Find common elements in three sorted arrays

Given three arrays sorted in non-decreasing order, print all common elements in these arrays.

Examples:

ar1[] = {1, 5, 10, 20, 40, 80}
ar2[] = {6, 7, 20, 80, 100}
ar3[] = {3, 4, 15, 20, 30, 70, 80, 120}
Output: 20, 80

ar1[] = {1, 5, 5}
ar2[] = {3, 4, 5, 5, 10}
ar3[] = {5, 5, 10, 20}
Outptu: 5, 5

A simple solution is to first find intersection of two arrays and store the intersection in a temporary array, then find the intersection of third array and temporary array. Time complexity of this solution is O(n1 + n2 + n3) where n1, n2 and n3 are sizes of ar1[], ar2[] and ar3[] respectively.

The above solution requires extra space and two loops, we can find the common elements using a single loop and without extra space. The idea is similar to intersection of two arrays. Like two arrays loop, we run a loop and traverse three arrays.
Let the current element traversed in ar1[] be x, in ar2[] be y and in ar3[] be z. We can have following cases inside the loop.
1) If x, y and z are same, we can simply print any of them as common element and move ahead in all three arrays.
2) Else If x < y, we can move ahead in ar1[] as x cannot be a common element 3) Else If y < z, we can move ahead in ar2[] as y cannot be a common element 4) Else (We reach here when x > y and y > z), we can simply move ahead in ar3[] as z cannot be a common element.

Following are implementations of the above idea.

• C++
• Python

// C++ program to print common elements in three arrays #include <iostream> using namespace std;   // This function prints common elements in ar1 int findCommon(int ar1[], int ar2[], int ar3[], int n1, int n2, int n3) {     // Initialize starting indexes for ar1[], ar2[] and ar3[]     int i = 0, j = 0, k = 0;       // Iterate through three arrays while all arrays have elements     while (i < n1 && j < n2 && k < n3)     {          // If x = y and y = z, print any of them and move ahead          // in all arrays          if (ar1[i] == ar2[j] && ar2[j] == ar3[k])          {   cout << ar1[i] << " ";   i++; j++; k++; }            // x < y          else if (ar1[i] < ar2[j])              i++;            // y < z          else if (ar2[j] < ar3[k])              j++;            // We reach here when x > y and z < y, i.e., z is smallest          else              k++;     } }   // Driver program to test above function int main() {     int ar1[] = {1, 5, 10, 20, 40, 80};     int ar2[] = {6, 7, 20, 80, 100};     int ar3[] = {3, 4, 15, 20, 30, 70, 80, 120};     int n1 = sizeof(ar1)/sizeof(ar1[0]);     int n2 = sizeof(ar2)/sizeof(ar2[0]);     int n3 = sizeof(ar3)/sizeof(ar3[0]);       cout << "Common Elements are ";     findCommon(ar1, ar2, ar3, n1, n2, n3);     return 0; }

Output:

Common Elements are 20 80

Time complexity of the above solution is O(n1 + n2 + n3). In worst case, the largest sized array may have all small elements and middle sized array has all middle elements.