Correctness and the Loop Invariant

Published on August 06, 2021
Last updated August 06, 2021

In the previous challenge, you wrote code to perform an Insertion Sort on an unsorted array. But how would you prove that the code is correct? I.e. how do you show that for any input your code will provide the right output?

Loop Invariant

In computer science, you could prove it formally with a loop invariant, where you state that a desired property is maintained in your loop. Such a proof is broken down into the following parts:

  • Initialization: It is true (in a limited sense) before the loop runs.
  • Maintenance: If it’s true before an iteration of a loop, it remains true before the next iteration.
  • Termination: It will terminate in a useful way once it is finished.


In the InsertionSort code below, there is an error. Can you fix it? Print the array only once, when it is fully sorted.

Input Format

There will be two lines of input: s - the size of the array arr - the list of numbers that makes up the array


  • 1<= s <= 1000
  • -1500 <= v <= 1500

Output Format

Output the numbers in order, space-separated on one line.

Link to the problem on hackerrank

Solution in java

import java.util.*;

public class Solution {
    public static void main(String[] args) {
        Scanner sc = new Scanner(;
        int n = sc.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = sc.nextInt();
        sort(n, arr);

    public static void sort(int n, int[] arr) {
        for (int i = 1; i < n; i++) {
            int key = arr[i];
            int j = i - 1;

            while (j >= 0 && arr[j] > key) {
                arr[j + 1] = arr[j];
            arr[j + 1] = key;

    public static void printArray(int[] arr) {
        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");

Solution in c

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>

void insertionSort(int N, int arr[]) {
    int i,j;
    int value;
        while(j>=0 && value<arr[j])
        printf(" ");

int main(void) {

    int N;
    scanf("%d", &N);
    int arr[N], i;
    for(i = 0; i < N; i++) {
        scanf("%d", &arr[i]);

    insertionSort(N, arr);

    return 0;

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