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

Maximum Nesting Depth of Parentheses

Strings

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given a valid parentheses string s, your task is to find the maximum nesting depth of parentheses in the string.

  • The nesting depth of a string is the maximum number of parentheses that are open at the same time.
  • Only the characters ( and ) affect the nesting depth. Other characters are ignored.

Return 0 if the string is empty or contains no parentheses.

Examples❯

Input String Maximum Nesting Depth Description
"(1+(2*3)+((8)/4))+1" 3 Deepest level is ((8)/4) → depth 3
"(1)+((2))+(((3)))" 3 Increasing levels of nested brackets
"1+(2*3)/(2-1)" 1 Only one pair of parentheses at a time
"1+2-3" 0 No parentheses present
"" 0 Empty string returns 0
"(()(()))" 3 Nested parentheses with maximum 3 levels
(a+(b*(c+(d)))) 4 Characters ignored, structure leads to depth 4

Visualization Player

Solution❯

To find the maximum nesting depth of parentheses in a string, we need to understand what 'nesting' really means. It simply refers to how many parentheses are open at the same time at any point in the string.

Let's say we see an opening bracket ( — we increase our current depth by 1. When we see a closing bracket ), we decrease the depth by 1. The maximum value that the current depth ever reaches is the maximum nesting depth.

For example, in the string (1+(2*3)+((8)/4))+1, when we reach ((8)/4), we have three ( brackets opened before any are closed. So, the nesting depth there is 3, and that’s the deepest it ever gets.

If the string is something simple like 1+2 or abc, there are no brackets, so the nesting depth is just 0.

Even in more complex-looking strings like (a+(b*(c+(d)))), we ignore all characters except the brackets. The string reaches a depth of 4 due to four levels of parentheses before they start closing.

If the string is empty, or contains only characters without any ( or ), then the answer is also 0 — there's no nesting at all.

What's great about this approach is that we don't need a stack. We just track how many parentheses are open as we scan left to right, and keep updating the maximum depth reached. It’s very efficient and runs in O(n) time.

Algorithm Steps❯

  1. Initialize two variables: depth = 0 and maxDepth = 0.
  2. Loop through each character ch in the string s.
  3. If ch == '(', increment depth and update maxDepth if depth > maxDepth.
  4. If ch == ')', decrement depth.
  5. Return maxDepth at the end.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
def max_depth(s):
    depth = 0
    max_depth = 0
    for ch in s:
        if ch == '(':
            depth += 1               # Increase current depth
            max_depth = max(max_depth, depth)  # Update max if needed
        elif ch == ')':
            depth -= 1               # Decrease depth on closing bracket
    return max_depth

# Sample input
print(max_depth("(1+(2*3)+((8)/4))+1"))  # Output: 3

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)We must scan every character once, even if there are few or no parentheses.
Average CaseO(n)Each character is checked, and counters are updated accordingly.
Worst CaseO(n)Even with maximum depth and complexity, each character is visited once.

Space Complexity❯

O(1)

Explanation: Only a few counters are used. No extra data structures like stacks are required.