动态规划算法

算法介绍：

背包问题01

代码实现

package com.hy.tenalgorithm;

/**
 * 动态规划算法
 *
 * @author hanyong
 * @date 2020/7/14 20:06
 */
public class DymanicAlgorithm {
    public static void main(String[] args) {
        int[] w = {1, 4, 3}; //物品的重量
        int[] val = {1500, 3000, 2000}; //物品的价值
        //背包的容量
        int m = 4;
        //物品的种类个数
        int n = val.length;

        int[][] v = new int[n + 1][m + 1];
        //创建一个数组记录商品放入情况
        int[][] path = new int[n + 1][m + 1];
        for (int i = 0; i < v.length; i++) {
            v[i][0] = 0;
        }

        for (int i = 0; i < v[0].length; i++) {
            v[0][i] = 0;
        }

        for (int i = 1; i < v.length; i++) {
            for (int j = 1; j < v[0].length; j++) {
                if (w[i - 1] > j) {
                    v[i][j] = v[i - 1][j];
                } else {
                    //v[i][j] = Math.max(v[i - 1][j], val[i - 1] + v[i - 1][j - w[i - 1]]);
                    if (v[i - 1][j] < val[i - 1] + v[i - 1][j - w[i - 1]]) {
                        v[i][j] = val[i - 1] + v[i - 1][j - w[i - 1]];

                        path[i][j] = 1;

                    } else {
                        v[i][j] = v[i - 1][j];
                    }
                }
            }
        }


        //遍历查看分配结果是否正确
        for (int i = 0; i < v.length; i++) {
            for (int j = 0; j < v[0].length; j++) {
                System.out.print(v[i][j] + "  ");
            }
            System.out.println();
        }

       /* for (int i = 0; i < path.length; i++) {
            for (int j = 0; j < path[i].length; j++) {
                if (path[i][j] == 1) {
                    System.out.printf("第%d个商品放入到背包\n", i);
                }
            }
        }*/

        int i = path.length - 1;
        int j = path[0].length - 1;
        while (i > 0 && j > 0) {
            if (path[i][j] == 1) {
                System.out.printf("第%d个商品放入到背包\n", i);
                j -= w[i - 1];
            }
            i--;
        }

    }

}