Recursion in JavaScript - Practical examples

Recursion is one of the most useful but very little understood programming technique. There are special kind of problems that can be solved very easy and elegant with a recursive function (e.g. locating a file in an hierarchical file system).

This article doesn't intend to offer an explanation of how recursion works ... but insted in presents you eight classical problems implemented both using a recursive solution as well as an iterative solution.

As you can probably see ... for some problems recursion comes more naturally, as for the others it should not be the first choise.

How to run the code?

Examples from this article have been developed using the codeguppy.com editor. However just by replacing println() with console.log() you can run it in any environment you prefer.

Without further ado, let's see the problems and their solutions.

1. Calculate the sum of natural number up to n

Recursive solution

let sum = addTo(10);
println(sum);

function addTo(n)
{
    if (n == 0)
        return 0;
    
    return n + addTo(n - 1);
}

Iterative solution

let sum = addTo(10);
println(sum);

function addTo(n)
{
    let sum = 0;
    
    for(let i = 1; i <= n; i++)
    {
        sum += i;
    }
    
    return sum;
}

2. Calculate factorial of n. Reminder n! = 1 * 2 * ... * n

Recursive solution

let prod = factorial(10);
println(prod);

function factorial(n)
{
    if (n <= 1)
        return 1;
        
    return n * factorial(n - 1);
}

Iterative solution

let prod = factorial(10);
println(prod);

function factorial(n)
{
    let prod = 1;
    
    for(let i = 1; i <= n; i++)
    {
        prod *= i;
    }
    
    return prod;
}

3. Calculate the value of n to the m power

Recursive solution

println(powerNo(3, 2));

function powerNo(n, m)
{
    if (m == 0)
        return 1;
    
    if (m == 1)
        return n;
        
    return n * powerNo(n, m - 1);
}

Iterative solution


println(powerNo(3, 2));

function powerNo(n, m)
{
    let prod = 1;
    
    for(let i = 1; i <= m; i++)
    {
        prod *= n;
    }
    
    return prod;
}

4. Find the nth Fibonacci number

Recursive solution

function findFibonacci(n)
{
    if (n == 0)
        return 0;
        
    if (n == 1)
        return 1;
        
    return findFibonacci(n - 1) + findFibonacci(n - 2);
}

let n = findFibonacci(10);
println(n);

Iterative solution

function findFibonacci(n)
{
    let fib0 = 0;
    let fib1 = 1;

    if (n == 0)
        return fib0;
        
    if (n == 1)
        return fib1;

    let fib;
    
    for(let i = 2; i <= n; i++)
    {
        fib = fib0 + fib1;
        
        fib0 = fib1;
        fib1 = fib;
    }
    
    return fib;
}

println(findFibonacci(10));

5. Calculate the sum of elements of an array of numbers

Recursive solution

let ar = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
let n = sum(ar);
println(n);


function sum(ar)
{
    return _sum(ar, ar.length - 1);
}

function _sum(ar, index)
{
    if (index == 0)
        return ar[0];
        
    return ar[index] + _sum(ar, index - 1);
}

Iterative solution

let ar = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
let n = sum(ar);
println(n);

function sum(ar)
{
    let sum = 0;
    
    for(let el of ar)
    {
        sum += el;
    }
    
    return sum;
}

6. Sort an array of numbers using bubble sort algorithm

Recursive solution

let ar = [23, 1000, 1, -1, 8, 3];
println(ar);
bubbleSort(ar);
println(ar);

function bubbleSort(ar)
{
    let shouldSort = false;

    for(let i = 0; i < ar.length - 1; i++)
    {
        let a = ar[i];
        if ( a > ar[i+1] )
        {
            ar[i] = ar[i+1];
            ar[i+1] = a;
            shouldSort = true;
        }
    }
    
    if (shouldSort)
    {
        bubbleSort(ar);
    }
}

Iterative solution

let ar = [23, 1000, 1, -1, 8, 3];
println(ar);
bubbleSort(ar);
println(ar);

function bubbleSort(ar)
{
    let shouldSort = true;

    while(shouldSort)
    {
        shouldSort = false;
        
        for(let i = 0; i < ar.length - 1; i++)
        {
            let a = ar[i];
            if ( a > ar[i+1] )
            {
                ar[i] = ar[i+1];
                ar[i+1] = a;
                shouldSort = true;
            }
        }
    }
}

7. Find a number in a sorted array (binary search)

Recursive solution

//        0   1   2   3   4   5   6   7   8   9
let ar = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100];

let position = findNumber(90, ar);
println(position);

// Find number n in sorted array ar
// Returns array index if found or -1 if not found
function findNumber(n, ar)
{
    return _findNumber(n, ar, 0, ar.length - 1);
}

// Find number n in sorted array ar in between indexes i1 and i2
// using recursive approach
function _findNumber(n, ar, i1, i2)
{
    if (i2 < i1)
        return -1;

    println("Checking interval: [" + i1 + ", " + i2 + "]");
    
    let mid = i1 + Math.floor((i2 - i1) / 2);
    
    if (n === ar[mid])
        return mid;
        
    if (n < ar[mid])
        return _findNumber(n, ar, i1, mid - 1);
        
    return _findNumber(n, ar, mid + 1, i2);
}

Iterative solution

//        0   1   2   3   4   5   6   7   8   9
let ar = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100];

let position = findNumber(90, ar);
println(position);

// Find number n in sorted array ar using iterative approach
// Returns array index if found or -1 if not found
function findNumber(n, ar)
{
    let i1 = 0;
    let i2 = ar.length - 1;
    
    while(i1 <= i2)
    {
        println("Checking interval: [" + i1 + ", " + i2 + "]");
        
        let mid = i1 + Math.floor((i2 - i1) / 2);
        
        if (n === ar[mid])
            return mid;

        if (n < ar[mid])
        {
            i2 = mid - 1;
        }
        else
        {
            i1 = mid + 1;
        }
    }
    
    return -1;
}

8. Find the maximum number in an array containing numbers or other arrays of numbers

Recursive solution

let ar = [2, 4, 10, [12, 4, [100, 99], 4], [3, 2, 99], 0];

let max = findMax(ar);
println("Max  = ", max);

// Use recursion to find the maximum numeric value in an array of arrays
function findMax(ar)
{
    let max = -Infinity;

    // Cycle through all the elements of the array
    for(let i = 0; i < ar.length; i++)
    {
        let el = ar[i];

        // If an element is of type array then invoke the same function
        // to find out the maximum element of that subarray
        if ( Array.isArray(el) )
        {
            el = findMax( el );
        }

        if ( el > max )
        {
            max = el;
        }
    }

    return max;
}

Iterative solution

// Find the maximum number in a jagged array of numbers or array of numbers
// Do not use recursion

let ar = [2, 4, 10, [12, 4, [100, 99], 4], [3, 2, 99], 0];

let max = findMax(ar);
println("Max  = ", max);

// Use a stack to find the maximum numeric value in an array of arrays
function findMax(arElements)
{
    let max = -Infinity;

    // This is the stack on which will put the first array and then 
    // all the other sub-arrays that we find as we traverse an array     
    let arrays = [];

    arrays.push(arElements);

    // Loop as long as are arrays added to the stack for processing
    while(arrays.length > 0)
    {
        // Extract an array from the stack
        ar = arrays.pop();
        
        // ... and loop through its elements
        for(let i = 0; i < ar.length; i++)
        {
            let el = ar[i];

            // If an element is of type array, we'll add it to stack
            // to be processed later
            if ( Array.isArray(el) )
            {
                arrays.push(el);
                continue;
            }
            
            if ( el > max )
            {
                max = el;
            }
        }
    }

    return max;
}

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Recursion in JavaScript - Practical examples