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}
Output: 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.

JAVA Programmming

// Java program to find common elements in three arrays
class FindCommon
{
    // This function prints common elements in ar1
    void findCommon(int ar1[], int ar2[], int ar3[])
    {
        // 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 < ar1.length && j < ar2.length && k < ar3.length)
        {
             // 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])
             {   System.out.print(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 code to test above
    public static void main(String args[])
    {
        FindCommon ob = new FindCommon();
 
        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};
 
        System.out.print("Common elements are ");
        ob.findCommon(ar1, ar2, ar3);
    }
}
/*This code is contributed by Rajat Mishra */