Python Program for Count pairs with given sum
Last Updated :
15 Feb, 2023
Given an array of integers, and a number 'sum', find the number of pairs of integers in the array whose sum is equal to 'sum'.
Examples:
Input : arr[] = {1, 5, 7, -1},
sum = 6
Output : 2
Pairs with sum 6 are (1, 5) and (7, -1)
Input : arr[] = {1, 5, 7, -1, 5},
sum = 6
Output : 3
Pairs with sum 6 are (1, 5), (7, -1) &
(1, 5)
Input : arr[] = {1, 1, 1, 1},
sum = 2
Output : 6
There are 3! pairs with sum 2.
Input : arr[] = {10, 12, 10, 15, -1, 7, 6,
5, 4, 2, 1, 1, 1},
sum = 11
Output : 9
Expected time complexity O(n)
Naive Solution - A simple solution is to traverse each element and check if there's another number in the array which can be added to it to give sum.
Python3
# Python3 implementation of simple method
# to find count of pairs with given sum.
# Returns number of pairs in arr[0..n-1]
# with sum equal to 'sum'
def getPairsCount(arr, n, sum):
count = 0 # Initialize result
# Consider all possible pairs
# and check their sums
for i in range(0, n):
for j in range(i + 1, n):
if arr[i] + arr[j] == sum:
count += 1
return count
# Driver function
arr = [1, 5, 7, -1, 5]
n = len(arr)
sum = 6
print("Count of pairs is",
getPairsCount(arr, n, sum))
# This code is contributed by Smitha Dinesh Semwal
OutputCount of pairs is 3
Time Complexity: O(n2)
Auxiliary Space: O(1)
Efficient solution -
A better solution is possible in O(n) time. Below is the Algorithm -
- Create a map to store frequency of each number in the array. (Single traversal is required)
- In the next traversal, for every element check if it can be combined with any other element (other than itself!) to give the desired sum. Increment the counter accordingly.
- After completion of second traversal, we'd have twice the required value stored in counter because every pair is counted two times. Hence divide count by 2 and return.
Below is the implementation of above idea :
Python3
# Python 3 implementation of simple method
# to find count of pairs with given sum.
import sys
# Returns number of pairs in arr[0..n-1]
# with sum equal to 'sum'
def getPairsCount(arr, n, sum):
m = [0] * 1000
# Store counts of all elements in map m
for i in range(0, n):
m[arr[i]] += 1
twice_count = 0
# Iterate through each element and increment
# the count (Notice that every pair is
# counted twice)
for i in range(0, n):
twice_count += m[sum - arr[i]]
# if (arr[i], arr[i]) pair satisfies the
# condition, then we need to ensure that
# the count is decreased by one such
# that the (arr[i], arr[i]) pair is not
# considered
if (sum - arr[i] == arr[i]):
twice_count -= 1
# return the half of twice_count
return int(twice_count / 2)
# Driver function
arr = [1, 5, 7, -1, 5]
n = len(arr)
sum = 6
print("Count of pairs is", getPairsCount(arr,
n, sum))
# This code is contributed by
# Smitha Dinesh Semwal
OutputCount of pairs is 3
Time Complexity: O(n)
Auxiliary Space: O(n)
The extra space is used to store the elements in the map.
Please refer complete article on Count pairs with given sum for more details!
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