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

Course Schedule Problem Using Graph Topological Sort

Problem Statement

You are given n tasks labeled from 0 to n - 1 and an array of prerequisite pairs. Each pair [a, b] indicates that task b must be completed before task a.

Return any valid order in which the tasks can be completed. If no such order exists (due to a cycle), return an empty array.

Examples

n Prerequisites Valid Output Description
2 [[1, 0]] [0, 1] Task 1 depends on 0, so 0 must come first
4 [[1, 0], [2, 0], [3, 1], [3, 2]] [0, 1, 2, 3] Task 3 depends on both 1 and 2, which in turn depend on 0
1 [] [0] Single task with no prerequisites
3 [[0, 1], [1, 2], [2, 0]] [] Cycle detected, impossible to complete all tasks
5 [] [0, 1, 2, 3, 4] No dependencies, any order is valid

Solution

Understanding the Problem

We are given a number of courses, and a list of prerequisite pairs. Each pair [a, b] means you must complete course b before course a. Our task is to determine if it’s possible to finish all courses, and if yes, return one possible order in which to take them.

This is a classic problem of dependency resolution and can be modeled as a directed graph where each course is a node, and each prerequisite is a directed edge. If the graph contains a cycle, then it is impossible to finish all courses. Otherwise, we can generate a valid course order using topological sorting.

Step-by-Step Solution with Example

Step 1: Represent the Problem as a Graph

We treat each course as a node. If course b is a prerequisite for course a, we draw a directed edge from b to a.

Example:
Let’s say numCourses = 4 and prerequisites = [[1,0],[2,0],[3,1],[3,2]].
This means:
- Take course 0 before 1
- Take course 0 before 2
- Take course 1 before 3
- Take course 2 before 3
So, the graph looks like:

0 → 1 → 3
        ↑
  → 2 ———┘

Step 2: Initialize In-Degree Array and Adjacency List

The in-degree of a node is the number of prerequisites it has. We create:

  • An adjacency list to store which courses depend on each course.
  • An in-degree array to count prerequisites for each course.

Step 3: Enqueue Courses with In-Degree 0

Courses with no prerequisites (in-degree 0) can be taken immediately. We add them to a queue.

In our example, only course 0 has in-degree 0 initially, so we enqueue it.

Step 4: Process the Queue

While the queue is not empty:

  • Remove a course from the queue and add it to the result list.
  • For each course that depends on it, reduce its in-degree by 1.
  • If any course’s in-degree becomes 0, enqueue it.

For our example:

  1. Start with [0]
  2. Process 0 → add [1, 2] to queue → result: [0]
  3. Process 1 → reduce in-degree of 3 → result: [0, 1]
  4. Process 2 → reduce in-degree of 3 → result: [0, 1, 2]
  5. Now 3 has in-degree 0 → enqueue → result: [0, 1, 2, 3]

Step 5: Check if All Courses Are Taken

If the result list contains all courses, we return it. If not, it means there’s a cycle and we return an empty array.

Edge Cases

  • Cycle in prerequisites: Example: [[1,0],[0,1]]. This creates a loop: 0 → 1 → 0. It’s impossible to finish all courses.
  • No prerequisites: All courses are independent. Any order is valid.
  • Single course: Always possible to finish it.
  • Multiple valid orders: For acyclic graphs, many topological sorts are possible.

Finally

This problem teaches us how to model real-world scheduling problems using graphs. Topological sorting is the key idea, and cycle detection helps us rule out impossible scenarios. By translating the prerequisites into a graph and using in-degree tracking, we can determine if all tasks (courses) can be completed, and in what order.

Algorithm Steps

  1. Create an adjacency list for the graph.
  2. Create an array to track in-degree for each task.
  3. Populate the adjacency list and in-degree array based on prerequisites.
  4. Initialize a queue with all tasks having in-degree 0.
  5. While the queue is not empty:
    1. Remove a task from the queue and add it to the result list.
    2. For each neighbor of that task, reduce its in-degree by 1.
    3. If any neighbor’s in-degree becomes 0, add it to the queue.
  6. After processing, if the result contains all tasks, return it.
  7. Otherwise, return an empty array (cycle detected).

Code

JavaScript
function findOrder(n, prerequisites) {
  const adj = Array.from({ length: n }, () => []);
  const inDegree = new Array(n).fill(0);

  for (const [a, b] of prerequisites) {
    adj[b].push(a);
    inDegree[a]++;
  }

  const queue = [], result = [];
  for (let i = 0; i < n; i++) {
    if (inDegree[i] === 0) queue.push(i);
  }

  while (queue.length > 0) {
    const node = queue.shift();
    result.push(node);
    for (const neighbor of adj[node]) {
      inDegree[neighbor]--;
      if (inDegree[neighbor] === 0) queue.push(neighbor);
    }
  }

  return result.length === n ? result : [];
}

console.log("Order for 2 tasks:", findOrder(2, [[1, 0]]));
console.log("Order for 4 tasks:", findOrder(4, [[1, 0], [2, 0], [3, 1], [3, 2]]));

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(V + E)In all cases, we must visit every node and edge to build the graph and perform topological sorting.
Average CaseO(V + E)Each course and each prerequisite relation must be examined exactly once.
Worst CaseO(V + E)Even with complex dependencies, we still process every node and edge once for sorting and cycle detection.

Space Complexity

O(V + E)

Explanation: We use an adjacency list (O(E)) and an in-degree array and queue (O(V)) to store and process the graph.


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