Program to create data structure to check pair sum is same as value in Python

Sometimes we need to build a data structure that efficiently checks if any two elements sum to a target value. This problem requires designing a class with two methods: add() to insert values and find() to check pair sums.

Problem Statement

We need to create a data structure with two operations ?

• add(val) − adds the value to the data structure
• find(val) − checks whether there are two elements whose sum equals val

The key requirement is efficiency − we should be able to answer queries quickly without searching through all numbers every time.

Example Scenario

If we add numbers 6, 14, 3, 8, 11, 15 and then query ?

• find(9) returns True (6 + 3 = 9)
• find(11) returns True (3 + 8 = 11)
• find(15) returns False (15 exists but no two numbers sum to 15)

Solution Approach

We use two sets to track numbers efficiently ?

• nums − stores unique numbers
• multiple − tracks numbers that appear more than once

This allows us to handle cases where the same number appears twice (like finding 6 + 6 = 12).

Implementation

class PairSumChecker:
    def __init__(self):
        self.nums = set()
        self.multiple = set()

    def add(self, val):
        if val in self.nums:
            self.multiple.add(val)
        else:
            self.nums.add(val)

    def find(self, val):
        for n in self.nums:
            if n + n == val:
                return n in self.multiple
            elif val - n in self.nums:
                return True
        return False

# Test the implementation
obj = PairSumChecker()
obj.add(6)
obj.add(14)
obj.add(3)
obj.add(8)
obj.add(11)
obj.add(15)

print(obj.find(9))   # 6 + 3 = 9
print(obj.find(11))  # 3 + 8 = 11
print(obj.find(15))  # No pair sums to 15

True
True
False

How It Works

Adding Numbers:

• If the number already exists in nums, add it to multiple
• Otherwise, add it to nums

Finding Pairs:

• For each number n, check if val - n exists in nums
• Special case: if n + n = val, ensure n appears multiple times

Example with Duplicates

obj = PairSumChecker()
obj.add(5)
obj.add(5)  # Now 5 appears twice
obj.add(10)

print(obj.find(10))  # 5 + 5 = 10, True
print(obj.find(15))  # 5 + 10 = 15, True
print(obj.find(20))  # No pair sums to 20, False

True
True
False

Time Complexity

• add(val): O(1) average case for set operations
• find(val): O(n) where n is the number of unique elements

Conclusion

This solution uses two sets to efficiently track numbers and their duplicates. The find() method checks all possible pairs by iterating through stored numbers and looking up their complements in constant time.