Coin change DP and REC

#include <functional>
#include <iostream>
#include <vector>
using namespace std;

#define MAX_VALUE 100000
vector<int> DP(MAX_VALUE + 1, MAX_VALUE + 1);

template <typename Less, typename... T>
constexpr auto& m_min(Less&& less, const T&... values) {
  return std::min({ std::cref(values)..., }, std::forward<Less>(less)).get();
}

int safe_access(vector<int> DP, int index) {
  if (index < 0) {
    return MAX_VALUE + 1;
  }
  return DP.at(index);
}

void coin_change(int value) {
  DP[0] = 1;
  DP[1] = DP[5] = DP[10] = DP[20] = DP[100] = 1;

  for (int i = 1; i <= value; i++) {
    DP[i] = m_min(
      std::less<int>(),
      safe_access(DP, i),
      safe_access(DP, i - 1) + 1,
      safe_access(DP, i - 5) + 1,
      safe_access(DP, i - 10) + 1,
      safe_access(DP, i - 20) + 1,
      safe_access(DP, i - 100) + 1
    );
  }

}

int coin_change_rec(int value) {
  if (value < 0) return MAX_VALUE + 1;
  if (value == 0) return 0;
  if (value == 1 || value == 5 || value == 10 || value == 20 || value == 100) {
    return 1;
  }

  return 1 + m_min(
        std::less<int>(),
        coin_change_rec(value - 1),
        coin_change_rec(value - 5),
        coin_change_rec(value - 10),
        coin_change_rec(value - 20),
        coin_change_rec(value - 100)
      );
}

int main() {
  int value;
  cin >> value;

  coin_change(value);
  cout << DP.at(value);
  return 0;
}