Python Program for Number of pairs with maximum sum

Write a python program for a given array arr[], count number of pairs arr[i], arr[j] such that arr[i] + arr[j] is maximum and i < j.

Example:

Input : arr[] = {1, 1, 1, 2, 2, 2}
Output: 3
Explanation: The maximum possible pair sum where i<j is 4, which is given by 3 pairs, so the answer is 3 the pairs are (2, 2), (2, 2) and (2, 2)

Input: arr[] = {1, 4, 3, 3, 5, 1}
Output: 1
Explanation: The pair 4, 5 yields the maximum sum i.e, 9 which is given by 1 pair only

Python program for Number of pairs with maximum sum using Naive Approach:

Traverse a loop i from 0 to n, i.e length of the array and another loop j from i+1 to n to find all possible pairs with i<j. Find the pair with the maximum possible sum, again traverse for all pairs and keep the count of the number of pairs which gives the pair sum equal to maximum .

Below is the Implementation of the above Approach:

Python3

# Python program to count pairs with
# maximum sum


def _sum(a, n):

    # traverse through all the pairs
    maxSum = -9999999
    for i in range(n):
        for j in range(n):
            maxSum = max(maxSum, a[i] + a[j])

    # traverse through all pairs and
    # keep a count of the number
    # of maximum pairs
    c = 0
    for i in range(n):
        for j in range(i+1, n):
            if a[i] + a[j] == maxSum:
                c += 1
    return c


# driver code
array = [1, 1, 1, 2, 2, 2]
n = len(array)
print(_sum(array, n))

# This code is contributed by "Abhishek Sharma 44"

Output

3

Time complexity: O(n2)
Auxiliary Space: O(1)

Efficient Method:

• Maximum element is always part of solution.
• If maximum element appears more than once, then result is maxCount * (maxCount – 1)/2. We basically need to choose 2 elements from maxCount (^maxCountC2).
• If maximum element appears once, then result is equal to count of second maximum element. We can form a pair with every second max and max.

Below is the Implementation of the above Approach:

Python3

# Python 3 program to count
# pairs with maximum sum.
import sys

# Function to find the number
# of maximum pair sums


def sum(a, n):

    # Find maximum and second maximum elements.
    # Also find their counts.
    maxVal = a[0]
    maxCount = 1
    secondMax = sys.maxsize

    for i in range(1, n):

        if (a[i] == maxVal):
            maxCount += 1

        elif (a[i] > maxVal):
            secondMax = maxVal
            secondMaxCount = maxCount
            maxVal = a[i]
            maxCount = 1

        elif (a[i] == secondMax):
            secondMax = a[i]
            secondMaxCount += 1

        elif (a[i] > secondMax):
            secondMax = a[i]
            secondMaxCount = 1

    # If maximum element appears more than once.
    if (maxCount > 1):
        return maxCount * (maxCount - 1) / 2

    # If maximum element appears only once.
    return secondMaxCount


# Driver Code
array = [1, 1, 1, 2, 2, 2, 3]
n = len(array)
print(sum(array, n))


# This code is contributed by Smitha Dinesh Semwal

Output

3

Time complexity: O(n)
Auxiliary Space: O(1)

Please refer complete article on Number of pairs with maximum sum for more details!