dynamic_programming.java

01背包问题

/*
 * Dynamic_Programming.java
 *
 * Created on 2007年6月3日, 下午4:13
 *
 * To change this template, choose Tools | Template Manager
 * and open the template in the editor.
 */

package sunfa;

/**
 *
 * @author Administrator
 */

public class Dynamic_Programming {
    
	public static void knapsack(int[] v, int[] w, int c, int[][] m)
    {
        /** v[] w[] c 分别是价值、重量、和背包容量数组
        m[i][j]表示有i~n个物品，背包容量为j的最大价值。*/

        int n = v.length-1;
        int jMax = Math.min(w[n]-1, c);
        for(int j = 0; j <= jMax; j++)  
            m[n][j] = 0;        //当w[n]>j 有 m[n][j]=0

        //m[n][j] 表示只有n物品，背包的容量为j时的最大价值
        for (int l = w[n]; l <= c; l++)
            m[n][l] = v[n];  //当w[n]<=j 有m[n][j]=v[n]

        //递规调用求出m[][]其它值，直到求出m[0][c]
        for(int i = n-1; i >=1; i--)
        {
            jMax = Math.min(w[i]-1,c);            
            for(int k = 0; k <=jMax; k++)
                m[i][k] = m[i+1][k];
                      
            for(int h = w[i]; h <= c; h++)
                m[i][h] = Math.max(m[i+1][h],m[i+1][h-w[i]]+v[i]);
        }
        m[0][c] = m[1][c];
        if(c >= w[0])
            m[0][c] = Math.max(m[0][c],m[1][c-w[0]]+v[0]);

    }
         
    public static void traceback(int[][] m, int[] w, int c, int[] x)
    {// 根据最优值求出最优解
        int n = w.length-1;
        for(int i = 0; i<n;i++)
            if(m[i][c] == m[i+1][c])
                x[i] = 0;
            else{
                x[i] = 1;
                c -= w[i];
            }
        x[n] = (m[n][c]>0)?1:0;
    }
    public static void main(String[] args)
    {
        //测试
        int[] ww = {2,2,6,5,4};
        int[] vv = {6,3,5,4,6};
        int[][] mm = new int[5][11];
        knapsack(vv,ww,10,mm);

        int[] xx =new int[ww.length];
        traceback(mm,ww,10,xx);
    }
}