Python program to print common elements in three arrays

Software Development
1

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

Examples:

Input:
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

Input:
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.

  • If x, y and z are same, we can simply print any of them as common element and move ahead in all three arrays.
  • Else If x < y, we can move ahead in ar1 as x cannot be a common element.
  • Else If x > z and y > z), we can simply move ahead in ar3 as z cannot be a common element.

Below is the implementation of the above approach:

  • Python

# Python function to print common elements in three sorted arrays

def findCommon(ar1, ar2, ar3, n1, n2, n3):

# Initialize starting indexes for ar1[], ar2[] and ar3[]

i, j, k = 0 , 0 , 0

# Iterate through three arrays while all arrays have elements

while (i < n1 and j < n2 and k< n3):

# If x = y and y = z, print any of them and move ahead

# in all arrays

if (ar1[i] = = ar2[j] and ar2[j] = = ar3[k]):

print ar1[i],

i + = 1

j + = 1

k + = 1

# x < y

elif ar1[i] < ar2[j]:

i + = 1

# y < z

elif ar2[j] < ar3[k]:

j + = 1

# We reach here when x > y and z < y, i.e., z is smallest

else :

k + = 1

# Driver program to check above function

ar1 = [ 1 , 5 , 10 , 20 , 40 , 80 ]

ar2 = [ 6 , 7 , 20 , 80 , 100 ]

ar3 = [ 3 , 4 , 15 , 20 , 30 , 70 , 80 , 120 ]

n1 = len (ar1)

n2 = len (ar2)

n3 = len (ar3)

print "Common elements are" ,

findCommon(ar1, ar2, ar3, n1, n2, n3)

Output

Common Elements are 20 80

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