Find whether an array is subset of another array - Added Method 3 in C++

In this problem, we are given two arrays of integers arr1[] and arr2[] of size m and n. Our task is to find whether an array is subset of another array - Added Method 3.

Both arrays arr1[] and arr2[] are unorders and have distinct elements.

Let's take an example to understand the problem,

Input : arr1[] = {5, 2, 1, 6, 8, 10}, arr2[] = {6, 2, 1}
Output : arr2 is a subset of arr1.

Solution Approach

To solve this problem, we have discussed multiple methods here. Let's see the working of each of them with a program.

Method 1

One method to solve the problem is by directly checking for subsets. This is done using nested loops, outer for each element of the array arr2[] and inner one, for each element of the array arr1[]. We will check if each element of arr2 is present in arr1, if it is return 1 ( arr2 is subarray of arr1) otherwise return 0 (arr2 is not subarray of arr1).

Example

Program to illustrate the working of our solution

#include 
using namespace std;
bool isSubsetArray(int arr1[], int arr2[], int m, int n){
   int j = 0;
   for (int i = 0; i 
Output
arr2[] is subset of arr1[]

Method 2
Another method to solve the problem is by checking if all elements of the arr2 are present in arr1. To do this effectively, we will sort the array arr1[] and then for each element of arr2, perform binary search to search for elements of arr2[] in arr1[]. Now, if any element is not found, return 0 (arr2 is not a subarray of arr1) and if all elements of arr2 are present in arr1, return 1 (arr2 is a subarray
of arr1).
Example
Program to illustrate the working of our solution
#include 
using namespace std;
int binarySearch(int arr[], int low, int high, int x){
   if (high >= low){
      int mid = (low + high) / 2;
      if ((mid == 0 || x > arr[mid - 1]) && (arr[mid] == x))
         return mid;
      else if (x > arr[mid])
         return binarySearch(arr, (mid + 1), high, x);
      else
         return binarySearch(arr, low, (mid - 1), x);
   }
   return -1;
}
bool isSubsetArray(int arr1[], int arr2[], int m, int n){
   int i = 0;
   sort(arr1, arr1 + m);
   for (i = 0; i 
Output
arr2[] is subset of arr1[]

Method 3
One more method to find the solution is by first sorting both the arrays arr1[] and arr2[]. Then for all elements of array arr2[] check if they are present in arr1[]. For this, we have a straight method which is using indexes of elements in both arrays.
Example
Program to illustrate the working of our solution
#include 
using namespace std;
bool isSubsetArray(int arr1[], int arr2[], int m, int n){
   int i = 0, j = 0;
   if (m  arr2[i])
         return 0;
   }
   return (i 
Output
arr2[] is subset of arr1[]

Method 4
One more method, to check if arr2 is a subset of arr1 is using hashing. We will create a hash table using all the elements of arr1 and then search for elements of arr2 in the hash table. If values are found, then return 1 (arr2 is a subset of arr1) else return 0 (arr2 is not a subset of arr1).
Example
Program to illustrate the working of our solution
#include 
using namespace std;
bool isSubsetArray(int arr1[], int arr2[], int m, int n){
   set arr1Hash;
   for (int i = 0; i 
Output
arr2[] is subset of arr1[]

Method 5
One more method to solve the problem is using the set data structure. We will create a new set with all values of arr1 and check its length. Then we will try to insert all values of arr2, if adding changes the length then arr2 is not a subset of arr1. If no change in length occurs after adding elements of arr2 then arr2 is a subset of arr1.
Example
Program to illustrate the working of our solution
#include 
using namespace std;
bool isSubsetArray(int arr1[], int arr2[], int m, int n){
   unordered_set arrSet;
   for (int i = 0; i 
Output
arr2[] is subset of arr1[]