[Project Euler] Problem 31

In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:

1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).

It is possible to make £2 in the following way:

1£1 + 150p + 220p + 15p + 12p + 31p

How many different ways can £2 be made using any number of coins?

典型的换硬币问题，典型的动态规划

#include <iostream>
usingnamespace std;

int main(){
    intbase[] ={1,2,5,10,20,50,100,200}; 
    int a[200][8] = {0};
    a[0][0]=1;
    for(int i=1; i<200; i++){
        for(int j=0; j<8; j++){
            if(i+1-base[j] >0){
                for(int k=0; k<=j; k++){
                    a[i][j] += a[i-base[j]][k];
                }
            }
            if(i+1-base[j] ==0){
                a[i][j] +=1;
            }
        }
    }
    int sum =0;
    for(int i=0; i<8; i++){
        sum += a[199][i];
    }
    cout << sum << endl;
}

把每个面额的换法按最大的零钱面值分成8种情况