Binary TreesBinary Trees36

  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Postorder Traversal of a Binary Tree Using Recursion
  4. 4Postorder Traversal of a Binary Tree using Iteration
  5. 5Level Order Traversal of a Binary Tree using Recursion
  6. 6Level Order Traversal of a Binary Tree using Iteration
  7. 7Reverse Level Order Traversal of a Binary Tree using Iteration
  8. 8Reverse Level Order Traversal of a Binary Tree using Recursion
  9. 9Find Height of a Binary Tree
  10. 10Find Diameter of a Binary Tree
  11. 11Find Mirror of a Binary Tree - Todo
  12. 12Inorder Traversal of a Binary Tree using Recursion
  13. 13Inorder Traversal of a Binary Tree using Iteration
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree

Two Sum Problem
Brute Force Approach



Problem Statement

Given an array of integers nums and a target number, your task is to find the indices of two numbers in the array that add up exactly to the target.

If no such pair exists, return an empty result.

Examples

Input ArrayTargetOutputDescription
[2, 7, 11, 15]9[0, 1]2 + 7 = 9
[3, 2, 4]6[1, 2]2 + 4 = 6
[3, 3]6[0, 1]3 + 3 = 6 (duplicate numbers allowed)
[1, 2, 3, 4, 5]10[]No two numbers add up to 10
[]5[]Empty array, no elements to check
[5]5[]Only one element, cannot form a pair

Solution

The brute force approach to solving the Two Sum problem is based on checking every possible pair of elements in the array to see if their sum equals the given target.

We start from the first element and for each element, we check all other elements that come after it in the array. For each pair, we calculate their sum and compare it to the target.

If we find such a pair, we return the indices of those two numbers. Since we’re guaranteed to have exactly one solution in valid cases, we can return as soon as we find the first match.

Different Scenarios Explained:

  • Normal Case: For an array like [2, 7, 11, 15] and target 9, the pair 2 + 7 gives 9, so we return [0, 1].
  • Duplicates Allowed: If an array has two identical numbers like [3, 3] and target is 6, we can still use both numbers as long as they are at different indices. So, the result is [0, 1].
  • No Valid Pair: If no two elements add up to the target, like in [1, 2, 3, 4, 5] with target 10, we return an empty result [].
  • Edge Case - Empty Array: If the input array is empty [], there are no elements to consider, so the result is [].
  • Edge Case - Single Element: With only one number in the array like [5], we can’t form a pair, so we return [].

Although this brute force method is simple and easy to understand, it is not the most efficient. It checks all possible combinations, resulting in a time complexity of O(n²). However, it's perfect for learning and understanding how the basic logic works.

Algorithm Steps

  1. Given an array of numbers nums and a target.
  2. For each element at index i from 0 to n-2 (where n is the array length), iterate over every element with index j from i+1 to n-1.
  3. For each pair (i, j), calculate the sum of nums[i] and nums[j].
  4. If the sum equals the target, return the indices [i, j].

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
class Solution:
    def twoSum(self, nums: List[int], target: int) -> List[int]:
        for i in range(len(nums) - 1):
            for j in range(i + 1, len(nums)):
                if nums[i] + nums[j] == target:
                    return [i, j]

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)If the required pair is found in the very first iteration.
Average CaseO(n^2)Each element is compared with every other element after it, resulting in a nested loop.
Average CaseO(n^2)In the worst case, all pairs must be checked before a match is found or concluded none exists.

Space Complexity

O(1)

Explanation: No additional data structures are used beyond a few variables.



Welcome to ProgramGuru

Sign up to start your journey with us

Support ProgramGuru.org

Mention your name, and programguru.org in the message. Your name shall be displayed in the sponsers list.

PayPal

UPI

PhonePe QR

MALLIKARJUNA M