找零 动态规划

#include <iostream>
#include <cstdlib>

using namespace std;

int count(int* s, int m, int n) {
    if (n == 0) return 1;
    if (n < 0 || m <= 0) return 0;
    return count(s, m - 1, n) + count(s, m, n-s[m-1]);
}

int main() {
    int arr[] = {1, 2, 3};
    int m = sizeof(arr) / sizeof(int);
    cout<<count(arr, m, 4)<<endl;
    system("pause");
    return 0;
}

int count_dp(int *s, int m, int n) {
    int rows = m + 1;
    int cols = n + 1;
    int* dp = new int[rows * cols];
    for (int i=0; i<cols; i++) dp[i] = 0;
    for (int i=0; i<rows; i++) dp[i * cols] = 1;
    
    for (int i=1; i<rows; i++) {
        int base = i * cols;
        for (int j=1; j<cols; j++) {
            int va = 0, vb = dp[base - cols + j];
            if (j - s[i-1] >= 0) {
                va = dp[base + j - s[i-1]];
            }
            dp[base + j] = va + vb;
        }
    }
    
    int ret = dp[cols * rows - 1];
    delete[] dp;
    return ret;
}