0-1背包问题动态规划算法

0-1背包问题动态规划算法

题目描述：

Java实现：

import java.util.Scanner;public class Knapsack {    public static void main(String[] args) {        Scanner scan = new Scanner(System.in);//       n = 4, c = 5;//       w[] = {0, 2, 1, 3, 2};//       v[] = {0, 12, 10, 20, 15};        //物品个数n        int n = scan.nextInt();        //背包容量c        int c = scan.nextInt();        //每个物品重量wi        int w[] = new int[n+1];        w[0] = 1;        for(int i=1; i<=n; i++)            w[i] = scan.nextInt();        //每个物品价值vi        int v[] = new int[n+1];        v[0] = 1;        for(int i=1; i<=n; i++)            v[i] = scan.nextInt();        //最优值数组        int m[][] = new int[n+1][c+1];        //物品的选择向量        int x[] = new int[n+1];        Knapsack1(v, w, c, n, m);        Traceback(m, w, c, n, x);        for(int i=1; i<x.length; i++)            System.out.print(x[i]+" ");    }    //v为价值数组,Vi(1 <= i <= n)  w为重量数组,Wi(1 <= i <= n)  c为背包容量  n为物品数量，若物品i，则1 <= i <= n    public static void Knapsack1(int v[], int w[], int c, int n,int m[][]){        int jMax = min(w[n]-1, c);        for(int j=0; j<=jMax; j++)//初始化m[n][j], 二维数组最下面一行            m[n][j] = 0;        for(int j=w[n]; j<=c; j++)//初始化m[n][j]            m[n][j] = v[n];        for(int i=n-1; i>0; i--){            jMax = min(w[i]-1, c);            for(int j=0; j<=jMax; j++)                m[i][j] = m[i+1][j];            for(int j=w[i]; j<=c; j++)                m[i][j] = max(m[i+1][j], m[i+1][j-w[i]]+v[i]);              }    }    public static void Traceback(int m[][], int w[], int c, int n, int x[]){        for(int i=1; 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 int min(int x, int y){return x<y?x:y;}    public static int max(int x, int y){return x>y?x:y;}}