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

Check if Array is Sorted using Loop - Optimal Algorithm

Arrays

Contents

ProblemExamplesVisualizationSolutionAlgorithmCodeTimeSpace Detailed Exmpl

Problem Statement❯

Given an array of integers, determine whether the array is sorted in strictly non-decreasing (ascending) order.

  • An array is considered sorted if for every index i, the condition arr[i] ≤ arr[i+1] holds.
  • If the array is empty or contains only one element, it is considered sorted.

Return true if the array is sorted, otherwise return false.

Examples❯

Input Array Is Sorted? Description
[1, 2, 3, 4, 5] true Strictly increasing orderVisualization
[1, 2, 2, 3, 4] true Non-decreasing (duplicates allowed)Visualization
[5, 4, 3, 2, 1] false Strictly decreasing<Visualization/td>
[10, 20, 15, 25] false Disorder between 20 and 15Visualization
[100] true Single-element array is always sortedVisualization
[] true Empty array is trivially sortedVisualization
[1, 3, 5, 7, 6] false Sorted until the last element breaks the orderVisualization
[1, 2, 3, 3, 3] true Flat segments are allowed in non-decreasing orderVisualization

Visualization Player

Solution❯

To determine if an array is sorted, we check whether each element is less than or equal to the one that comes after it. This is because in a non-decreasing (ascending) order, every element should be ≤ the next one.

What Happens in Different Cases?

  • Fully Sorted Array: If the elements go up or stay the same from left to right (like [1, 2, 2, 3, 5]), then it is sorted.
  • Unsorted Array: If there’s any element that is greater than the one after it (like [3, 5, 4]), the order is broken, and we return false.
  • Array with Duplicates: Duplicates do not break the sorting as long as the order doesn't decrease (e.g., [1, 1, 2, 2] is sorted).
  • Single-Element Array: A single number is always considered sorted since there are no comparisons to make.
  • Empty Array: An empty list has no elements out of order. So by definition, it is sorted.

This solution works by simply looping once through the array and checking every pair of neighboring elements. If we ever find a case where a number is greater than the one after it, we know the array is not sorted and can return false immediately. If we reach the end without such a case, the array is sorted.

Why This Works Efficiently

We only look at each element once, so the entire process takes O(n) time where n is the size of the array. This is the most optimal way to check for sorting.

Algorithm Steps❯

  1. Given an array arr.
  2. Iterate through the array from index 0 to n - 2.
  3. For each index i, check if arr[i] > arr[i + 1].
  4. If the condition is true, return false (array is not sorted).
  5. If the loop completes without finding any such case, return true.

Code

Python
JavaScript
Java
C++
C
def is_sorted(arr):
    for i in range(len(arr) - 1):
        if arr[i] > arr[i + 1]:
            return False
    return True

# Sample Input
arr = [10, 20, 30, 40, 50]
print("Is Sorted:", is_sorted(arr))

Time Complexity❯

CaseTime ComplexityExplanation
Best CaseO(1)If the array is not sorted and the first pair is unsorted, the algorithm returns immediately.
Average CaseO(n)The loop may check several elements before detecting disorder in a random unsorted array.
Worst CaseO(n)If the array is fully sorted, the algorithm needs to scan all elements from index 0 to n - 2.

Space Complexity❯

O(1)

Explanation: The algorithm uses only constant space for the loop counter and comparisons, without any additional data structures.

Detailed Step by Step Example❯

Let's check if the following array is sorted in ascending order.

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

Compare index 0 and 1

Compare 10 and 20.

10 ≤ 20 → OK

{ "array": [10,20,30,40,50], "showIndices": true, "highlightIndices": [0,1], "labels": {"0":"i","1":"i+1"} }

Compare index 1 and 2

Compare 20 and 30.

20 ≤ 30 → OK

{ "array": [10,20,30,40,50], "showIndices": true, "highlightIndices": [1,2], "labels": {"1":"i","2":"i+1"} }

Compare index 2 and 3

Compare 30 and 40.

30 ≤ 40 → OK

{ "array": [10,20,30,40,50], "showIndices": true, "highlightIndices": [2,3], "labels": {"2":"i","3":"i+1"} }

Compare index 3 and 4

Compare 40 and 50.

40 ≤ 50 → OK

{ "array": [10,20,30,40,50], "showIndices": true, "highlightIndices": [3,4], "labels": {"3":"i","4":"i+1"} }

Final Result:

Array is sorted.