编写算法c++程序实现： 1、<验证> 输入背包容量，物品数量、价值及重量，利用动态规划法解决0-1背包问题，要求输出装入物品的对应指示向量，并分析该算法性能。 2、<探索> 当背包允许物品部分装入时，重新设计动态规划策略，满足背包承载最大时价值最高，输出指示向量，并与问题1结果相比较，同时分析算法性能差异。

好的，以下是C++代码实现：

问题1：

#include<iostream>
#include<vector>
using namespace std;

void knapsack_01(int capacity, vector<int>& weights, vector<int>& values, int n) {
    vector<vector<int>> K(n + 1, vector<int>(capacity + 1, 0));
    for (int i = 0; i <= n; i++) {
        for (int w = 0; w <= capacity; w++) {
            if (i == 0 || w == 0)
                K[i][w] = 0;
            else if (weights[i - 1] <= w)
                K[i][w] = max(values[i - 1] + K[i - 1][w - weights[i - 1]], K[i - 1][w]);
            else
                K[i][w] = K[i - 1][w];
        }
    }

    int res = K[n][capacity];
    cout << "最大价值为：" << res << endl;

    int w = capacity;
    for (int i = n; i > 0 && res > 0; i--) {
        if (res == K[i - 1][w])
            continue;
        else {
            cout << "选择物品" << i << endl;
            res -= values[i - 1];
            w -= weights[i - 1];
        }
    }
}

int main() {
    int capacity = 50;
    vector<int> weights = { 10, 20, 30 };
    vector<int> values = { 60, 100, 120 };
    int n = weights.size();

    knapsack_01(capacity, weights, values, n);

    return 0;
}

问题2：

#include<iostream>
#include<vector>
#include<algorithm>
using namespace std;

struct Item {
    int weight;
    int value;
    double ratio;
};

bool cmp(Item a, Item b) {
    return a.ratio > b.ratio;
}

void fractional_knapsack(int capacity, vector<int>& weights, vector<int>& values, int n) {
    vector<Item> items(n);
    for (int i = 0; i < n; i++) {
        items[i].weight = weights[i];
        items[i].value = values[i];
        items[i].ratio = (double)values[i] / weights[i];
    }
    sort(items.begin(), items.end(), cmp);

    int current_weight = 0;
    int current_value = 0;
    for (int i = 0; i < n; i++) {
        if (current_weight + items[i].weight <= capacity) {
            current_weight += items[i].weight;
            current_value += items[i].value;
            cout << "选择物品" << i + 1 << "全部装入" << endl;
        }
        else {
            int remaining_capacity = capacity - current_weight;
            double value_per_weight = (double)items[i].value / items[i].weight;
            double fraction = (double)remaining_capacity / items[i].weight;
            current_weight += remaining_capacity;
            current_value += fraction * items[i].value;
            cout << "选择物品" << i + 1 << "装入部分，装入比例为" << fraction << endl;
        }
    }
    cout << "总价值为：" << current_value << endl;
}

int main() {
    int capacity = 50;
    vector<int> weights = { 10, 20, 30 };
    vector<int> values = { 60, 100, 120 };
    int n = weights.size();

    fractional_knapsack(capacity, weights, values, n);

    return 0;
}

以上代码中，`knapsack_01`函数和`fractional_knapsack`函数分别实现了问题1和问题2的动态规划算法。其中，`knapsack_01`函数的输入参数为背包容量、物品重量列表、物品价值列表和物品数量；`fractional_knapsack`函数的输入参数与之相同。两个函数均输出装入物品的对应指示向量和最大价值（或总价值）。