#CodeChallenge Given a set of coins denominations calculate the minimum combinations to get the target amount

NumberOfCoinsForChange.cpp

#include <vector>
#include <climits>
using namespace std;

// O(dn) time | O(n) space
int minNumberOfCoinsForChange(int n, vector<int> denoms) {
  // Create a matrix, to store the best possiblitites until target.
	vector<int> numOfCoins(n + 1, INT_MAX); // +1, to include zero.
	numOfCoins[0] = 0; // Starts at zero because, how many 0 coins do I  need to make 0 in value.
  for (int denomination : denoms) {
		// Create the matrix to store the best combination so far
		for (int amountTarget = 0; amountTarget < numOfCoins.size(); amountTarget++) {
			// Is possible to make it with that bill?
			if (denomination <= amountTarget) {
				// if I can't create the number in the past, then keep infinity to avoid flip C++ SHIT. (if int_max + 1 == min_int)
				int newTarget = numOfCoins[amountTarget - denomination];
				int toCompare = newTarget == INT_MAX ? newTarget : newTarget + 1;
				// Should I include or exclude the coin?, keep the min
				numOfCoins[amountTarget] = min(numOfCoins[amountTarget], toCompare);
			}
		}
	}
  return numOfCoins[n] != INT_MAX ? numOfCoins[n] : -1;
}