Introduction The 2 Sum problem is a fundamental algorithm challenge in computer science. Given an array of integers and a target sum, the goal is to find two numbers in the array that sum up to the given target. This problem is often encountered in coding interviews and has practical applications in various domains such as financial analysis, data mining, and image processing. Brute Force Approach The most straightforward approach to solving the 2 Sum problem is to iterate through all possible pairs of numbers in the array and check if their sum equals the target. This brute force approach has a time complexity of O(n^2), where n is the number of elements in the array. Hash Table Approach A more efficient approach is to use a hash table. The key idea is to store the complement of each number in the array as the key in the hash table. When we encounter a number, we check if its complement is already in the hash table. If it is, then we have found a pair of numbers that sum up to the target. The hash table approach has a time complexity of O(n), where n is the number of elements in the array. Implementation Here’s a sample Python implementation of the 2 Sum problem using the hash table approach:
def two_sum(nums, target):
hashmap = {}
for i, num in enumerate(nums):
complement = target - num
if complement in hashmap:
return [hashmap[complement], i]
hashmap[num] = i
return None
Complexity Analysis
| Approach | Time Complexity | Space Complexity |
|---|---|---|
| Brute Force | O(n^2) | O(1) |
| Hash Table | O(n) | O(n) |
| Conclusion | ||
| Mastering the 2 Sum problem is essential for aspiring programmers. The brute force approach is easy to understand but inefficient. The hash table approach is more efficient and is widely used in real-world applications. By understanding these approaches and their complexities, you can effectively solve this problem in coding interviews and practical scenarios. |
Original source: https://youtube.com/watch?v=q4Y-Gon16D8&si=K7KiAf0M_nxyr-Q4