HDU 3680 Naughty fairies BigInteger + Java +DP

注：http://poj.org/problem?id=3278 为此题的缩水版 BFS能过

思路：

Step1:将数转换为二进制

Step2:因为有-1的操作 所以不能直接贪心 通过观察可得 b是a的二进制前缀与b是二进制的前缀+1同样重要 考虑 dp[位数][状态] (状态为前缀 和前缀+1)

Step3:建立初值 dp[i][j]=abs(a-toBase10(b的前i+1位))

Step4:

    if(b的二进制表示第i位==0)     dp[i][0]=min(dp[i-1][0]+1,dp[i-1][1]+2)

                                dp[i][1]=min(dp[i-1][0]+2,dp[i-1][1]+2)

    else                        dp[i][0]=min(dp[i-1][0]+2,dp[i-1][1]+2)

                                dp[i][1]=min(dp[i-1][0]+2,dp[i-1][1]+1)

 

代码（Java）：

 

    
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {
    public static BigInteger one=BigInteger.valueOf(1);
    public static BigInteger two=BigInteger.valueOf(2);
    public static String tobase2(BigInteger x){
        StringBuffer str=new StringBuffer();
        while(!x.equals(BigInteger.ZERO)){
            if(x.mod(two).equals(BigInteger.ONE)) str.append('1');
            else str.append('0');
            x=x.divide(two);
        }
        return new String(str);
    }
    public static BigInteger Min(BigInteger a,BigInteger b){
        if(a.compareTo(b)<0) return a;
        else return b;
    }
    public static BigInteger solve(BigInteger a,BigInteger b){
        String sb=tobase2(b);
        BigInteger dp[][]=new BigInteger[sb.length()][2];
        BigInteger tmp=new BigInteger("0");

        for(int i=0;i<sb.length();i++){
            tmp=tmp.multiply(two);
            if(sb.charAt(sb.length()-1-i)=='1') tmp=tmp.add(BigInteger.ONE);        
            for(int j=0;j<2;j++) {
                dp[i][j]=a.subtract(tmp.add(BigInteger.valueOf(j))).abs();
            }
        }
        for(int i=1;i<sb.length();i++)
        {
            if(sb.charAt(sb.length()-1-i)=='0'){
                dp[i][0]=Min(dp[i][0], Min(dp[i-1][0].add(one), dp[i-1][1].add(two)));
                dp[i][1]=Min(dp[i][1], Min(dp[i-1][0].add(two), dp[i-1][1].add(two)));
            }else{
                dp[i][0]=Min(dp[i][0], Min(dp[i-1][0].add(two), dp[i-1][1].add(two)));
                dp[i][1]=Min(dp[i][1], Min(dp[i-1][0].add(two), dp[i-1][1].add(one)));
            }
        }
        return Min(dp[sb.length()-1][0], dp[sb.length()-1][1].add(one));
    }
    public static void main(String[] args) {
        Scanner cin=new Scanner(System.in);
        while(true){
            BigInteger b=cin.nextBigInteger();
            BigInteger a=cin.nextBigInteger();
            if(a.equals(b) && a.equals(BigInteger.ZERO)) break;
            if(a.compareTo(b)>=0){
                System.out.println(a.subtract(b));
                continue;
            }else{
                BigInteger ans=solve(a,b);
                System.out.println(ans);
            }
        }
        cin.close();
    }
}