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 Floor and Ceiling in Sorted Array Binary Search Approach

Problem Statement

Given a sorted array of integers and a target number x, your task is to find the floor and ceil of x in the array.

  • The floor of x is the greatest number in the array that is less than or equal to x.
  • The ceil of x is the smallest number in the array that is greater than or equal to x.

If the floor or ceil does not exist, return -1 for that value.

Examples

Input Array Key (x) Floor Ceil Description
[10, 20, 30, 40, 50] 35 30 40 35 lies between 30 and 40
[10, 20, 30, 40, 50] 10 10 10 Exact match, floor and ceil are the same
[10, 20, 30, 40, 50] 5 -1 10 No floor exists, ceil is the first element
[10, 20, 30, 40, 50] 55 50 -1 Floor exists, no ceil since key is greater than all
[10, 20, 30, 40, 50] 25 20 30 25 lies between 20 and 30
[15] 15 15 15 Single element match
[15] 10 -1 15 Single element greater than key
[15] 20 15 -1 Single element less than key

Visualization Player

Solution

Understanding the Problem

We are given a sorted array and a number x. Our task is to find two special values:

  • Floor – the largest number in the array that is less than or equal to x.
  • Ceiling – the smallest number in the array that is greater than or equal to x.

This means we’re looking for the closest values that "hug" x from below and above. The solution must work efficiently, especially for large arrays.

Step-by-Step Plan Using an Example

Example

Array = [1, 3, 5, 7, 9] x = 6

Here, floor(6) should be 5 and ceiling(6) should be 7.

Step 1: Use Binary Search

Since the array is sorted, we’ll use binary search to reduce our work by half at every step.

We maintain two pointers: low and high. At each step, we calculate mid and compare the middle element with x.

Step 2: Apply the Three Cases

  • If arr[mid] == x → We found an exact match. Both floor and ceiling are x.
  • If arr[mid] < x → This could be a floor. We move low = mid + 1.
  • If arr[mid] > x → This could be a ceiling. We move high = mid - 1.

Step 3: Track Closest Values

During the search, we keep updating two variables:

  • floor gets updated when we find a number ≤ x
  • ceiling gets updated when we find a number ≥ x

Final Result

When the loop ends, floor and ceiling will hold our answers.

Incorporating Edge Cases

Let’s handle some special situations:

  • If x is smaller than all elements in the array → floor doesn’t exist, only ceiling.
  • If x is greater than all elements → ceiling doesn’t exist, only floor.
  • If x exactly matches an element → both floor and ceiling are x.

Our code needs to check and return null or a special value (like -1) when a floor or ceiling doesn’t exist.

Why Binary Search Works

Binary Search divides the search space in half at every step, so it runs in O(log n) time. This makes it very efficient for large arrays.

Since the array is sorted, we never miss any candidates—we just have to make the right decisions at each midpoint.

Beginner Tip

Always test your algorithm with:

  • Values smaller than the first element
  • Values larger than the last element
  • Values in the middle
  • Exact matches

This builds confidence that your logic is covering all edge cases.

Algorithm Steps

  1. Given a sorted array arr and a target value x.
  2. Initialize floor = -1 and ceil = -1.
  3. Use binary search to find floor:
  4. → While low ≤ high, compute mid.
  5. → If arr[mid] == x, both floor and ceil are arr[mid]. Return.
  6. → If arr[mid] < x, update floor = arr[mid], search right.
  7. → If arr[mid] > x, update ceil = arr[mid], search left.
  8. Continue until low > high.
  9. Return the computed floor and ceil.

Code

Python
JavaScript
Java
C++
C
def find_floor_ceil(arr, x):
    low, high = 0, len(arr) - 1
    floor, ceil = -1, -1

    while low <= high:
        mid = (low + high) // 2
        if arr[mid] == x:
            # Exact match is both floor and ceil
            return arr[mid], arr[mid]
        elif arr[mid] < x:
            # Current element could be a candidate for floor
            floor = arr[mid]
            low = mid + 1  # Search in the right half
        else:
            # Current element could be a candidate for ceil
            ceil = arr[mid]
            high = mid - 1  # Search in the left half

    return floor, ceil

# Sample Input
arr = [1, 2, 4, 6, 10, 12]
x = 5
print("Floor and Ceil:", find_floor_ceil(arr, x))

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)The target value is found at the mid index during the first iteration of binary search, requiring no further comparisons.
Average CaseO(log n)The binary search halves the search space in each step until the correct floor and ceiling values are found.
Worst CaseO(log n)In the worst case, the search continues until only one element remains, after which the floor and ceiling values are determined.

Space Complexity

O(1)

Explanation: The algorithm operates using a constant number of variables (like low, high, mid, floor, ceil), without requiring additional memory.


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