Yandex

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

GraphsGraphs46

  1. 1Breadth-First Search in Graphs
  2. 2Depth-First Search in Graphs
  3. 3Number of Provinces in an Undirected Graph
  4. 4Connected Components in a Matrix
  5. 5Rotten Oranges Problem - BFS in Matrix
  6. 6Flood Fill Algorithm - Graph Based
  7. 7Detect Cycle in an Undirected Graph using DFS
  8. 8Detect Cycle in an Undirected Graph using BFS
  9. 9Distance of Nearest Cell Having 1 - Grid BFS
  10. 10Surrounded Regions in Matrix using Graph Traversal
  11. 11Number of Enclaves in Grid
  12. 12Word Ladder - Shortest Transformation using Graph
  13. 13Word Ladder II - All Shortest Transformation Sequences
  14. 14Number of Distinct Islands using DFS
  15. 15Check if a Graph is Bipartite using DFS
  16. 16Topological Sort Using DFS
  17. 17Topological Sort using Kahn's Algorithm
  18. 18Cycle Detection in Directed Graph using BFS
  19. 19Course Schedule - Task Ordering with Prerequisites
  20. 20Course Schedule 2 - Task Ordering Using Topological Sort
  21. 21Find Eventual Safe States in a Directed Graph
  22. 22Alien Dictionary Character Order
  23. 23Shortest Path in Undirected Graph with Unit Distance
  24. 24Shortest Path in DAG using Topological Sort
  25. 25Dijkstra's Algorithm Using Set - Shortest Path in Graph
  26. 26Dijkstra’s Algorithm Using Priority Queue
  27. 27Shortest Distance in a Binary Maze using BFS
  28. 28Path With Minimum Effort in Grid using Graphs
  29. 29Cheapest Flights Within K Stops - Graph Problem
  30. 30Number of Ways to Reach Destination in Shortest Time - Graph Problem
  31. 31Minimum Multiplications to Reach End - Graph BFS
  32. 32Bellman-Ford Algorithm for Shortest Paths
  33. 33Floyd Warshall Algorithm for All-Pairs Shortest Path
  34. 34Find the City With the Fewest Reachable Neighbours
  35. 35Minimum Spanning Tree in Graphs
  36. 36Prim's Algorithm for Minimum Spanning Tree
  37. 37Disjoint Set (Union-Find) with Union by Rank and Path Compression
  38. 38Kruskal's Algorithm - Minimum Spanning Tree
  39. 39Minimum Operations to Make Network Connected
  40. 40Most Stones Removed with Same Row or Column
  41. 41Accounts Merge Problem using Disjoint Set Union
  42. 42Number of Islands II - Online Queries using DSU
  43. 43Making a Large Island Using DSU
  44. 44Bridges in Graph using Tarjan's Algorithm
  45. 45Articulation Points in Graphs
  46. 46Strongly Connected Components using Kosaraju's Algorithm

TriesTries1

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.

  • Each input will have exactly one solution.
  • You may not use the same element twice.

If no such pair exists, return an empty result.

Examples

Input Array Target Output Description
[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.
Worst 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.



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