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

Count Number of Substrings

Strings

Contents

ProblemExamplesSolutionAlgorithmCodeTimeSpace

Problem Statement❯

Given a string of length n, your task is to count the total number of substrings present in it.

A substring is a contiguous part of the string. For example, in the string "abc", the substrings are: "a", "b", "c", "ab", "bc", and "abc".

Note: Do not confuse substrings with subsequences. A substring maintains the original order and continuity of characters, whereas a subsequence can skip characters.

If the input string is empty, the number of substrings is 0.

Examples❯

Input String Length (n) Total Substrings Description
"abc" 3 6 Substrings: a, b, c, ab, bc, abc
"abcd" 4 10 Total = 4 + 3 + 2 + 1 = 10 substrings
"a" 1 1 Only one character, one substring
"aa" 2 3 Substrings: a, a, aa
"" 0 0 No characters, so no substrings

Solution❯

To count the number of substrings in a given string, we need to understand how substrings work.

What Is a Substring?

A substring is any sequence of characters that appears contiguously in the original string. For example, in the word "cat", the substrings include "c", "a", "t", "ca", "at", and "cat".

How to Count Them

For a string of length n, the total number of substrings can be found using a simple formula: n * (n + 1) / 2.

This formula works because:

  • From index 0, you can make n substrings
  • From index 1, you can make n - 1 substrings
  • From index 2, you can make n - 2 substrings
  • ... and so on, down to 1
Add them up and you get: n + (n-1) + (n-2) + ... + 1 = n * (n + 1) / 2.

Case Discussion

  • Normal Case: If the input is "abc", it has 3 characters, so it has 3 * 4 / 2 = 6 substrings.
  • Single Character: If the input is "a", there's only 1 substring: "a".
  • All Characters Same: If the input is "aaa", substrings can still overlap: "a", "a", "a", "aa", "aa", and "aaa" — still 6 substrings in total.
  • Empty String: If the input string is empty (length 0), there are no substrings, so the answer is 0.

This formula gives us the count only—not the actual substrings. It’s very efficient because we don’t have to generate or store anything to get the result. The time complexity is O(1).

Algorithm Steps❯

  1. Find the length of the input string n.
  2. Apply the formula n * (n + 1) / 2.
  3. Return the result as the total number of substrings.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
def count_substrings(s):
    n = len(s)
    # Total substrings = n * (n + 1) // 2
    return n * (n + 1) // 2

# Example
s = "abc"
print("Total substrings:", count_substrings(s))

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(1)Only a single formula is evaluated regardless of string length.
Average CaseO(1)Computation does not depend on content, just length.
Worst CaseO(1)Even for the largest strings, only the length is used in a constant time operation.

Space Complexity❯

O(1)

Explanation: The algorithm uses a constant amount of memory for computation.