Binary TreesBinary Trees36
❯
  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Inorder Traversal of a Binary Tree using Recursion
  4. 4Inorder Traversal of a Binary Tree using Iteration
  5. 5Postorder Traversal of a Binary Tree Using Recursion
  6. 6Postorder Traversal of a Binary Tree using Iteration
  7. 7Level Order Traversal of a Binary Tree using Recursion
  8. 8Level Order Traversal of a Binary Tree using Iteration
  9. 9Reverse Level Order Traversal of a Binary Tree using Iteration
  10. 10Reverse Level Order Traversal of a Binary Tree using Recursion
  11. 11Find Height of a Binary Tree
  12. 12Find Diameter of a Binary Tree
  13. 13Find Mirror of a Binary Tree
  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

Insert Word in Trie

Tries

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given a Trie (prefix tree), insert a word into it. A Trie is used to efficiently store and retrieve strings, especially useful for prefix-based searches. The objective is to add the given word into the Trie character by character such that each character leads to a node, and the final character marks the end of the word.

Examples❯

Case Input Trie Word to Insert Expected Result
Normal Case Trie with 'cat', 'car'.
'cart' Adds 't' after 'car' branch and mark 't' as end of word. Visualization
Prefix Exists Trie with 'apple'
'app' 'app' already exists as a prefix. Mark 'p' as end of word; no need to add new nodes. Visualization
Empty Trie Empty
'dog' Creates a new path: 'd' → 'o' → 'g' Visualization
Empty Word Trie with 'cat'
'' No changes; nothing is inserted Visualization
Word Already Exists Trie with 'hello'
'hello' Since the word already exists, nothing has to be done to the trie. Visualization

Visualization Player

Solution❯

To insert a word into a Trie, we follow a step-by-step character-wise traversal:

  • Case 1: Normal Case

    1. Suppose the Trie already contains some words like 'cat' and 'car'.
    2. When we try to insert 'cart', we follow the path 'c' → 'a' → 'r'.
    3. Since 'r' exists, we don't create it again. Now we see 't' is not present as a child of 'r', so we create a new node for 't'.
    4. And mark 't' as the end of the word.

  • Case 2: Prefix Exists

    1. If the Trie already has 'apple' and we want to insert 'app'
    2. we follow 'a' → 'p' → 'p'. Since these nodes already exist, we don’t need to create them again.
    3. But since 'app' ends here, we mark the current 'p' as the end of a valid word (it may not have been marked earlier).

  • Case 3: Empty Trie

    1. When inserting into an empty Trie (i.e., it has only the root node), we create a new child node for each character in the word. For 'dog',
    2. we create 'd',
    3. then 'o',
    4. then 'g',
    5. marking 'g' as the end of the word.
  • Case 4: Empty Word – If the input word is an empty string, there’s nothing to insert. No operation is performed, and the Trie remains unchanged.
  • Case 5: Word Already Exists – If the word to insert is already in the Trie, the traversal simply follows the existing path. We just ensure that the last character is marked as the end of a valid word. This helps if the word was previously just a prefix and not marked as a complete word.

Algorithm Steps❯

  1. Initialize a pointer to the root node of the Trie.
  2. Iterate through each character of the input word:
    1. If the character does not exist in the current node's children, create a new node for it.
    2. Move the pointer to this child node.
  3. After processing all characters, mark the last node as the end of a valid word.

Code

Python
Java
JavaScript
C
C++
class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False

class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_end_of_word = True

# Example usage:
trie = Trie()
trie.insert("code")
trie.insert("coder")
trie.insert("coding")
print(trie.root.children)

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)In the best case, the algorithm still needs to traverse all n characters of the input word to insert it into the Trie, even if all nodes already exist.
Average CaseO(n)On average, the algorithm traverses and possibly creates n new nodes for a word of length n. Each character requires a constant-time operation.
Worst CaseO(n)In the worst case, none of the characters exist in the Trie, so the algorithm creates a new node for each of the n characters in the input word.

Space Complexity❯

O(n)

Explanation: In the worst case, the algorithm adds n new nodes for a word of length n, resulting in linear space usage. No additional auxiliary space is used.