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

Koko Eating Bananas Optimal Binary Search Approach

Problem Statement

Koko the monkey loves bananas. She has a list of banana piles, and she wants to eat all of them within h hours. Each hour, Koko chooses any pile and eats up to k bananas from it. If the pile has fewer than k bananas, she eats the entire pile and moves on.

Your task is to help Koko determine the minimum integer eating speed k such that she can finish all the bananas in at most h hours.

If the list of banana piles is empty, return 0 as there are no bananas to eat.

Examples

Banana Piles Hours (h) Minimum Eating Speed (k) Description
[3, 6, 7, 11] 8 4 Koko can eat all piles in 8 hours if she eats 4 bananas/hour
[30, 11, 23, 4, 20] 5 30 She must eat very fast to finish in just 5 hours
[30, 11, 23, 4, 20] 6 23 With 6 hours, speed of 23 is sufficient
[1, 1, 1, 1] 4 1 Minimum speed needed is 1 banana/hour
[1000000000] 2 500000000 Single large pile, she must eat half in each hour
[] 5 0 No piles to eat, so minimum speed is 0
[10] 1 10 Only one pile, must eat all in one hour

Visualization Player

Solution

Understanding the Problem

We are given a list of banana piles, and a total number of hours h within which Koko must finish eating all the bananas. Each hour, Koko chooses one pile and eats up to k bananas from it. If the pile has fewer than k bananas, she eats all of them and doesn’t continue to another pile in the same hour.

The goal is to find the minimum integer speed k such that Koko can finish eating all the bananas within h hours. This is essentially an optimization problem — we want the smallest value of k for which the total time taken does not exceed h.

Step-by-Step Solution with Example

Step 1: Understand how time is calculated

If Koko eats at a speed k, then for each pile, the number of hours she needs is ceil(pile / k). We need to compute this for all piles and add it up to find the total time.

Step 2: Choose an example

Let's say the piles are [3, 6, 7, 11] and h = 8. Koko must eat all bananas in at most 8 hours.

Step 3: Identify possible range for k

The minimum speed is 1 banana per hour. The maximum speed is the largest pile, 11, because if she can finish the biggest pile in one hour, she can finish any pile in one hour.

Step 4: Use Binary Search to find the minimum k

We now perform binary search between 1 and 11:

  • Mid = 6: Total time = ceil(3/6) + ceil(6/6) + ceil(7/6) + ceil(11/6) = 1 + 1 + 2 + 2 = 6 (less than 8) → try smaller speed.
  • Mid = 3: Total time = ceil(3/3) + ceil(6/3) + ceil(7/3) + ceil(11/3) = 1 + 2 + 3 + 4 = 10 (too much) → try higher speed.
  • Mid = 4: Total time = 1 + 2 + 2 + 3 = 8 (just fits) → try smaller speed to optimize further.
  • Mid = 3: already tested, doesn’t work → so answer is 4.

Step 5: Return the result

The minimum speed k that allows Koko to finish within h = 8 hours is 4.

Edge Cases

  • Exact Fit: If h equals the number of piles, then Koko must eat one pile per hour. So the speed must be at least as large as the largest pile.
  • Very Large h: If h is very high, Koko can eat slowly. Even speed = 1 might be enough.
  • Only One Pile: Then the speed is just ceil(pile / h).
  • No Piles: If the list is empty, return 0 since there's nothing to eat.
  • All piles are size 1: The total time is equal to the number of piles, and any k ≥ 1 would work if h is enough.

Finally

This problem is a great example of combining simulation with optimization using binary search. The key insight is understanding how ceil(pile / k) affects total time and narrowing the search space smartly. Always consider edge cases — especially empty input, minimum and maximum bounds — when crafting such a solution.

Algorithm Steps

  1. Initialize low = 1, high = max(piles), and answer = max(piles).
  2. While low ≤ high:
  3. → Compute mid = (low + high) / 2 as current eating speed.
  4. → For each pile, calculate hours = ceil(pile / mid).
  5. → Sum total hours for all piles.
  6. → If total hours ≤ h: update answer = mid, and search left by setting high = mid - 1.
  7. → Else, search right with low = mid + 1.
  8. Return answer as the minimum valid eating speed.

Code

Python
Java
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
import math

def minEatingSpeed(piles, h):
    low, high = 1, max(piles)  # Possible eating speeds range from 1 to max pile
    answer = high

    while low <= high:
        mid = (low + high) // 2
        hours = sum(math.ceil(p / mid) for p in piles)  # Total hours at speed 'mid'

        if hours <= h:
            answer = mid       # Try a smaller speed
            high = mid - 1
        else:
            low = mid + 1      # Need more speed to eat faster

    return answer

# Example
print(minEatingSpeed([3, 6, 7, 11], 8))  # Output: 4

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n * log m)Where n = number of piles, m = max(pile). Binary search over m with O(n) check each time.
Average CaseO(n * log m)Performs log(m) iterations of binary search with O(n) check per iteration.
Worst CaseO(n * log m)In worst case, binary search runs full range from 1 to max(pile), checking all piles each time.

Space Complexity

O(1)

Explanation: Only a constant number of variables are used for computation. No additional memory is required.


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