动态规划理解

1.卡尔算法讲解

2.B站背包讲解

1.案例

 

 

 2.动态过程

 

 3.归纳

 

 4.代码

public class CodeBag {
    public static void main(String[] args) {
        int[] weight = {1, 3, 4};
        int[] value = {15, 20, 30};
        int bagsize = 4;
        testweightbagproblem(weight, value, bagsize);
    }

    public static void testweightbagproblem(int[] weight, int[] value, int bagsize) {
        int wlen = weight.length, value0 = 0;
        //定义dp数组：dp[i][j]表示背包容量为j时，前i个物品能获得的最大价值
        int[][] dp = new int[wlen + 1][bagsize + 1];
        //初始化：背包容量为0时，能获得的价值都为0
        for (int i = 0; i <= wlen; i++) {
            dp[i][0] = value0;
        }
        //遍历顺序：先遍历物品，再遍历背包容量
        for (int i = 1; i <= wlen; i++) {
            for (int j = 1; j <= bagsize; j++) {
                if (j < weight[i - 1]) {//weight只有0以后的，计算判断时以前一个weight对应
                    dp[i][j] = dp[i - 1][j];
                } else {
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i - 1][j - weight[i - 1]] + value[i - 1]);
                }
            }
        }
        //打印dp数组
        for (int i = 0; i <= wlen; i++) {
            for (int j = 0; j <= bagsize; j++) {
                System.out.print(dp[i][j] + " ");
            }
            System.out.print("\n");
        }
    }
}