POJ 刷题系列：1837. Balance

Posted 2023-02-15 Demon的黑与白

POJ 刷题系列：1837. Balance

传送门：1837. Balance

题意：

一个天枰上有C个钩子，把M个砝码挂在这些C个钩子上，问多少种平衡的挂法。

思路：
首先考虑单个砝码在天枰的位置，可以得到C个状态，对应的平衡度为:G[0] * C[i]，记录这些初始平衡度的个数。这样当放入第二个砝码时，可以遍历这些平衡度，从而得到一个新的平衡度。此时，不同位置，不同质量的砝码可能拥有相同平衡度，个数直接顺延给下一平衡度状态：$当前平衡度+ G[1] * C[i] \\space for \\space i \\in [-15, 15]$

详见https://blog.csdn.net/lyy289065406/article/details/6648094/

代码如下：

import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Map;
import java.util.StringTokenizer;

public class Main

    String INPUT = "./data/judge/201805/P2187.txt";

    public static void main(String[] args) throws IOException 
        new Main().run();
    

    void read() 
        int C = in.nextInt();
        int G = in.nextInt();
        int[] CS = new int[C];
        int[] GS = new int[G];
        for (int i = 0; i < C; ++i) CS[i] = in.nextInt();
        for (int j = 0; j < G; ++j) GS[j] = in.nextInt();
        int[][] dp = new int[21][15001];
        dp[0][7500] = 1;
        for (int i = 1; i <= G; ++i)  // 一个物品 每个 钩子 都放过一遍
            for (int j = 0; j <= 15000; ++j) 
                if (dp[i - 1][j] > 0) 
                    for (int k = 0; k < C; ++k) 
                        dp[i][j + GS[i - 1] * CS[k]] += dp[i - 1][j];
                    
                
            
        
        System.out.println(dp[G][7500]);
    

    FastScanner in;
    PrintWriter out;

    void run() throws IOException 
        boolean oj;
        try 
            oj = ! System.getProperty("user.dir").equals("F:\\\\oxygen_workspace\\\\Algorithm");
         catch (Exception e) 
            oj = System.getProperty("ONLINE_JUDGE") != null;
        

        InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));
        in = new FastScanner(is);
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        read();
        out.flush();
        if (!oj)
            System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");
        
    

    public boolean more()
        return in.hasNext();
    

    public int ni()
        return in.nextInt();
    

    public long nl()
        return in.nextLong();
    

    public double nd()
        return in.nextDouble();
    

    public String ns()
        return in.nextString();
    

    public char nc()
        return in.nextChar();
    

    class FastScanner 
        BufferedReader br;
        StringTokenizer st;
        boolean hasNext;

        public FastScanner(InputStream is) throws IOException 
            br = new BufferedReader(new InputStreamReader(is));
            hasNext = true;
        

        public String nextToken() 
            while (st == null || !st.hasMoreTokens()) 
                try 
                    st = new StringTokenizer(br.readLine());
                 catch (Exception e) 
                    hasNext = false;
                    return "##";
                
            
            return st.nextToken();
        

        String next = null;
        public boolean hasNext()
            next = nextToken();
            return hasNext;
        

        public int nextInt() 
            if (next == null)
                hasNext();
            
            String more = next;
            next = null;
            return Integer.parseInt(more);
        

        public long nextLong() 
            if (next == null)
                hasNext();
            
            String more = next;
            next = null;
            return Long.parseLong(more);
        

        public double nextDouble() 
            if (next == null)
                hasNext();
            
            String more = next;
            next = null;
            return Double.parseDouble(more);
        

        public String nextString()
            if (next == null)
                hasNext();
            
            String more = next;
            next = null;
            return more;
        

        public char nextChar()
            if (next == null)
                hasNext();
            
            String more = next;
            next = null;
            return more.charAt(0);
        
    

    static class D

        public static void pp(int[][] board, int row, int col) 
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) 
                for (int j = 0; j < col; ++j) 
                    sb.append(board[i][j] + (j + 1 == col ? "\\n" : " "));
                
            
            System.out.println(sb.toString());
        

        public static void pp(char[][] board, int row, int col) 
            StringBuilder sb = new StringBuilder();
            for (int i = 0; i < row; ++i) 
                for (int j = 0; j < col; ++j) 
                    sb.append(board[i][j] + (j + 1 == col ? "\\n" : " "));
                
            
            System.out.println(sb.toString());
        
    

    static class ArrayUtils 

        public static void fill(int[][] f, int value) 
            for (int i = 0; i < f.length; ++i) 
                Arrays.fill(f[i], value);
            
        

        public static void fill(int[][][] f, int value) 
            for (int i = 0; i < f.length; ++i) 
                fill(f[i], value);
            
        

        public static void fill(int[][][][] f, int value) 
            for (int i = 0; i < f.length; ++i) 
                fill(f[i], value);
            
        
    

    static class Num
        public static <K> void inc(Map<K, Integer> mem, K k) 
            if (!mem.containsKey(k)) mem.put(k, 0);
            mem.put(k, mem.get(k) + 1);