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

Find Second Largest in Array using Loop - Optimal Solution

Arrays

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace Detailed Exmpl

Problem Statement❯

Given an array of integers, your task is to find the second largest element in the array.

  • The second largest element is the value that is smaller than the maximum but larger than all other elements in the array.
  • If there is no valid second largest (like in case of duplicate values or very small arrays), return -1.

Examples❯

Input Array Second Largest Description
[10, 20, 30, 40, 50] 40 50 is the largest, 40 is the next highestVisualization
[5, 1, 5, 3] 3 5 is the largest, 3 is the next distinct largestVisualization
[8, 8, 8] -1 All elements are the same, no second largestVisualization
[100] -1 Only one element, so no second largestVisualization
[20, 20, 10] 10 20 is the largest, 10 is the next distinctVisualization
[1, 2] 1 2 is the largest, 1 is the second largestVisualization
[7, 7, 7, 3] 3 7 is the largest, 3 is the next distinct valueVisualization
[] -1 Empty array, so no elements to compareVisualization
[9, 9] -1 Only one unique element presentVisualization

Visualization Player

Solution❯

To find the second largest number in an array, we need to identify two values: the largest and the one that is just smaller than the largest. But it’s not as simple as sorting the array or removing duplicates — we want an optimal solution that works in a single pass.

We begin by checking if the array is empty or contains fewer than two unique elements. If so, there can be no second largest number, and we return -1.

Next, we traverse the array using two variables:

  • max_val – to keep track of the current largest value seen so far
  • second_max – to keep track of the best candidate for the second largest

As we go through each element:

  • If we find a number greater than max_val, then this number becomes the new max_val, and the old max_val becomes the new second_max.
  • If the number is smaller than max_val but greater than second_max, we update second_max.
  • We make sure not to count the same number twice. For example, in [5, 5, 5], the second largest should be -1, not 5 again.

This approach covers different cases:

  • Normal case: In arrays like [10, 20, 30], 30 is the largest, and 20 is the second largest.
  • Duplicates: In [5, 5, 3], the largest is 5, and 3 is the next distinct largest.
  • Single element: Arrays like [100] don’t have enough data for a second largest.
  • All equal elements: In [8, 8, 8], there’s no second distinct value.
  • Empty array: No values mean no second largest.

This method ensures we find the second largest in just one loop — making it fast, memory-efficient, and easy to understand once you break it down by logic.

Algorithm Steps❯

  1. Given an array of numbers arr.
  2. If there are less than two unique elements in the array, then return -1.
  3. Initialize max_val and second_max to -Infinity.
  4. Iterate through each element in the array.
  5. If the current element is greater than max_val, update second_max to max_val, and then update max_val.
  6. Else if the current element is greater than second_max and not equal to max_val, update second_max.
  7. After the loop, return second_max.

Code

Python
JavaScript
Java
C++
C
def find_second_largest(arr):
    if len(set(arr)) < 2:
        return -1
    max_val = float('-inf')
    second_max = float('-inf')
    for num in arr:
        if num > max_val:
            second_max = max_val
            max_val = num
        elif num > second_max and num != max_val:
            second_max = num
    return second_max

# Sample Input
arr = [30, 20, 10, 50, 60, 40]
print("Second Largest:", find_second_largest(arr))

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)The algorithm always traverses the entire array once to ensure it captures both the largest and second largest elements.
Average CaseO(n)Regardless of the input distribution, the algorithm iterates through all elements to maintain max and second max values.
Worst CaseO(n)Even in the worst case where the second largest is the last element, the algorithm still requires a full pass through the array.

Space Complexity❯

O(1)

Explanation: The algorithm uses only a fixed number of variables (max_val and second_max) and does not require any extra space that grows with input size.

Detailed Step by Step Example❯

Let's find the second largest number in the array using a loop.

{ "array": [30,20,10,50,60,40], "showIndices": true }

Initialize max = -Infinity and secondMax = -Infinity.

Check index 0

Current element is 30. Compare with max = -Infinity and secondMax = -Infinity.

30 is greater than current max. Update: secondMax = -Infinity, max = 30.

{ "array": [30,20,10,50,60,40], "showIndices": true, "highlightIndices": [0], "labels": {"0":"i"} }
{ "array": [0,30,null], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }

Check index 1

Current element is 20. Compare with max = 30 and secondMax = -Infinity.

20 is greater than current secondMax and not equal to max. Update: secondMax = 20.

{ "array": [30,20,10,50,60,40], "showIndices": true, "highlightIndices": [1], "labels": {"1":"i"} }
{ "array": [0,30,20], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }

Check index 2

Current element is 10. Compare with max = 30 and secondMax = 20.

No update required.

{ "array": [30,20,10,50,60,40], "showIndices": true, "highlightIndices": [2], "labels": {"2":"i"} }
{ "array": [0,30,20], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }

Check index 3

Current element is 50. Compare with max = 30 and secondMax = 20.

50 is greater than current max. Update: secondMax = 30, max = 50.

{ "array": [30,20,10,50,60,40], "showIndices": true, "highlightIndices": [3], "labels": {"3":"i"} }
{ "array": [0,50,30], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }

Check index 4

Current element is 60. Compare with max = 50 and secondMax = 30.

60 is greater than current max. Update: secondMax = 50, max = 60.

{ "array": [30,20,10,50,60,40], "showIndices": true, "highlightIndices": [4], "labels": {"4":"i"} }
{ "array": [0,60,50], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }

Check index 5

Current element is 40. Compare with max = 60 and secondMax = 50.

No update required.

{ "array": [30,20,10,50,60,40], "showIndices": true, "highlightIndices": [5], "labels": {"5":"i"} }
{ "array": [0,60,50], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }

Final Result:

Second Largest Element = 50

{ "array": [30,20,10,50,60,40], "showIndices": true, "labels": { "4": "max", "3": "secondMax" } }
{ "array": [0,60,50], "showIndices": false, "highlightIndicesGreen": [1, 2], "emptyCompIndices": [0], "labels": { "1": "max", "2": "secondMax" } }