アルゴリズムをどのように設計するか?一般的なアルゴリズム パラダイムの紹介

function binarySearchRecursive(array, value, low, high) {
    if (low <= high) {
        const mid = Math.floor((low + high) / 2);
        const element = array[mid];

        if (element < value) {
            return binarySearchRecursive(array, value, mid + 1, high);
        } else if (element > value) {
            return binarySearchRecursive(array, value, low, mid - 1);
        } else {
            return mid;
        }
    }
    return null;
}

export function binarySearch(array, value) {
    const sortedArray = quickSort(array);
    const low = 0;
    const high = sortedArray.length - 1;

    return binarySearchRecursive(array, value, low, high);
}

function minCoinChange(coins, amount) {
    const cache = [];
    const makeChange = (value) => {
        if (!value) {
            return [];
        }
        if (cache[value]) {
            return cache[value];
        }
        let min = [];
        let newMin;
        let newAmount;
        for (let i = 0; i < coins.length; i++) {
            const coin = coins[i];
            newAmount = value - coin;
            if (newAmount >= 0) {
                newMin = makeChange(newAmount);
            }
            if (newAmount >= 0 && 
            (newMin.length < min.length - 1 || !min.length) && (newMin.length || !newAmount)) {
                min = [coin].concat(newMin);
            }
        }
        return (cache[value] = min);
    }
    return makeChange(amount);
}

console.log(minCoinChange([1, 2, 5 10, 20], 37)); // => [2, 5, 10, 20]
console.log(minCoinChange([1, 3, 4], 6)) // => [3, 3]

function minCoinChange(coins, amount) {
    const change = [];
    let total = 0;
    for (let i = coins.length; i>= 0; i--) {
        const coin = coins[i];
        while (total + coin <= amount) {
            change.push(coin);
            total += coin;
        }
    }
    return change;
}

console.log(minCoinChange([1, 2, 5 10, 20], 37)); // => [2, 5, 10, 20]
console.log(minCoinChange([1, 3, 4], 6)) // => [4, 1, 1]