HackerRank Correctness and the Loop Invariant Solution

HackerRank Correctness and the Loop Invariant solution – In this HackerRank Correctness and the Loop Invariant problem, In the InsertionSort code below, there is an error. Can you fix it? Print the array only once, when it is fully sorted.

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.

Insertion Sort’s Invariant
Say, you have some InsertionSort code, where the outer loop goes through the whole array A:

for(int i = 1; i < A.length; i++){
//insertion sort code

You could then state the following loop invariant:

At the start of every iteration of the outer loop (indexed with i), the subarray until ar[i] consists of the original elements that were there, but in sorted order.

To prove Insertion Sort is correct, you will then demonstrate it for the three stages:

• Initialization – The subarray starts with the first element of the array, and it is (obviously) sorted to begin with.
• Maintenance – Each iteration of the loop expands the subarray, but keeps the sorted property. An element V gets inserted into the array only when it is greater than the element to its left. Since the elements to its left have already been sorted, it means V is greater than all the elements to its left, so the array remains sorted. (In Insertion Sort 2 we saw this by printing the array each time an element was properly inserted.)
• Termination – The code will terminate after i has reached the last element in the array, which means the sorted subarray has expanded to encompass the entire array. The array is now fully sorted.

HackerRank Correctness and the Loop Invariant solution in Python.

def insert_sort(A):
	m = len(A)
  
	for x in range(1,m):
		k = A[x]
		j=x
		while(j>0 and A[j-1]>k):
			A[j] = A[j-1]
			j-=1
      
		A[j]=k
        
	return A

i = int(input())
N = [int(c) for c in input().split()]
N = insert_sort(N)


for a in N:
  print(a, end=" ")
     

HackerRank Correctness and the Loop Invariant solution in Java.

import java.io.*;
import java.util.*;

public class Solution {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int numElements = in.nextInt();
        int[] array = new int[numElements];
        for (int i = 0; i < array.length; i++) {
            array[i] = in.nextInt();
        }

        sort(array);
    }

    public static void sort(int[] array) {
        for (int i = 1; i < array.length; i++) {
            int index = i;
            while (index > 0 && array[index] < array[index - 1]) {
                int temp = array[index];
                array[index] = array[index - 1];
                array[index - 1] = temp;
                index--;
            }
        }
        
        printArray(array);
    }

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

}

Problem solution in C++ programming.

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>
#include <iostream>
using namespace std;
/* Head ends here */
void merge(int p[], int m, int q[], int n, int r[]){
    for(int rb=0, pf=0,qf=0;rb<m+n;rb++){
        if(pf<m&&qf<n){
            if(p[pf]<=q[qf]){
                r[rb]=p[pf];
                pf++;
            }
            else{
                r[rb]=q[qf];
                qf++;
            }
        }
        else if(pf<m){
            r[rb]=p[pf];
            pf++;
        }
        else{
            r[rb]=q[qf];
            qf++;
        }
    }
}

void mergesort(int*r,int n){
    if(n>1){
        int p[n/2],q[n-n/2];
        for(int i=0;i<n/2;i++)p[i]=r[i];
        for(int i=n/2;i<n;i++)q[i-n/2]=r[i];
        mergesort(p,n/2);
        mergesort(q,n-n/2);
        merge(p,n/2,q,n-n/2,r);
    }
}
/* Tail starts here */
int main(void) {
   
   int _ar_size;
cin>>_ar_size;
int _ar[_ar_size], _ar_i;
for(_ar_i = 0; _ar_i < _ar_size; _ar_i++) { 
   cin>>_ar[_ar_i];
}

mergesort(_ar,_ar_size);
   
    for(int i=0;i<_ar_size;i++)cout<<_ar[i]<<" ";
    cout<<endl;
   return 0;
}

Problem solution in C programming.

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
#include <assert.h>
/* Head ends here */
#include <stddef.h>
void insertionSort(int ar_size, int *  ar) {    
    int i,j;
    int value;
    for(i=1;i<ar_size;i++)
    {
        value=ar[i];
        j=i-1;
        while(j>=0 && value<ar[j])
        {
            ar[j+1]=ar[j];
            j=j-1;
        }
        ar[j+1]=value;        
    }
    for(j=0;j<ar_size;j++)
        {
            printf("%d",ar[j]);
            printf(" ");
        }
}
/* Tail starts here */
int main(void) {   
   int _ar_size;
scanf("%d", &_ar_size);
int _ar[_ar_size], _ar_i;
for(_ar_i = 0; _ar_i < _ar_size; _ar_i++) { 
   scanf("%d", &_ar[_ar_i]); 
}

insertionSort(_ar_size, _ar);
   
   return 0;
}

Problem solution in JavaScript programming.

function insertionSort (ar) {

    for(i = 1; i < ar.length; i++){
        var value = ar[i];
        var prevIndex = i - 1;
        while(prevIndex >= 0 && ar[prevIndex] > value){
            ar[prevIndex + 1] = ar[prevIndex];
            prevIndex--;
        }
        ar[prevIndex + 1] = value;
    }
    return ar;

}

function processData(input) {
    var inputArray = input.split('n');
    var numArray = inputArray[1].split(" ");
    for(var i=0;i<numArray.length;i++) {
        numArray[i] = parseInt(numArray[i]);
    }
    console.log(insertionSort(numArray).join(" "));
}

process.stdin.resume();
process.stdin.setEncoding("ascii");
_input = "";
process.stdin.on("data", function (input) {
    _input += input;
});

process.stdin.on("end", function () {
   processData(_input);
});