Step by Step solution about How to resolve the algorithm Count the coins step by step in the JavaScript programming language

First Response:

• Provides a detailed explanation of the first function, countcoins, which uses dynamic programming to count the number of ways to make change for a given target amount using a specific set of coins.
• Explains the algorithm, variable initialization, and recursive iteration to calculate the result.
• However, it does not mention the second and third functions.

Second Response:

• Briefly describes the second function, countcoins, but does not provide a detailed explanation.
• Fails to explain the third function.
• Presents a different implementation of the coin change problem using dynamic programming but does not relate it to the first two functions.

Detailed Explanation:

The provided source code contains three JavaScript functions that solve the coin change problem:

1. Function countcoins (Dynamic Programming):

• This function takes two parameters: t (the target amount) and o (an array of coin denominations).
• It initializes a table t of size targetsLength = t + 1, where targetLength represents the target amount plus one.
• It iterates through all coins in o and all target values in t.
• For each pair of coin and target, it accumulates the number of ways to reach that target using the current coin and previous targets.
• The result is stored in t[targetsLength - 1], which represents the number of ways to make change for the target amount.

2. Function countcoins (Recursive Permutation):

• This function is an alternative solution to the coin change problem using recursion.
• It initializes a variable solutions to count the number of ways to reach the target amount.
• It calls a recursive function permutate that takes two parameters: a (the current amount) and x (the index of the last used coin).
• The permutate function explores all possible combinations of coins to reach the target recursively.
• When the current amount equals the target amount, it increments the solutions counter.
• The result is returned as the number of solutions.

3. Coin Change Problem with Dynamic Programming:

• This is another implementation of the coin change problem using dynamic programming.
• It uses a table t of size amount + 1, where amount is the target amount.
• It initializes t[amount] to 0 and iterates through all coins and all target values up to the target amount.
• For each pair of coin and target, it accumulates the number of ways to reach that target using the current coin and previous targets.
• The result is stored in t[amount], which represents the number of ways to make change for the target amount.

function countcoins(t, o) {
    'use strict';
    var targetsLength = t + 1;
    var operandsLength = o.length;
    t = [1];

    for (var a = 0; a < operandsLength; a++) {
        for (var b = 1; b < targetsLength; b++) {

            // initialise undefined target
            t[b] = t[b] ? t[b] : 0;

            // accumulate target + operand ways
            t[b] += (b < o[a]) ? 0 : t[b - o[a]];
        }
    }

    return t[targetsLength - 1];
}


countcoins(100, [1,5,10,25]);
242


function countcoins(t, o) {
    'use strict';
    var operandsLength = o.length;
    var solutions = 0;

    function permutate(a, x) {

        // base case
        if (a === t) {
            solutions++;
        }

        // recursive case
        else if (a < t) {
            for (var i = 0; i < operandsLength; i++) {
                if (i >= x) {
                    permutate(o[i] + a, i);
                }
            }
        }
    }

    permutate(0, 0);
    return solutions;
}


countcoins(100, [1,5,10,25]);
242


var amount = 100,
    coin = [1, 5, 10, 25]
var t = [1];
for (t[amount] = 0, a = 1; a < amount; a++) t[a] = 0 // initialise t[0..amount]=[1,0,...,0]
for (var i = 0, e = coin.length; i < e; i++)
    for (var ci = coin[i], a = ci; a <= amount; a++)
        t[a] += t[a - ci]
document.write(t[amount])