[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 + 1 50p + 2 20p + 1 5p + 1 2p + 3 1p

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 >
using namespace std;

int main(){
int base [] = { 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