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

Selection Sort - Algorithm, Visualization, Examples

Sorting

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace Detailed Exmpl

Problem Statement❯

Given an array of integers, your task is to sort the array in ascending order using the Selection Sort algorithm.

Selection Sort works by repeatedly selecting the smallest element from the unsorted portion of the array and moving it to the correct position in the sorted portion.

The algorithm is in-place and does not require extra space, but it is not the most efficient for large datasets.

Examples❯

Input Array Sorted Output Description
[64, 25, 12, 22, 11] [11, 12, 22, 25, 64] Unsorted array with multiple elementsVisualization
[1, 2, 3, 4, 5] [1, 2, 3, 4, 5] Already sorted arrayVisualization
[5, 4, 3, 2, 1] [1, 2, 3, 4, 5] Reverse sorted arrayVisualization
[1] [1] Single-element array remains unchangedVisualization
[] [] Empty array has nothing to sort
[7, 7, 7, 7] [7, 7, 7, 7] All elements are equalVisualization
[3, -1, 0, -5, 2] [-5, -1, 0, 2, 3] Array with negative and positive numbersVisualization

Visualization Player

Solution❯

Selection Sort is a comparison-based sorting algorithm. It builds the final sorted array by repeatedly finding the minimum element from the unsorted part and putting it at the beginning of the sorted part.

How It Works

Imagine you're sorting cards on a table. You start from the left and look through all the remaining cards to find the smallest one. Once found, you swap it with the card you were initially pointing at. You then move one position to the right and repeat the process until all cards are sorted.

The same logic is applied in Selection Sort. At each step:

  1. We assume the current position has the smallest value.
  2. We scan through the remaining part of the array to find if there is a smaller number.
  3. If we find one, we swap it with the current position.
    The value in the current position is sorted.
  4. We repeat this until we reach the end of the array.

Case Analysis

  • Normal Case: In an average unsorted array like [64, 25, 12, 22, 11], the algorithm will perform several swaps to sort the values step-by-step into ascending order.
  • Already Sorted: If the array is already sorted, Selection Sort will still go through all comparisons but no swaps will be needed.
  • Reverse Sorted: If the array is in descending order, the algorithm performs the maximum number of swaps, moving the smallest values from the back to the front.
  • Single Element: If there's only one element, it's already sorted by default.
  • Empty Array: There's nothing to sort, so the result is simply an empty array.
  • All Elements Equal: Since all elements are the same, no swaps are needed, and the array remains unchanged.
  • Mixed Values: The algorithm still works correctly with negative numbers, zero, and positive values. It always selects the smallest from the remaining section.

Why Use Selection Sort?

Selection Sort is a great algorithm for teaching and understanding sorting logic because of its simplicity. However, for very large arrays or when performance matters, faster algorithms like Merge Sort or Quick Sort are preferred.

Algorithm Steps❯

  1. Start at the beginning of the array.
  2. Assume the first unsorted element is the smallest.
  3. Scan the remaining unsorted elements to find the smallest element.
  4. Swap the smallest element with the first unsorted element.
  5. Repeat the process for the rest of the array until it is sorted.

Code

Python
Java
JavaScript
C
C++
C#
Go
def selection_sort(arr):
    n = len(arr)
    for i in range(n):
        min_index = i
        for j in range(i + 1, n):
            if arr[j] < arr[min_index]:
                min_index = j
        arr[i], arr[min_index] = arr[min_index], arr[i]
    return arr

if __name__ == '__main__':
    arr = [6, 3, 8, 2, 7, 4]
    selection_sort(arr)
    print("Sorted array is:", arr)

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(n)In the best case, the array is already sorted. Bubble sort can be optimized to stop early if no swaps are made during a pass, resulting in linear time.
Average CaseO(n^2)On average, bubble sort performs n/2 swaps per pass for n passes, resulting in a quadratic number of comparisons and swaps.
Worst CaseO(n^2)In the worst case (reverse sorted array), bubble sort needs to perform the maximum number of swaps and comparisons, resulting in O(n^2) time complexity.

Space Complexity❯

O(1)

Explanation: Bubble sort is performed in-place and only requires a constant amount of additional space for temporary variables used in swapping.

Detailed Step by Step Example❯

Let us take the following array and apply the Selection Sort algorithm to sort the array in ascending order.

{ "array": [6,3,8,2,7,4], "showIndices": true, "specialIndices": [] }

Pass 1

Assume index 0 (6) is the minimum in the unsorted portion of array.

➜ Comparing current minimum 6 at index=0 with 3 at index=1

{ "array": [6,3,8,2,7,4], "showIndices": true, "highlightIndices": [0,1], "highlightIndicesGreen": [], "specialIndices": [], "labels": { "0": "min" } }

Found new minimum 3 at index=1.

➜ Comparing current minimum 3 at index=1 with 8 at index=2

{ "array": [6,3,8,2,7,4], "showIndices": true, "highlightIndices": [1,2], "highlightIndicesGreen": [], "specialIndices": [], "labels": { "1": "min" } }

No change. 8 is not smaller than current minimum.

➜ Comparing current minimum 3 at index=1 with 2 at index=3

{ "array": [6,3,8,2,7,4], "showIndices": true, "highlightIndices": [1,3], "highlightIndicesGreen": [], "specialIndices": [], "labels": { "1": "min" } }

Found new minimum 2 at index=3.

➜ Comparing current minimum 2 at index=3 with 7 at index=4

{ "array": [6,3,8,2,7,4], "showIndices": true, "highlightIndices": [3,4], "highlightIndicesGreen": [], "specialIndices": [], "labels": { "3": "min" } }

No change. 7 is not smaller than current minimum.

➜ Comparing current minimum 2 at index=3 with 4 at index=5

{ "array": [6,3,8,2,7,4], "showIndices": true, "highlightIndices": [3,5], "highlightIndicesGreen": [], "specialIndices": [], "labels": { "3": "min" } }

No change. 4 is not smaller than current minimum.

➜ Minimum in the unsorted portion of array is 2 at index=3.

{ "array": [6,3,8,2,7,4], "showIndices": true, "highlightIndices": [3], "highlightIndicesGreen": [], "specialIndices": [] }

Swapping 6 and 2 to place the smallest element at correct position.

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [0,3], "highlightIndicesGreen": [0], "specialIndices": [] }

Element 2 is now at its correct position.

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndicesGreen": [0], "specialIndices": [] }

Pass 2

Assume index 1 (3) is the minimum in the unsorted portion of array.

➜ Comparing current minimum 3 at index=1 with 8 at index=2

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [1,2], "highlightIndicesGreen": [0], "specialIndices": [], "labels": { "1": "min" } }

No change. 8 is not smaller than current minimum.

➜ Comparing current minimum 3 at index=1 with 6 at index=3

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [1,3], "highlightIndicesGreen": [0], "specialIndices": [], "labels": { "1": "min" } }

No change. 6 is not smaller than current minimum.

➜ Comparing current minimum 3 at index=1 with 7 at index=4

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [1,4], "highlightIndicesGreen": [0], "specialIndices": [], "labels": { "1": "min" } }

No change. 7 is not smaller than current minimum.

➜ Comparing current minimum 3 at index=1 with 4 at index=5

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [1,5], "highlightIndicesGreen": [0], "specialIndices": [], "labels": { "1": "min" } }

No change. 4 is not smaller than current minimum.

➜ Minimum in the unsorted portion of array is 3 at index=1.

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [1], "highlightIndicesGreen": [0], "specialIndices": [] }

No swap needed. Minimum element is already at the correct position.

Element 3 is now at its correct position.

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndicesGreen": [0,1], "specialIndices": [] }

Pass 3

Assume index 2 (8) is the minimum in the unsorted portion of array.

➜ Comparing current minimum 8 at index=2 with 6 at index=3

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [2,3], "highlightIndicesGreen": [0,1], "specialIndices": [], "labels": { "2": "min" } }

Found new minimum 6 at index=3.

➜ Comparing current minimum 6 at index=3 with 7 at index=4

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [3,4], "highlightIndicesGreen": [0,1], "specialIndices": [], "labels": { "3": "min" } }

No change. 7 is not smaller than current minimum.

➜ Comparing current minimum 6 at index=3 with 4 at index=5

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [3,5], "highlightIndicesGreen": [0,1], "specialIndices": [], "labels": { "3": "min" } }

Found new minimum 4 at index=5.

➜ Minimum in the unsorted portion of array is 4 at index=5.

{ "array": [2,3,8,6,7,4], "showIndices": true, "highlightIndices": [5], "highlightIndicesGreen": [0,1], "specialIndices": [] }

Swapping 8 and 4 to place the smallest element at correct position.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndices": [2,5], "highlightIndicesGreen": [0,1,2], "specialIndices": [] }

Element 4 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndicesGreen": [0,1,2], "specialIndices": [] }

Pass 4

Assume index 3 (6) is the minimum in the unsorted portion of array.

➜ Comparing current minimum 6 at index=3 with 7 at index=4

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndices": [3,4], "highlightIndicesGreen": [0,1,2], "specialIndices": [], "labels": { "3": "min" } }

No change. 7 is not smaller than current minimum.

➜ Comparing current minimum 6 at index=3 with 8 at index=5

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndices": [3,5], "highlightIndicesGreen": [0,1,2], "specialIndices": [], "labels": { "3": "min" } }

No change. 8 is not smaller than current minimum.

➜ Minimum in the unsorted portion of array is 6 at index=3.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndices": [3], "highlightIndicesGreen": [0,1,2], "specialIndices": [] }

No swap needed. Minimum element is already at the correct position.

Element 6 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndicesGreen": [0,1,2,3], "specialIndices": [] }

Pass 5

Assume index 4 (7) is the minimum in the unsorted portion of array.

➜ Comparing current minimum 7 at index=4 with 8 at index=5

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndices": [4,5], "highlightIndicesGreen": [0,1,2,3], "specialIndices": [], "labels": { "4": "min" } }

No change. 8 is not smaller than current minimum.

➜ Minimum in the unsorted portion of array is 7 at index=4.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndices": [4], "highlightIndicesGreen": [0,1,2,3], "specialIndices": [] }

No swap needed. Minimum element is already at the correct position.

Element 7 is now at its correct position.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndicesGreen": [0,1,2,3,4], "specialIndices": [] }

Array is fully sorted.

{ "array": [2,3,4,6,7,8], "showIndices": true, "highlightIndicesGreen": [0,1,2,3,4,5], "specialIndices": [] }