动态规划(背包问题）

1. 记录局部最优解，作为下次求解的基础
2. 重要公式
   w[i] > j： v[i][j] = v[i][j];
   w[i] <= j : v[i][j] = Math.max(v[i][j], v[i][j - w[i]] + val[i]);

public class KnapsackProblem {

    public static void main(String[] args) {
        KnapsackProblem kp = new KnapsackProblem();
        kp.knapsack();

    }

    public void knapsack() {
        int[] w = {1, 4, 3};
        int[] val = {1500, 3000, 2000};
        int m = 4;
        int n = w.length;
        int[][] v = 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], v[i - 1][j - w[i-1]] + val[i-1]);
                }
            }
        }
        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();
        }
    }
}