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 Smallest in Array using Loop - Optimal Algorithm

Problem Statement

Given an array of numbers, your task is to find the second smallest element in the array.

  • The second smallest element is the smallest number that is strictly greater than the minimum value.
  • If the array has fewer than 2 distinct elements, then the second smallest does not exist.

If a second smallest number cannot be found, return -1.

Examples

Input Array Second Smallest Description
[3, 1, 4, 2] 2 1 is the smallest, 2 is the next smallestVisualization
[7, 7, 7, 7] -1 All elements are the same, no second smallestVisualization
[5] -1 Only one element, second smallest doesn't existVisualization
[] -1 Empty array, no elements to compareVisualization
[9, 3, 6, 3, 5] 5 3 is the smallest, 5 is the smallest value strictly greater than 3Visualization
[2, 1] 2 1 is smallest, 2 is second smallestVisualization
[100, 50, 50, 50, 60] 60 50 is smallest, 60 is the next smallest valueVisualization
[5, 4, 3, 2, 1] 2 1 is smallest, 2 is next smallestVisualization

Visualization Player

Solution

To find the second smallest element in an array, we need to track the two smallest distinct values during a single pass through the array.

We begin by assuming that both the min_val (smallest value) and second_min are Infinity. As we loop through the array, we update these variables as follows:

  • If the current number is less than min_val, then we found a new smallest number. So, the previous min_val becomes the new second_min, and we update min_val.
  • If the current number is not equal to min_val but less than second_min, then it becomes our new second smallest number.

This way, we only pass through the array once and always keep track of the two smallest distinct numbers.

Edge Case Handling

  • Empty Array: There are no elements to compare, so we return -1.
  • Only One Element: We can't find a second smallest if there's only one value, so return -1.
  • All Elements Equal: If all numbers are the same, there is no second distinct value, so we return -1.

Why This Approach is Optimal

This solution uses only one pass through the array (O(n) time) and constant space (O(1)), making it optimal in terms of both time and memory. It avoids sorting or using extra space like sets or arrays to find unique values.

By comparing carefully and avoiding duplicates, this approach ensures that only distinct values are considered, which is crucial for finding the second smallest correctly.

Algorithm Steps

  1. Given an array of numbers arr.
  2. Initialize min_val and second_min to Infinity.
  3. Iterate through each element in the array.
  4. If the current element is less than min_val, update second_min to min_val, and then update min_val.
  5. Else if the current element is less than second_min and not equal to min_val, update second_min.
  6. After the loop, return second_min.

Code

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

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

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n)Even in the best case, all elements must be checked at least once to ensure the smallest and second smallest are correctly identified.
Average CaseO(n)The algorithm iterates through the array exactly once, making one comparison per element.
Worst CaseO(n)Regardless of element arrangement, all values must be visited to determine the second smallest accurately.

Space Complexity

O(1)

Explanation: The algorithm uses a constant amount of space, with only two variables needed for tracking smallest and second smallest.

Detailed Step by Step Example

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

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

Initialize min = Infinity and secondMin = Infinity.

Check index 0

Current element is 30. Compare with min = Infinity and secondMin = Infinity.

30 is smaller than current min. Update: secondMin = Infinity, min = 30.

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

Check index 1

Current element is 20. Compare with min = 30 and secondMin = Infinity.

20 is smaller than current min. Update: secondMin = 30, min = 20.

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

Check index 2

Current element is 10. Compare with min = 20 and secondMin = 30.

10 is smaller than current min. Update: secondMin = 20, min = 10.

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

Check index 3

Current element is 50. Compare with min = 10 and secondMin = 20.

No update required.

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

Check index 4

Current element is 60. Compare with min = 10 and secondMin = 20.

No update required.

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

Check index 5

Current element is 40. Compare with min = 10 and secondMin = 20.

No update required.

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

Final Result:

Second Smallest Element = 20

{ "array": [30,20,10,50,60,40], "showIndices": true, "labels": { "2": "min", "1": "secondMin" } }
{ "array": ["",10,20], "showIndices": false, "emptyIndices": [1, 2], "emptyCompIndices": [0], "labels": { "1": "min", "2": "secondMin" } }