I'm trying to understand the following algorithm. Its function is to
take as input an integer signifying a certain number of cents, and then
any number of integers representing coin denominations from greatest
to least. A 1 cent coin is required. The output is the minimum number
of coins necessary to produce the total number of cents from the
denominations provided. For example,
15 5 1
would output 3, as 5+5+5 is the minimum way to make 15

Using divide and modulus won't work because of cases like 15 6 5 1,
because using 6 cent coins would result in using 5 total.


#include <iostream>
using namespace std;

int min(int a, int b){
  if(a<b)
    return a;
  return b;
}

int main(){
  int amt;
  int den;
  int coins=0;
  int * store;
  int maxguess=0;
  while(cin>>amt>>den){
    store=new int[amt+1];
    for(int n=0;n<amt+1;n++)
      store[n]=n;
    while(den>1){
      for(int j=den; j<=amt;j++){
        store[j]=min(store[j], store[j-den]+1);
      }
      cin>>den;
    } 
    cout<<store[amt]<<'\n'; 
    delete store;
  }
  return 0;
}

Everything except

for(int j=den; j<=amt;j++){
store[j]=min(store[j], store[j-den]+1);
}

is pretty trivial. Any ideas how this thing works?  The store[j-den]+1
has me especially confused.