Python Program to Find a pair with the given difference

Given an unsorted array and a number n, find if there exists a pair of elements in the array whose difference is n. 
Examples:

Input: arr[] = {5, 20, 3, 2, 50, 80}, n = 78
Output: Pair Found: (2, 80)

Input: arr[] = {90, 70, 20, 80, 50}, n = 45
Output: No Such Pair

The simplest method is to run two loops, the outer loop picks the first element (smaller element) and the inner loop looks for the element picked by outer loop plus n. Time complexity of this method is O(n^2).
We can use sorting and Binary Search to improve time complexity to O(nLogn). The first step is to sort the array in ascending order. Once the array is sorted, traverse the array from left to right, and for each element arr[i], binary search for arr[i] + n in arr[i+1..n-1]. If the element is found, return the pair. 
Both first and second steps take O(nLogn). So overall complexity is O(nLogn). 
The second step of the above algorithm can be improved to O(n). The first step remain same. The idea for second step is take two index variables i and j, initialize them as 0 and 1 respectively. Now run a linear loop. If arr[j] – arr[i] is smaller than n, we need to look for greater arr[j], so increment j. If arr[j] – arr[i] is greater than n, we need to look for greater arr[i], so increment i. Thanks to Aashish Barnwal for suggesting this approach. 
The following code is only for the second step of the algorithm, it assumes that the array is already sorted. 

Python

# Python program to find a pair with the given difference

# The function assumes that the array is sorted
def findPair(arr,n):

    size = len(arr)

    # Initialize positions of two elements
    i,j = 0,1

    # Search for a pair
    while i < size and j < size:

        if i != j and arr[j]-arr[i] == n:
            print "Pair found (",arr[i],",",arr[j],")"
            return True

        elif arr[j] - arr[i] < n:
            j+=1
        else:
            i+=1
    print "No pair found"
    return False

# Driver function to test above function
arr = [1, 8, 30, 40, 100]
n = 60
findPair(arr, n)

# This code is contributed by Devesh Agrawal

Output

Pair found ( 40 , 100 )

Time Complexity: O(n*log(n)) [Sorting is still required as first step], Where n is number of element in given array.

Efficient Approach:  Hashing can also be used to solve this problem. We first create an empty hash table HT. We then traverse in the array and use array elements as hash keys and enter them in HT. While traversing, if the given difference is 0 then we will check if any element is occurring more than one time or not. If n!=0, then we again Traverse the array and look for the value n + arr[i] in HT(hash table) as the difference between n+arr[i] and arr[i] is n.

Below is the code for the above approach.

Python3

# Python program to find a pair with the given difference

def findPair(arr, size, n):

    # Initialising an empty hash table
    mp = {}
    for i in range(size):
        # Using array elements as hash keys
        # and entering them in Hash table.
        if arr[i] in mp.keys():
            mp[arr[i]] += 1
            # For n==0, checking if any element
            # is occurring more than 1 times or not
            if(n == 0 and mp[arr[i]] > 1):
                return True
        else:
            mp[arr[i]] = 1

    # Check if the difference is
    # still 0 with no element
    # occurring more than 1 times
    if(n == 0):
        return False

    for i in range(size):
        # Checking if arr[i]+n is present or not
        if n + arr[i] in mp.keys():
            print("Pair Found: " + "(" + str(arr[i]) + ", " + str(n + arr[i]) + ")")
            return True

    print("No such pair")
    return False

# Driver program to test above function
arr = [ 1, 8, 30, 40, 100 ]
size = len(arr)
n = 60
findPair(arr, size, n)

# This code is contributed by Pushpesh Raj

Output

Pair Found: (40, 100)

Time Complexity: O(n)
Auxiliary Space: O(n) 

Please refer complete article on Find a pair with the given difference for more details!