how many coins

#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <iostream>
#include <vector>

constexpr unsigned COINS[] = {1, 5, 16, 23, 33};
constexpr unsigned COINS_CNT = sizeof(COINS) / sizeof(unsigned);

unsigned greedy(unsigned amount) {
    unsigned cnt[COINS_CNT] = {0};

    for (int i = COINS_CNT - 1; i >= 0; i--) {
        cnt[i] = amount / COINS[i];
        amount %= COINS[i];
    }

    unsigned sum = 0;
    for (size_t i = 0; i < COINS_CNT; i++) {
        sum += cnt[i];
        printf("%u * %u\t", cnt[i], COINS[i]);
    }

    return sum;
}

std::pair<unsigned, std::vector<unsigned>>
exhaustive_internal(unsigned amount, size_t coin_index) {
    unsigned coin = COINS[coin_index];
    unsigned max_cnt = amount / coin;
    unsigned min_cnt = UINT32_MAX;
    std::vector<unsigned> min_result;

    if (coin_index == 0) {
        if (amount % coin == 0) {
            return {max_cnt, {max_cnt}};
        } else {
            return {min_cnt, {}};
        }
    }

    for (size_t i = 0; i <= max_cnt; i++) {
        auto [min, result] =
            exhaustive_internal(amount - i * coin, coin_index - 1);
        if (min < min_cnt && min + i < min_cnt) {
            min_cnt = min + i;
            result.push_back(i);
            min_result = result;
        }
    }

    return {min_cnt, min_result};
}

unsigned exhaustive(unsigned amount) {
    auto [min, min_result] = exhaustive_internal(amount, COINS_CNT - 1);

    for (size_t i = 0; i < COINS_CNT; i++) {
        printf("%u * %u\t", min_result[i], COINS[i]);
    }

    return min;
}

int main() {
    for (unsigned amount = 1; amount < 100; amount++) {
        std::cout << "========== " << amount << " ==========" << std::endl;
        std::cout << greedy(amount) << std::endl;
        std::cout << exhaustive(amount) << std::endl;
    }
}