Recursion is one of the most useful but very little understood programming techniques. Special kinds of problems can be solved easily and effectively with a recursive function (e.g., locating a file in a hierarchical file system).
This article doesn't intend to explain how recursion works ... but instead, it presents you eight classical problems implemented using a recursive and an iterative solution.
As you can probably see, for some problems, recursion comes more naturally, but for others, it should not be the first choice.
How to run the code?
Examples from this article have been developed using the codeguppy.com editor.
To run the code in this article, paste in the codeguppy.com editor the appropriate code snippet.
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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;
}
Article reprinted from: https://codeguppy.com/blog/recursion-in-javascript-practical-examples/index.html
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