0-1背包问题

二维数组

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;
    //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] = 0;
    }
    //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]){
                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");
    }
}

一维数组

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

public static void testWeightBagProblem(int[] weight, int[] value, int bagWeight){
    int wLen = weight.length;
    //定义dp数组：dp[j]表示背包容量为j时，能获得的最大价值
    int[] dp = new int[bagWeight + 1];
    //遍历顺序：先遍历物品，再遍历背包容量
    for (int i = 0; i < wLen; i++){
    	//必须逆序
        for (int j = bagWeight; j >= weight[i]; j--){
            dp[j] = Math.max(dp[j], dp[j - weight[i]] + value[i]);
        }
    }
    //打印dp数组
    for (int j = 0; j <= bagWeight; j++){
        System.out.print(dp[j] + " ");
    }
}