Introduction
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 8 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
var sum = addTo(10);
println(sum);
function addTo(n)
{
if (n == 0)
return 0;
return n + addTo(n - 1);
}
Iterative solution
var sum = addTo(10);
println(sum);
function addTo(n)
{
var sum = 0;
for(var i = 1; i <= n; i++)
{
sum += i;
}
return sum;
}
2. Calculate factorial of n. Reminder n! = 1 * 2 * ... * n
Recursive solution
var prod = factorial(10);
println(prod);
function factorial(n)
{
if (n <= 1)
return 1;
return n * factorial(n - 1);
}
Iterative solution
var prod = factorial(10);
println(prod);
function factorial(n)
{
var prod = 1;
for(var 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)
{
var prod = 1;
for(var 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);
}
var n = findFibonacci(10);
println(n);
Iterative solution
function findFibonacci(n)
{
var fib0 = 0;
var fib1 = 1;
if (n == 0)
return fib0;
if (n == 1)
return fib1;
var fib;
for(var 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
var ar = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
var 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
var ar = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
var n = sum(ar);
println(n);
function sum(ar)
{
var sum = 0;
for(var el of ar)
{
sum += el;
}
return sum;
}
6. Sort an array of numbers using bubble sort algorithm
Recursive solution
var ar = [23, 1000, 1, -1, 8, 3];
println(ar);
bubbleSort(ar);
println(ar);
function bubbleSort(ar)
{
var shouldSort = false;
for(var i = 0; i < ar.length - 1; i++)
{
var 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
var ar = [23, 1000, 1, -1, 8, 3];
println(ar);
bubbleSort(ar);
println(ar);
function bubbleSort(ar)
{
var shouldSort = true;
while(shouldSort)
{
shouldSort = false;
for(var i = 0; i < ar.length - 1; i++)
{
var 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
var ar = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100];
var 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 + "]");
var 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
var ar = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100];
var 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)
{
var i1 = 0;
var i2 = ar.length - 1;
while(i1 <= i2)
{
println("Checking interval: [" + i1 + ", " + i2 + "]");
var 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
var ar = [2, 4, 10, [12, 4, [100, 99], 4], [3, 2, 99], 0];
var max = findMax(ar);
println("Max = ", max);
// Use recursion to find the maximum numeric value in an array of arrays
function findMax(ar)
{
var max = -Infinity;
// Cycle through all the elements of the array
for(var i = 0; i < ar.length; i++)
{
var 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
var ar = [2, 4, 10, [12, 4, [100, 99], 4], [3, 2, 99], 0];
var max = findMax(ar);
println("Max = ", max);
// Use a stack to find the maximum numeric value in an array of arrays
function findMax(arElements)
{
var 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
var 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(var i = 0; i < ar.length; i++)
{
var 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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