【51nod 1092】 回文字符串（区间DP）

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回文串是指aba、abba、cccbccc、aaaa这种左右对称的字符串。每个字符串都可以通过向中间添加一些字符，使之变为回文字符串。

例如：abbc 添加2个字符可以变为 acbbca，也可以添加3个变为 abbcbba。方案1只需要添加2个字符，是所有方案中添加字符数量最少的。

Input

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输入一个字符串Str，Str的长度 <= 1000。

Output

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输出最少添加多少个字符可以使之变为回文字串。

Input示例

abbc

Output示例

2

题解

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很明显的区间dp

\(dp[l][r]=min(dp[l+1][r],dp[l][r-1])+1\)

\(dp[l][r]=dp[l+1][r-1]\;if(a[l]==a[r])\)

练习了下区间dp的两种写法

记忆化搜索

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

public class Main {
	static final int N=(int)1005;
	static int dp[][]=new int[N][N];
	static char a[]=new char[N];
	static int solve(int l,int r) {
		if(l>=r) return 0;
		if(dp[l][r]!=-1) return dp[l][r];
		int ans=0;
		if(a[l]==a[r]) ans=solve(l+1,r-1);
		else ans=Math.min(solve(l+1,r),solve(l,r-1))+1;
		return dp[l][r]=ans;
	}
    public static void main(String[] args) {
        InputStream sys=System.in;
        InputReader in=new InputReader(sys);
        PrintWriter out=new PrintWriter(System.out);
        a=in.next().toCharArray();
        for(int i=0;i<a.length;i++) Arrays.fill(dp[i], -1);
        out.println(solve(0,a.length-1));
	    out.flush();
    }
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}

二维循环

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

public class Main {
	static final int N=(int)1005;
	static int dp[][]=new int[N][N];
	static char a[]=new char[N];
    public static void main(String[] args) {
        InputStream sys=System.in;
        InputReader in=new InputReader(sys);
        PrintWriter out=new PrintWriter(System.out);
        a=in.next().toCharArray();
        for(int i=a.length-2;i>=0;i--) {
        	dp[i][i]=0;
        	dp[i][i+1]=(a[i]==a[i+1]?0:1);
        	for(int j=i+2;j<=a.length-1;j++) {
        		if(a[i]!=a[j])
        		dp[i][j]=Math.min(dp[i+1][j], dp[i][j-1])+1;
        		else
        			dp[i][j]=dp[i+1][j-1];
        	}
        }
        out.println(dp[0][a.length-1]);
	    out.flush();
    }
	static class InputReader {
		public BufferedReader reader;
		public StringTokenizer tokenizer;

		public InputReader(InputStream stream) {
			reader = new BufferedReader(new InputStreamReader(stream), 32768);
			tokenizer = null;
		}

		public String next() {
			while (tokenizer == null || !tokenizer.hasMoreTokens()) {
				try {
					tokenizer = new StringTokenizer(reader.readLine());
				} catch (IOException e) {
					throw new RuntimeException(e);
				}
			}
			return tokenizer.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}
	}
}