Coin change problem

const coin_change_bottom_up = (coins, sum) => { let memo = new Array(sum + 1).fill(Infinity); memo[0] = 0; for (let i = 1; i <= sum; i++) { for (let coin = 0; coin < coins.length; coin++) { if (coins[coin] <= i) { memo[i] = Math.min(memo[i], 1 + memo[i - coins[coin]]); } } } return memo[sum]; // O(n*m) }; let coins = [1, 5, 10, 25]; let sum = 18; console.log(coin_change_bottom_up(coins, sum)); //--------------------------------- const coin_change_top_dowm = (coins, sum, memo) => { if (sum == 0) return 0; if (sum < 0) return 1e9; // 1e9 = 1,000,000,000 // already solved cases: let ans = Infinity; for (let coin = 0; coin < coins.length; coin++) { if (coins[coin] <= sum) { let sub_ans = 1 + coin_change_top_dowm(coins, sum - coins[coin], memo); // console.log(sub_ans); ans = Math.min(ans, sub_ans); } } memo[sum] = ans; return memo[sum]; }; let memo = new Array(sum + 1).fill(Infinity); console.log(coin_change_top_dowm(coins, sum, memo));