Union and Intersection of two sorted arrays

Software Development
#1

Given two sorted arrays, find their union and intersection.
Example:

Input : arr1[] = {1, 3, 4, 5, 7}
arr2[] = {2, 3, 5, 6}
Output : Union : {1, 2, 3, 4, 5, 6, 7}
Intersection : {3, 5}

Input : arr1[] = {2, 5, 6}
arr2[] = {4, 6, 8, 10}
Output : Union : {2, 4, 5, 6, 8, 10}
Intersection : {6}

Union of arrays arr1[] and arr2[]

To find union of two sorted arrays, follow the following merge procedure :

  1. Use two index variables i and j, initial values i = 0, j = 0
  2. If arr1[i] is smaller than arr2[j] then print arr1[i] and increment i.
  3. If arr1[i] is greater than arr2[j] then print arr2[j] and increment j.
  4. If both are same then print any of them and increment both i and j.
  5. Print remaining elements of the larger array.

Below is the implementation of the above approach :

// C++ program to find union of

// two sorted arrays

#include <bits/stdc++.h>

using namespace std;

/* Function prints union of arr1[] and arr2[]

m is the number of elements in arr1[]

n is the number of elements in arr2[] */

void printUnion( int arr1[], int arr2[], int m, int n)

{

int i = 0, j = 0;

while (i < m && j < n) {

if (arr1[i] < arr2[j])

cout << arr1[i++] << " " ;

else if (arr2[j] < arr1[i])

cout << arr2[j++] << " " ;

else {

cout << arr2[j++] << " " ;

i++;

}

}

/* Print remaining elements of the larger array */

while (i < m)

cout << arr1[i++] << " " ;

while (j < n)

cout << arr2[j++] << " " ;

}

/* Driver program to test above function */

int main()

{

int arr1[] = { 1, 2, 4, 5, 6 };

int arr2[] = { 2, 3, 5, 7 };

int m = sizeof (arr1) / sizeof (arr1[0]);

int n = sizeof (arr2) / sizeof (arr2[0]);

// Function calling

printUnion(arr1, arr2, m, n);

return 0;

}

Output:

1 2 3 4 5 6 7

Time Complexity : O(m + n)
Handling duplicates in any of the array : Above code does not handle duplicates in any of the array. To handle the duplicates, just check for every element whether adjacent elements are equal.
Below is the implementation of this approach.

// Java program to find union of two

// sorted arrays (Handling Duplicates)

class FindUnion {

static void UnionArray( int arr1[],

int arr2[])

{

// Taking max element present in either array

int m = arr1[arr1.length - 1 ];

int n = arr2[arr2.length - 1 ];

int ans = 0 ;

if (m > n) {

ans = m;

}

else

ans = n;

// Finding elements from 1st array

// (non duplicates only). Using

// another array for storing union

// elements of both arrays

// Assuming max element present

// in array is not more than 10^7

int newtable[] = new int [ans + 1 ];

// First element is always

// present in final answer

System.out.print(arr1[ 0 ] + " " );

// Incrementing the First element's count

// in it's corresponding index in newtable

++newtable[arr1[ 0 ]];

// Starting traversing the first

// array from 1st index till last

for ( int i = 1 ; i < arr1.length; i++) {

// Checking whether current element

// is not equal to it's previous element

if (arr1[i] != arr1[i - 1 ]) {

System.out.print(arr1[i] + " " );

++newtable[arr1[i]];

}

}

// Finding only non common

// elements from 2nd array

for ( int j = 0 ; j < arr2.length; j++) {

// By checking whether it's already

// present in newtable or not

if (newtable[arr2[j]] == 0 ) {

System.out.print(arr2[j] + " " );

++newtable[arr2[j]];

}

}

}

// Driver Code

public static void main(String args[])

{

int arr1[] = { 1 , 2 , 2 , 2 , 3 };

int arr2[] = { 2 , 3 , 4 , 5 };

UnionArray(arr1, arr2);

}

}

Intersection of arrays arr1[] and arr2[]

To find intersection of 2 sorted arrays, follow the below approach :

  1. Use two index variables i and j, initial values i = 0, j = 0
  2. If arr1[i] is smaller than arr2[j] then increment i.
  3. If arr1[i] is greater than arr2[j] then increment j.
  4. If both are same then print any of them and increment both i and j.

Below is the implementation of the above approach :

// C++ program to find intersection of

// two sorted arrays

#include <bits/stdc++.h>

using namespace std;

/* Function prints Intersection of arr1[] and arr2[]

m is the number of elements in arr1[]

n is the number of elements in arr2[] */

void printIntersection( int arr1[], int arr2[], int m, int n)

{

int i = 0, j = 0;

while (i < m && j < n) {

if (arr1[i] < arr2[j])

i++;

else if (arr2[j] < arr1[i])

j++;

else /* if arr1[i] == arr2[j] */

{

cout << arr2[j] << " " ;

i++;

j++;

}

}

}

/* Driver program to test above function */

int main()

{

int arr1[] = { 1, 2, 4, 5, 6 };

int arr2[] = { 2, 3, 5, 7 };

int m = sizeof (arr1) / sizeof (arr1[0]);

int n = sizeof (arr2) / sizeof (arr2[0]);

// Function calling

printIntersection(arr1, arr2, m, n);

return 0;

}

Output:

2 5

Time Complexity : O(m + n)