j<=i;j++){
                f[i]= Math.min(f[i-j*j]+1,f[i]);
            }
        }
        
        return f[n];
    }
}

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108. Palindrome Partitioning

https://www.lintcode.com/problem/palindrome-partitioning-ii/description?_from=ladder&&fromId=16

public class Solution {
    /**
     * @param s: A string
     * @return: An integer
     */
    public int minCut(String ss) {
        // write your code here
        if(ss==null || ss.length()==0){
            return 0;
        }
        
        char[] s = ss.toCharArray();
        int[] f = new int[s.length+1];
        boolean[][] isPalin = calcPalin(s);
        for(int i=1;i<=s.length;i++){
            f[i]= Integer.MAX_VALUE;
            
            for(int j=0;j<i;++j){
                if(isPalin[j][i-1]){
                    f[i]= Math.min(f[i],f[j]  +1);
                }
            }
        }
        
        return f[s.length]-1;
        
    }
    
    private boolean[][] calcPalin(char[] s){
        int n = s.length;
        boolean [][] isPalin = new boolean[n][n];
    
        
        for(int mid =0;mid<n;mid++){
            int i = mid;
            int j = mid;
            while(i>=0 && j<n && s[i]==s[j]){
                isPalin[i][j]= true;
                --i;
                ++j;
            }
            
            i= mid;
            j= mid+1;
            while(i>=0 && j<n && s[i]==s[j]){
                isPalin[i][j]= true;
                --i;
                ++j;
            }
        }
        
        return isPalin;
    }
}

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博弈型动态规划：

394. Coins in a Line

public class Solution {
    /**
     * @param n: An integer
     * @return: A boolean which equals to true if the first player will win
     */
    public boolean firstWillWin(int n) {
        // write your code here
        if(n==0) return false;
        if(n==2 || n==1) return true;
        boolean[] f = new boolean[n+1];
        
        f[1]=f[2]=true;
        f[0]=false;
        
        for(int i=2;i<=n;i++){
            f[i] = !f[i-1]||!f[i-2];
        }
        
        return f[n];
    }
}

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