Codeforces 339CXenia and Weights

Posted 2021-02-12 awcxv

【链接】 我是链接,点我呀:)
【题意】

在天平上放砝码
你要在左边放一下然后到右边放一下
一直重复这样放m次
每次你放在其中一边都要让另外一边的重量比你少
你可以用1~10中的某些砝码
问你要怎样放才行,或者告知系统不能放m次

【题解】

动态规划
设dp[i][j][k]表示第i轮结束之后,左边右边的重量差的绝对值为j,最后一个放的砝码重量为k的情况能否达到
枚举一下每次用哪种砝码(只要不和之前一个状态最后一个用的一样就好)做一下转移即可。
(倒推然后写一个记忆化搜索可能更方便,因为可以直接打印出最后的结果

【代码】

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

public class Main {
    
    
    static InputReader in;
    static PrintWriter out;
        
    public static void main(String[] args) throws IOException{
        //InputStream ins = new FileInputStream("E:\rush.txt");
        InputStream ins = System.in;
        in = new InputReader(ins);
        out = new PrintWriter(System.out);
        //code start from here
        new Task().solve(in, out);
        out.close();
    }
    
    static int N = 10;
    static int M = 1000;
    static class Task{
        
        String s;
        int a[] = new int[N+10],n;
        boolean can[][][] = new boolean[M+10][N+10][N+10];
        int pre[][][] = new int[M+10][N+10][N+10];
        int m;
        
        void dfs(int dep,int delta,int last) {
            if (dep==0) return;
            int prelast = pre[dep][delta][last];
            dfs(dep-1,last-delta,prelast);
            out.print(last+" ");
        }
        
        public void solve(InputReader in,PrintWriter out) {
            s = in.next();
            m = in.nextInt();
            for (int i = 1;i <= 10;i++)
                if (s.charAt(i-1)=='1') {
                    a[++n] = i;
                }
            can[0][0][0] = true;
            for (int i = 0;i < m;i++)
                for (int delta = 0;delta <= N;delta++)
                    for (int j = 0;j <= N;j++)
                        if (can[i][delta][j]==true) {
                            for (int j2 = 1;j2 <= n;j2++)
                                if (a[j2]>delta && a[j2]!=j) {
                                    can[i+1][a[j2]-delta][a[j2]] = true;
                                    pre[i+1][a[j2]-delta][a[j2]] = j;
                                }
                        }
            for (int delta = 0;delta <= N;delta++)
                for (int j = 0;j <= N;j++)
                    if (can[m][delta][j]) {
                        out.println("YES");
                        dfs(m,delta,j);
                        return;
                    }
            out.println("NO");
        }
    }

    

    static class InputReader{
        public BufferedReader br;
        public StringTokenizer tokenizer;
        
        public InputReader(InputStream ins) {
            br = new BufferedReader(new InputStreamReader(ins));
            tokenizer = null;
        }
        
        public String next(){
            while (tokenizer==null || !tokenizer.hasMoreTokens()) {
                try {
                tokenizer = new StringTokenizer(br.readLine());
                }catch(IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        
        public int nextInt() {
            return Integer.parseInt(next());
        }
    }
}