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Các chuyên đề ngoại khóa THPT

[Biên dịch trực tuyến]

[Chuyển C sang Pascal]

[Chương trình THPT chuyên – Môn Tin học]

Ngoại khóa

  1. Lớp 10: Chuyên đề 1: Ngôn ngữ lập trình
  2. Lớp 10: Chuyên đề 2: Phân tích, thiết kế và cài đặt thuật toán
  3. Lớp 11: Chuyên đề 1: Thuật toán quy hoạch động
  4. Lớp 11: Chuyên đề 2: Lý thuyết trò chơi
  5. Lớp 11: Chuyên đề 3: Duyệt toàn bộ nâng cao
  6. Lớp 11: Chuyên đề 4: Bài toán luồng cực đại trong mạng và ứng dụng
  7. Lớp 11: Chuyên đề 5: Bài toán lập lịch
  8. Lớp 12: Chuyên đề 1: Tính toán hình học
  9. Lớp 12: Chuyên đề 2: Độ phưc tạp của bài toán
  10. Lớp 12: Chuyên đề 3: Các cấu trúc dữ liệu nâng cao
  11. Lớp 12: Chuyên đề 4: Các cách tiếp cận bài toán NP khó
  12. Lớp 12: Chuyên đề 5: Các thuật toán tiến hóa
  13. _
  14. _
  15. _
  16. _
  17. _

Tài liệu tham khảo

  1. Giải thuật và lập trình – Lê Minh Hoàng
  2. Tham khảo các bài toán về NP-đầy đủ
  3. Tham khảo các bài toán NP khó
  4. _
  5. _

Analysis of Algorithms:

  1. Asymptotic Analysis
  2. Worst, Average and Best Cases
  3. Asymptotic Notations
  4. Analysis of Loops
  5. Solving Recurrences
  6. Amortized Analysis
  7. What does ‘Space Complexity’ mean?
  8. Pseudo-polynomial Algorithms
  9. NP-Completeness Introduction
  10. Polynomial Time Approximation Scheme
  11. A Time Complexity Question
  12. Time Complexity of building a heap
  13. Time Complexity where loop variable is incremented by 1, 2, 3, 4 ..
  14. Time Complexity of Loop with Powers
  15. Performance of loops (A caching question)

Recent Articles on Analysis of Algorithms

Quiz on Analysis of Algorithms

Quiz on Recurrences

Searching and Sorting:

  1. Binary Search, Jump Search, Interpolation Search
  2. Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort, Counting Sort, Bucket Sort, ShellSort, Comb Sort, Pigeonhole Sort
  3. Interpolation search vs Binary search
  4. Stability in sorting algorithms
  5. When does the worst case of Quicksort occur?
  6. Lower bound for comparison based sorting algorithms
  7. Which sorting algorithm makes minimum number of memory writes?
  8. Find the Minimum length Unsorted Subarray, sorting which makes the complete array sorted
  9. Merge Sort for Linked Lists
  10. Sort a nearly sorted (or K sorted) array
  11. Iterative Quick Sort
  12. QuickSort on Singly Linked List
  13. QuickSort on Doubly Linked List
  14. Find k closest elements to a given value
  15. Sort n numbers in range from 0 to n^2 – 1 in linear time
  16. A Problem in Many Binary Search Implementations
  17. Search in an almost sorted array
  18. Sort an array in wave form
  19. Why is Binary Search preferred over Ternary Search?
  20. K’th Smallest/Largest Element in Unsorted Array
  21. K’th Smallest/Largest Element in Unsorted Array in Expected Linear Time
  22. K’th Smallest/Largest Element in Unsorted Array in Worst Case Linear Time
  23. Find the closest pair from two sorted arrays
  24. Find common elements in three sorted arrays
  25. Given a sorted array and a number x, find the pair in array whose sum is closest to x
  26. Count 1’s in a sorted binary array
  27. Binary Insertion Sort
  28. Insertion Sort for Singly Linked List
  29. Why Quick Sort preferred for Arrays and Merge Sort for Linked Lists?
  30. Merge Sort for Doubly Linked List

Recent Articles on Searching

Recent Articles on Sorting

Quiz on Searching

Quiz on Sorting

Coding Practice on Searching

Coding Practice on Sorting

Greedy Algorithms:

  1. Activity Selection Problem
  2. Kruskal’s Minimum Spanning Tree Algorithm
  3. Huffman Coding
  4. Efficient Huffman Coding for Sorted Input
  5. Prim’s Minimum Spanning Tree Algorithm
  6. Prim’s MST for Adjacency List Representation
  7. Dijkstra’s Shortest Path Algorithm
  8. Dijkstra’s Algorithm for Adjacency List Representation
  9. Job Sequencing Problem
  10. Quiz on Greedy Algorithms
  11. Greedy Algorithm to find Minimum number of Coins
  12. K Centers Problem

Recent Articles on Greedy Algorithms

Quiz on Greedy Algorithms

Coding Practice on Greedy Algorithms

Dynamic Programming:

  1. Overlapping Subproblems Property
  2. Optimal Substructure Property
  3. Longest Increasing Subsequence
  4. Longest Common Subsequence
  5. Edit Distance
  6. Min Cost Path
  7. Coin Change
  8. Matrix Chain Multiplication
  9. Binomial Coefficient
  10. 0-1 Knapsack Problem
  11. Egg Dropping Puzzle
  12. Longest Palindromic Subsequence
  13. Cutting a Rod
  14. Maximum Sum Increasing Subsequence
  15. Longest Bitonic Subsequence
  16. Floyd Warshall Algorithm
  17. Palindrome Partitioning
  18. Partition problem
  19. Word Wrap Problem
  20. Maximum Length Chain of Pairs
  21. Variations of LIS
  22. Box Stacking Problem
  23. Program for Fibonacci numbers
  24. Minimum number of jumps to reach end
  25. Maximum size square sub-matrix with all 1s
  26. Ugly Numbers
  27. Largest Sum Contiguous Subarray
  28. Longest Palindromic Substring
  29. Bellman–Ford Algorithm for Shortest Paths
  30. Optimal Binary Search Tree
  31. Largest Independent Set Problem
  32. Subset Sum Problem
  33. Maximum sum rectangle in a 2D matrix
  34. Count number of binary strings without consecutive 1?s
  35. Boolean Parenthesization Problem
  36. Count ways to reach the n’th stair
  37. Minimum Cost Polygon Triangulation
  38. Mobile Numeric Keypad Problem
  39. Count of n digit numbers whose sum of digits equals to given sum
  40. Minimum Initial Points to Reach Destination
  41. Total number of non-decreasing numbers with n digits
  42. Find length of the longest consecutive path from a given starting character
  43. Tiling Problem
  44. Minimum number of squares whose sum equals to given number n
  45. Find minimum number of coins that make a given value
  46. Collect maximum points in a grid using two traversals
  47. Shortest Common Supersequence
  48. Compute sum of digits in all numbers from 1 to n
  49. Count possible ways to construct buildings
  50. Maximum profit by buying and selling a share at most twice
  51. How to print maximum number of A’s using given four keys
  52. Find the minimum cost to reach destination using a train
  53. Vertex Cover Problem | Set 2 (Dynamic Programming Solution for Tree)
  54. Count number of ways to reach a given score in a game
  55. Weighted Job Scheduling
  56. Longest Even Length Substring such that Sum of First and Second Half is same

Recent Articles on Dynamic Programming

Quiz on Dynamic Programming

Coding Practice on Dynamic Programing

Pattern Searching:

  1. Naive Pattern Searching
  2. KMP Algorithm
  3. Rabin-Karp Algorithm
  4. A Naive Pattern Searching Question
  5. Finite Automata
  6. Efficient Construction of Finite Automata
  7. Boyer Moore Algorithm – Bad Character Heuristic
  8. Suffix Array
  9. Anagram Substring Search (Or Search for all permutations)
  10. Pattern Searching using a Trie of all Suffixes
  11. Aho-Corasick Algorithm for Pattern Searching
  12. kasai’s Algorithm for Construction of LCP array from Suffix Array
  13. Z algorithm (Linear time pattern searching Algorithm)

Recent Articles on Pattern Searching

Other String Algorithms:

  1. Manacher’s Algorithm – Linear Time Longest Palindromic Substring – Part 1, Part 2, Part 3, Part 4
  2. Longest Even Length Substring such that Sum of First and Second Half is same
  3. Print all possible strings that can be made by placing spaces

Recent Articles on Strings

Coding practice on Strings


  1. Print all permutations of a given string
  2. The Knight’s tour problem
  3. Rat in a Maze
  4. N Queen Problem
  5. Subset Sum
  6. m Coloring Problem
  7. Hamiltonian Cycle
  8. Sudoku
  9. Tug of War
  10. Solving Cryptarithmetic Puzzles

Recent Articles on Backtracking

Coding Practice on Backtracking

Divide and Conquer:

  1. Introduction
  2. Write your own pow(x, n) to calculate x*n
  3. Median of two sorted arrays
  4. Count Inversions
  5. Closest Pair of Points
  6. Strassen’s Matrix Multiplication

Recent Articles on Divide and Conquer

Quiz on Divide and Conquer

Coding practice on Divide and Conquer

Geometric Algorithms:

  1. Closest Pair of Points | O(nlogn) Implementation
  2. How to check if two given line segments intersect?
  3. How to check if a given point lies inside or outside a polygon?
  4. Convex Hull | Set 1 (Jarvis’s Algorithm or Wrapping)
  5. Convex Hull | Set 2 (Graham Scan)
  6. Given n line segments, find if any two segments intersect
  7. Check whether a given point lies inside a triangle or not
  8. How to check if given four points form a square

Recent Articles on Geometric Algorithms

Coding Practice on Geometric Algorithms

Mathematical Algorithms:

  1. Write an Efficient Method to Check if a Number is Multiple of 3
  2. Efficient way to multiply with 7
  3. Write a C program to print all permutations of a given string
  4. Lucky Numbers
  5. Write a program to add two numbers in base 14
  6. Babylonian method for square root
  7. Multiply two integers without using multiplication, division and bitwise operators, and no loops
  8. Print all combinations of points that can compose a given number
  9. Write you own Power without using multiplication(*) and division(/) operators
  10. Program for Fibonacci numbers
  11. Average of a stream of numbers
  12. Count numbers that don’t contain 3
  13. MagicSquare
  14. Sieve of Eratosthenes
  15. Find day of the week for a given date
  16. DFA based division
  17. Generate integer from 1 to 7 with equal probability
  18. Given a number, find the next smallest palindrome
  19. Make a fair coin from a biased coin
  20. Check divisibility by 7
  21. Find the largest multiple of 3
  22. Lexicographic rank of a string
  23. Print all permutations in sorted (lexicographic) order
  24. Shuffle a given array
  25. Space and time efficient Binomial Coefficient
  26. Reservoir Sampling
  27. Pascal’s Triangle
  28. Select a random number from stream, with O(1) space
  29. Find the largest multiple of 2, 3 and 5
  30. Efficient program to calculate e^x
  31. Measure one litre using two vessels and infinite water supply
  32. Efficient program to print all prime factors of a given number
  33. Print all possible combinations of r elements in a given array of size n
  34. Random number generator in arbitrary probability distribution fashion
  35. How to check if a given number is Fibonacci number?
  36. Russian Peasant Multiplication
  37. Count all possible groups of size 2 or 3 that have sum as multiple of 3
  38. Tower of Hanoi
  39. Horner’s Method for Polynomial Evaluation
  40. Count trailing zeroes in factorial of a number
  41. Program for nth Catalan Number
  42. Generate one of 3 numbers according to given probabilities
  43. Find Excel column name from a given column number
  44. Find next greater number with same set of digits
  45. Count Possible Decodings of a given Digit Sequence
  46. Calculate the angle between hour hand and minute hand
  47. Count number of binary strings without consecutive 1?s
  48. Find the smallest number whose digits multiply to a given number n
  49. Draw a circle without floating point arithmetic
  50. How to check if an instance of 8 puzzle is solvable?
  51. Birthday Paradox
  52. Multiply two polynomials
  53. Count Distinct Non-Negative Integer Pairs (x, y) that Satisfy the Inequality x*x + y*y < n
  54. Count ways to reach the n’th stair
  55. Replace all ‘0’ with ‘5’ in an input Integer
  56. Program to add two polynomials
  57. Print first k digits of 1/n where n is a positive integer
  58. Given a number as a string, find the number of contiguous subsequences which recursively add up to 9

Recent Articles on Mathematical Algorithms

Coding Practice on Mathematical Algorithms

Bit Algorithms:

  1. Find the element that appears once
  2. Detect opposite signs
  3. Set bits in all numbers from 1 to n
  4. Swap bits
  5. Add two numbers
  6. Smallest of three
  7. A Boolean Array Puzzle
  8. Set bits in an (big) array
  9. Next higher number with same number of set bits
  10. Optimization Technique (Modulus)
  11. Add 1 to a number
  12. Multiply with 3.5
  13. Turn off the rightmost set bit
  14. Check for Power of 4
  15. Absolute value (abs) without branching
  16. Modulus division by a power-of-2-number
  17. Minimum or Maximum of two integers
  18. Rotate bits
  19. Find the two non-repeating elements in an array
  20. Number Occurring Odd Number of Times
  21. Check for Integer Overflow
  22. Little and Big Endian
  23. Reverse Bits of a Number
  24. Count set bits in an integer
  25. Number of bits to be flipped to convert A to B
  26. Next Power of 2
  27. Check if a Number is Multiple of 3
  28. Find parity
  29. Multiply with 7
  30. Find whether a no is power of two
  31. Position of rightmost set bit
  32. Binary representation of a given number
  33. Swap all odd and even bits
  34. Find position of the only set bit
  35. Karatsuba algorithm for fast multiplication
  36. How to swap two numbers without using a temporary variable?
  37. Check if a number is multiple of 9 using bitwise operators
  38. Swap two nibbles in a byte
  39. How to turn off a particular bit in a number?
  40. Check if binary representation of a number is palindrome

Recent Articles on Bit Algorithms

Quiz on Bit Algorithms

Coding Practice on Bit Algorithms

Graph Algorithms:

Introduction, DFS and BFS:

  1. Graph and its representations
  2. Breadth First Traversal for a Graph
  3. Depth First Traversal for a Graph
  4. Applications of Depth First Search
  5. Detect Cycle in a Directed Graph
  6. Detect Cycle in a an Undirected Graph
  7. Detect cycle in an undirected graph
  8. Longest Path in a Directed Acyclic Graph
  9. Topological Sorting
  10. Check whether a given graph is Bipartite or not
  11. Snake and Ladder Problem
  12. Biconnected Components
  13. Check if a given graph is tree or not

Minimum Spanning Tree:

  1. Prim’s Minimum Spanning Tree (MST))
  2. Applications of Minimum Spanning Tree Problem
  3. Prim’s MST for Adjacency List Representation
  4. Kruskal’s Minimum Spanning Tree Algorithm
  5. Boruvka’s algorithm for Minimum Spanning Tree

Shortest Paths:

  1. Dijkstra’s shortest path algorithm
  2. Dijkstra’s Algorithm for Adjacency List Representation
  3. Bellman–Ford Algorithm
  4. Floyd Warshall Algorithm
  5. Johnson’s algorithm for All-pairs shortest paths
  6. Shortest Path in Directed Acyclic Graph
  7. Some interesting shortest path questions
  8. Shortest path with exactly k edges in a directed and weighted graph


  1. Find if there is a path between two vertices in a directed graph
  2. Connectivity in a directed graph
  3. Articulation Points (or Cut Vertices) in a Graph
  4. Biconnected graph
  5. Bridges in a graph
  6. Eulerian path and circuit
  7. Fleury’s Algorithm for printing Eulerian Path or Circuit
  8. Strongly Connected Components
  9. Transitive closure of a graph
  10. Find the number of islands
  11. Count all possible walks from a source to a destination with exactly k edges
  12. Euler Circuit in a Directed Graph
  13. Biconnected Components
  14. Tarjan’s Algorithm to find Strongly Connected Components

Hard Problems:

  1. Graph Coloring (Introduction and Applications)
  2. Greedy Algorithm for Graph Coloring
  3. Travelling Salesman Problem (Naive and Dynamic Programming)
  4. Travelling Salesman Problem (Approximate using MST)
  5. Hamiltonian Cycle
  6. Vertex Cover Problem (Introduction and Approximate Algorithm)
  7. K Centers Problem (Greedy Approximate Algorithm)

Maximum Flow:

  1. Ford-Fulkerson Algorithm for Maximum Flow Problem
  2. Find maximum number of edge disjoint paths between two vertices
  3. Find minimum s-t cut in a flow network
  4. Maximum Bipartite Matching
  5. Channel Assignment Problem


  1. Find if the strings can be chained to form a circle
  2. Given a sorted dictionary of an alien language, find order of characters
  3. Karger’s algorithm for Minimum Cut
  4. Karger’s algorithm for Minimum Cut | Set 2 (Analysis and Applications)
  5. Hopcroft–Karp Algorithm for Maximum Matching | Set 1 (Introduction)
  6. Hopcroft–Karp Algorithm for Maximum Matching | Set 2 (Implementation)
  7. Length of shortest chain to reach a target word
  8. Find same contacts in a list of contacts

All Algorithms on Graph

Quiz on Graph

Quiz on Graph Traversals

Quiz on Graph Shortest Paths

Quiz on Graph Minimum Spanning Tree

Coding Practice on Graph

Randomized Algorithms:

  1. Linearity of Expectation
  2. Expected Number of Trials until Success
  3. Randomized Algorithms | Set 0 (Mathematical Background)
  4. Randomized Algorithms | Set 1 (Introduction and Analysis)
  5. Randomized Algorithms | Set 2 (Classification and Applications)
  6. Randomized Algorithms | Set 3 (1/2 Approximate Median)
  7. Karger’s algorithm for Minimum Cut
  8. K’th Smallest/Largest Element in Unsorted Array | Set 2 (Expected Linear Time)
  9. Reservoir Sampling
  10. Shuffle a given array
  11. Select a Random Node from a Singly Linked List

Recent Articles on Randomized Algorithms

Branch and Bound:

  1. Branch and Bound | Set 1 (Introduction with 0/1 Knapsack)
  2. Branch and Bound | Set 2 (Implementation of 0/1 Knapsack)
  3. Branch and Bound | Set 3 (8 puzzle Problem)
  4. Branch And Bound | Set 4 (Job Assignment Problem)
  5. Branch and Bound | Set 5 (N Queen Problem)
  6. Branch And Bound | Set 6 (Traveling Salesman Problem)

Recent Articles on Branch and Bound

Quizzes on Algorithms:

  1. Analysis of Algorithms
  2. Sorting
  3. Divide and Conquer
  4. Greedy Algorithms
  5. Dynamic Programming
  6. Backtracking
  7. Misc
  8. NP Complete
  9. Searching
  10. Analysis of Algorithms (Recurrences)
  11. Recursion
  12. Bit Algorithms
  13. Graph Traversals
  14. Graph Shortest Paths
  15. Graph Minimum Spanning Tree


  1. Commonly Asked Algorithm Interview Questions | Set 1
  2. Given a matrix of ‘O’ and ‘X’, find the largest subsquare surrounded by ‘X’
  3. Nuts & Bolts Problem (Lock & Key problem)
  4. Flood fill Algorithm – how to implement fill() in paint?
  5. Given n appointments, find all conflicting appointments
  6. Check a given sentence for a given set of simple grammer rules
  7. Find Index of 0 to be replaced with 1 to get longest continuous sequence of 1s in a binary array
  8. How to check if two given sets are disjoint?
  9. Minimum Number of Platforms Required for a Railway/Bus Station
  10. Length of the largest subarray with contiguous elements | Set 1
  11. Length of the largest subarray with contiguous elements | Set 2
  12. Print all increasing sequences of length k from first n natural numbers
  13. Given two strings, find if first string is a subsequence of second
  14. Snake and Ladder Problem
  15. Write a function that returns 2 for input 1 and returns 1 for 2
  16. Connect n ropes with minimum cost
  17. Find the number of valid parentheses expressions of given length
  18. Longest Monotonically Increasing Subsequence Size (N log N): Simple implementation
  19. Generate all binary permutations such that there are more 1’s than 0’s at every point in all permutations
  20. Lexicographically minimum string rotation
  21. Construct an array from its pair-sum array
  22. Program to evaluate simple expressions
  23. Check if characters of a given string can be rearranged to form a palindrome
  24. Print all pairs of anagrams in a given array of strings

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