Understanding Insertion Sort for beginners


How to solve Insertion Sort for beginners in JS

If you don’t know what insertion sort is I recommend giving it a try at the problem for 10 minutes then come back or just check out how to implement it.

Here is Free Code Camps explanation: This method works by building up a sorted array at the beginning of the list. It begins the sorted array with the first element. Then it inspects the next element and swaps it backwards into the sorted array until it is in sorted position. It continues iterating through the list and swapping new items backwards into the sorted portion until it reaches the end. This algorithm has quadratic time complexity in the average and worst cases. Insertion Sort Problem here are the instructions from Free Code Camp

Instructions: Write a function insertionSort which takes an array of integers as input and returns an array of these integers in sorted order from least to greatest.

Insertion Sort is a quadratic algorithm meaning its O(n^2) making it a bad algorithm for production as it can cause performance issues. That being said I think its a nice algo to learn to practice solving coding interview questions.

This algo is also known as destructive as it operates on the array that is passed in on the function.

The code

function insertionSort(array) {
  for (let i = 1; i < array.length; i++) {
    let numberToInsert = array[i];
    let j;
    for (j = i - 1; array[j] > numberToInsert && j >= 0; j--) {
      array[j + 1] = array[j];
    }
    array[j + 1] = numberToInsert;
  }
  return array;
}
// commented
function insertionSort(array) {
    // We make a double for loop
    // Notice the index starts at 1 leaving index 0 as the sorted array
    for(let i = 1; i < array.length; i++){
        // the number to insert will always be the number we currently are on in this loop
        let numberToInsert = array[i]
         // We also initialize j
        let j;
        // does the insertion when either array[j] > numberToInsert or j >= 0 // j  >= 0 is checking if j every goes out of bounds if it is we shouldn't keep moving things to the right
        for(j = i - 1; array[j] > numberToInsert && j >= 0; j--){
        // walk number (array[j]) greater than numberToInsert to the right
        // effecively makes room for numberToInsert to be inserted if above condition is falsy
          array[j + 1] = array[j]
        }
        // does the insertion
        array[j + 1] = numberToInsert

    }
    return array
  }

Explanation

We will start with this array to sort [1|3,-1,5,6]

Everything to the left of the pipe character is assumed to be the sorted array everything to the right is the unsorted.

function insertionSort(array) {
  for (let i = 1; i < array.length; i++) {
    let numberToInsert = array[i];
    let j;
    for (j = i - 1; array[j] > numberToInsert && j >= 0; j--) {
      array[j + 1] = array[j];
    }
    array[j + 1] = numberToInsert;
  }
  return array;
}

First iteration of outer loop

The whole point or jist of Insertion sort is that we assume we have a sorted half and a unsorted half and go from there.

let array = [1|3,-1,5,6]

First iteration of inner loop

first iteration would look like the array above. We are choosing index zero to be sorted and assuming the right side is unsorted.

numberToInsert = array\[1\] and j = 0

In the for loop we ask if array[j] > numberToInsert && j >= 0 // this is false

So we move out of the loop and insert, now 3 is part of the sorted array

array[1] = numberToInsert;

[1,3|-1,5,6]

Second iteration of outer loop

[1,3|-1,5,6]

Now numberToInsert = array\[2\] and j = 1

First iteration of inner loop

[1,3|-1,5,6]

We then ask if array[1] > numberToInsert && j >= 0 // this is true

So we move array[j] one to the right

[1, |3,5,6] // notice array[1] is now empty

the -1 is on to with the numberToInsert variable.

Second iteration of inner loop

We then ask if array[0] > numberToInsert && j >= 0 // this is true

so we move to the array[0] to the right

[ ,1,3,5,6] // notice array[0] is now empty

Third iteration of inner loop

We then ask if array[-1] > numberToInsert && j >= 0 // this is false

j is not >= 0 so we don’t do anything and move on from the loop

we do the insertion

[-1,1|3,5,6]

Third iteration of outer loop

Now numberToInsert = array\[3\] and j = 2

First Iteration of inner loop

[-1,1,3|5,6] // notice the array is already sorted, but the algorithm (Insertion Sort) doesn’t know that.

We then ask if array[2] > numberToInsert && j >= 0 // this is false

So we insert at 5, 5 is already there

[-1,1,3,5|6]

now the array looks like that^

//The last iteration of the is going to look very similar as this iteration.

Comment on any questions and let me know how I can improve my explanation. This algo took me longer to understand than I thought it would so if you are struggling, know I did too!

Resources and Others:

Great explanation from Brain Holt on his Frontend Masters course website includes an explanation of the big o complexity of this algorithm Insertion Sort Problem

Also, take a look at a visualization at 7 VisuAlgo.net

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