C++ 换钱最少货币数 动态规划 + 空间优化 o(n)

#include <iostream>
const int jud = 65535; //32位 int型最大整数 用来进行数组的赋值

int minCoins(const int arr[], const int &length, const int &aim);
int minCoins_pro(const int arr[], const int &length, const int &aim);

int main()
{
    int arr[10];
    int aim = 0, n = 0, num = 0;
    std::cout << "Input n length: ";
    std::cin >> n;
    std::cout << "Input aim: ";
    std::cin >> aim;
    for (int i = 0; i < n; ++i)
    {
        std::cin >> num;
        arr[i] = num;
    }
    std::cout << minCoins_pro(arr, n, aim);

    system("pause");
    return 0;
}

int minCoins(const int arr[], const int &length, const int &aim)
{
    if (aim == 0 || arr == nullptr)
    {
        return 0;
    }

    int minCoins = 0;             //用来记录函数返回值，在函数返回之前需要将动态分配的内存释放
    int **dp = new int *[length]; //动态申请一个dp[length][aim + 1]的数组
    for (int i = 0; i < length; ++i)
    {
        dp[i] = new int[aim + 1];
    }

    for (int i = 0; i < length; ++i) //dp数组第一列全部赋值为0
    {
        dp[i][0] = 0;
    }

    for (int i = 1; i < aim + 1; ++i) //第一行数组将i的值为arr[0]的倍数的dp[0][i]递增存储，其他为jud
    {
        if (i - arr[0] >= 0 && dp[0][i - arr[0]] != jud)
        {
            dp[0][i] = dp[0][i - arr[0]] + 1;
        }
        else
            dp[0][i] = jud;
    }

    int left = 0;
    for (int i = 1; i < length; ++i)
    {
        for (int j = 1; j < aim + 1; ++j)
        {
            left = jud;
            if (j - arr[i] >= 0 && dp[i][j - arr[i]] != jud)
            {
                left = dp[i][j - arr[i]] + 1;
            }
            dp[i][j] = left < dp[i - 1][j] ? left : dp[i - 1][j];
        }
    }

    minCoins = dp[length - 1][aim];

    for (int i = 0; i < length; ++i) //释放动态申请的数组
    {
        delete[] dp[i];
    }
    delete[] dp;

    return minCoins == jud ? -1 : minCoins;
}

int minCoins_pro(const int arr[], const int &length, const int &aim)
{
    if (arr == nullptr || aim == 0)
    {
        return 0;
    }

    int *pArr = new int[aim + 1];
    int minCoins = 0;
    int left = 0;

    pArr[0] = 0;
    for (int i = 1; i < aim + 1; ++i) //初始化数组
    {
        if (i - arr[0] >= 0 && pArr[i - arr[0]] != jud)
        {
            pArr[i] = pArr[i - arr[0]] + 1;
        }
        else
            pArr[i] = jud;
    }

    for (int i = 1; i < length; ++i)
    {
        for (int j = 1; j < aim + 1; ++j)
        {
            left = jud;
            if (j - arr[i] >= 0 && pArr[j - arr[i]] != jud)
            {
                left = pArr[j - arr[i]] + 1;
            }
            pArr[j] = left <= pArr[j] ? left : pArr[j];
        }
    }

    minCoins = pArr[aim];

    delete[] pArr;
    return minCoins == jud ? -1 : minCoins;
}