# Python Program for Count pairs with given sum

• Last Updated : 30 Dec, 2021

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`
Output
`Count 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 –

1. Create a map to store frequency of each number in the array. (Single traversal is required)
2. 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.
3. 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`
Output
`Count of pairs is 3`

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