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

Stock Buy and Sell Optimal Solution using Single Pass

Problem Statement

Given an array prices, where prices[i] represents the stock price on the ith day, your task is to find the maximum profit you can achieve by choosing a single day to buy one stock and a different day in the future to sell that stock.

  • You must buy the stock before you sell it.
  • If there is no way to make a profit, return 0.

Examples

Input Prices Maximum Profit Description
[7, 1, 5, 3, 6, 4] 5 Buy at 1 and sell at 6 (6 - 1 = 5)Visualization
[7, 6, 4, 3, 1] 0 Prices continuously decline — no profit is possibleVisualization
[1, 2, 3, 4, 5] 4 Buy at 1 and sell at 5 — increasing pricesVisualization
[2, 4, 1, 5] 4 Buy at 1 and sell at 5Visualization
[5] 0 Only one price — no possible transactionVisualization
[] 0 Empty array — no data to work withVisualization

Visualization Player

Solution

Understanding the Problem

We are given an array of stock prices, where each element represents the price of a stock on a particular day. Our goal is to find the best day to buy and the best day to sell the stock to maximize profit. However, we are allowed to make this transaction only once, and we must buy the stock before we sell it.

In simple terms, we want to choose two days: one for buying and one for selling. The profit is the difference between the selling price and the buying price. If no profit is possible (i.e., prices only go down), we return 0.

Step-by-Step Solution with Explanation

1. Track the Minimum Price

As we go through the list, we will keep track of the lowest price we’ve seen so far. This will represent the best day to buy so far.

2. Calculate Profit

At each step, we calculate the profit if we were to sell the stock on that day, using the lowest price we've seen before. If this profit is greater than the best profit we’ve recorded, we update our best profit.

3. Use Example for Better Understanding

Let’s understand this with a beginner-friendly example: [7, 1, 5, 3, 6, 4]

  • Day 1: Price = 7 → minPrice = 7
  • Day 2: Price = 1 → minPrice = 1 (found a cheaper buy)
  • Day 3: Price = 5 → profit = 5 - 1 = 4 → maxProfit = 4
  • Day 4: Price = 3 → profit = 3 - 1 = 2 → maxProfit remains 4
  • Day 5: Price = 6 → profit = 6 - 1 = 5 → maxProfit = 5
  • Day 6: Price = 4 → profit = 4 - 1 = 3 → maxProfit remains 5

Result: Best profit is 5 (Buy at 1, sell at 6)

Handling Edge Cases

Case 1: Prices Only Go Down

Example: [7, 6, 4, 3, 1]
The price keeps dropping. Any buy-sell pair results in a loss. So, the maximum profit is 0.

Case 2: Constant or Steady Increase

Example: [1, 2, 3, 4, 5]
Here, buying at day 1 and selling at day 5 gives the best result: profit = 5 - 1 = 4.

Case 3: Single Price

Example: [10]
We can’t sell if we buy on the only day available. So, the profit is 0.

Case 4: Empty Array

There are no prices at all, so no transaction can be made. The answer is 0.

Algorithm Steps

  1. Given an array prices where prices[i] represents the price of a stock on the ith day.
  2. Initialize min_price to a very large number and max_profit to 0.
  3. Traverse through the array:
  4. → If prices[i] is less than min_price, update min_price.
  5. → Else, calculate the profit by prices[i] - min_price and update max_profit if it is greater.
  6. After the loop, return max_profit.

Code

Python
JavaScript
Java
C++
C
def max_profit(prices):
    min_price = float('inf')
    max_profit = 0
    for price in prices:
        if price < min_price:
            min_price = price
        elif price - min_price > max_profit:
            max_profit = price - min_price
    return max_profit

# Sample Input
prices = [7, 1, 5, 3, 6, 4]
print("Max Profit:", max_profit(prices))

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n)Even in the best case (increasing prices), the algorithm must scan all elements to compute maximum profit.
Average CaseO(n)The algorithm performs a single pass over the array to track the minimum price and compute the maximum profit.
Worst CaseO(n)In the worst case (decreasing prices), the algorithm still traverses the entire array to ensure no profit is possible.

Space Complexity

O(1)

Explanation: The solution uses a constant amount of extra space, maintaining only variables like min_price and max_profit.


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