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Recursion

Recursive algorithms provide a powerful framework for solving problems by breaking them down into smaller, self-similar subproblems. By focusing on the decomposition process and understanding how to express solutions recursively, you'll gain a deeper understanding of algorithmic design principles that can be applied to a wide range of problems.

1. Arrange balls

2. Find Binomial coefficient

3. Find Nth Catalan Number

4. Climbing stairs with 3 moves

5. Climbing stairs

6. Find minimum coins to make change

7. Find number of way to make coin change

8. Find all subsequence combinations of a string

9. Count number of derangements

10. Find all distinct subset sums of an array

11. Find Nth Fibonacci number

12. House robber

13. Find minimum of jumps to reach end

14. 0/1 Knapsack problem

15. Unbounded knapsack

16. Longest common increasing subsequence (LCS + LIS)

17. Find longest common subsequence (LCS)

18. Find longest common substring

19. Find longest increasing subsequence (LIS)

20. Longest palindromic subsequence (LPS)

21. Maximum size of square sub-matrix with all 1s

22. Min cost path

23. Minimum insertions to form a palindrome

24. Find the minimum number of edits

25. Number of unique BST with N keys

26. Maximize number segments of cutted in length x, y and z

27. Find number of ways paint a fence with n posts and k colors

28. Partition a set into two subsets of equal sum

29. Pascal's Triangle

30. Regular expression wildcard pattern matching

31. Find number of permutation with K inversions

32. Print maximum number of A’s using given four keys

33. Stacking box

34. Subsequence with difference of 1

35. Subset sum

36. Maximize total tips

37. Find Nth Tribonacci number

38. Count unique paths in matrix from top left to bottom right

39. Weighted interval job scheduling

40. Word Break

Backtracking

A backtracking algorithm tries to construct a solution to a computational problem incrementally, one small piece at a time. Whenever the algorithm needs to decide between multiple alternatives to the next component of the solution, it recursively evaluates every alternative and then chooses the best one.

1. Find largest divisible subset in array

2. The Knight's tour problem

3. Permutations of a given string

4. Rat in a maze

Sort

Sorting algorithms move elements in a list into a specific order. They work by comparing elements to determine their order, and then moving them into a new order.

1. Bubble Sort

2. Merge Sort

3. Quick Sort

Search

Search algorithms work by analyzing a user's query and finding the most relevant results.

1. Array Subset

2. Common in 3 Sorted Arrays

3. Search missing element from array

4. Find second largest in an array of positive integers

5. Search subarray whose sum equals a target value

Hash

1. Array Subset

Array

An array algorithm works by utilizing the structure of an array to efficiently access and manipulate data using indices.

1. Count occurrences

2. Find duplicate

3. Find the majority element in the array

4. Find minimum and maximum of an array using minimum number of comparisons

5. Move negative to the beginning

6. Find peak element in array

7. Reverse an array

8. Cyclically rotate

9. Sort an array of 0s, 1s and 2s

10. Sort array

Linked list

1. Check if a linked list is circular

Queue

Stack

1. The celebrity

Matrix

Most matrix algorithms use nested loops to iterate through the rows and columns of the matrices, performing the necessary calculations for each element of the resulting matrix

1. Boolean matrix

2. Print boundary elements of a matrix

3. Find common elements in all rows in one iteration

4. Find number of islands inside a matrix.

5. Find max number in each row of a matrix

6. Multiplay two matrices

7. Find peaks inside matrix

8. Rotate matrix clockwise by 1

9. Rotate matrix 180 degree

10. Rotate matrix 270 degree

11. Rotate matrix 90 degree

12. Sort matrix in a strict order

13. Find max sub rectangle

14. Transpose of Matrix

15. Travesal matrix in a spiral form

Tree

Heap

Graph

A graph algorithm works by traversing the nodes and edges of a graph, following the connections between them to solve a specific problem, like finding the shortest path between two nodes, identifying connected components, or detecting cycles, by exploring the graph step-by-step based on a set of rules, often using techniques like Depth-First Search (DFS) or Breadth-First Search (BFS) to visit each node in a structured order.

1. Bellman–Ford algorithm

2. Dijkstra's algorithm

3. Floyd Warshall algorithm

4. Find shortest path in an unweighted graph

Number

A "number algorithm" generally performs mathematical operations on numbers. The core of a number algorithm involves basic mathematical operations like addition, subtraction, multiplication, and division, often combined in complex ways depending on the problem.

1. Find the factorial of a large number

String

A string algorithm, also called a string matching algorithm, generally searching for occurrences of a "pattern" within a "text" by comparing characters at each position and shifting the pattern along the text until a match is found.

1. Convert Decimal number between 1 to 3999 to Roman numbers

2. Number of Distinct Subsequences

3. Given a number N, check if it is divisible by 7 or not.

4. Encrypt string

5. Find equal point of brackets in a string

6. Isomorphic strings

7. Check if two strings are k-anagrams or not

8. Find longest common prefix in list of strings

9. Find minimum distance between the given two words

10. Find minimum number of deletions to make a string palindrome

11. Panagram checking

12. Reverse words

13. Convert Roman number to integer

14. Check if string is rotated by two places

Dynamic Programming

Recursive algorithms, while conceptually elegant, can be computationally expensive due to overlapping subproblems. Dynamic Programming techniques, encompassing memoization and tabulation, mitigate this inefficiency by storing the solutions to these subproblems. This allows for efficient retrieval and reuse of previously computed results, leading to a substantial improvement in the algorithm's overall time complexity.

1. Arrange balls
   [Memoization] [Tabulation]

2. Find Binomial coefficient
   [Memoization] [Tabulation]

3. Find Nth Catalan Number
   [Memoization] [Tabulation]

4. Climbing stairs with 3 moves
   [Memoization] [Tabulation]

5. Climbing stairs
   [Memoization] [Tabulation]

6. Find minimum coins to make change
   [Memoization] [Tabulation]

7. Find number of way to make coin change
   [Memoization] [Tabulation]

8. Find all subsequence combinations of a string
   [Memoization] [Tabulation]

9. Count number of derangements
   [Memoization] [Tabulation]

10. Find all distinct subset sums of an array
    [Memoization] [Tabulation]

11. Find Nth Fibonacci number
    [Memoization] [Tabulation]

12. House robber
    [Memoization] [Tabulation]

13. Find minimum of jumps to reach end
    [Memoization] [Tabulation]

14. 0/1 Knapsack problem
    [Memoization] [Tabulation]

15. Unbounded knapsack
    [Memoization] [Tabulation]

16. Longest common increasing subsequence (LCS + LIS)
    [Memoization] [Tabulation]

17. Find longest common subsequence (LCS)
    [Memoization] [Tabulation]

18. Find longest common substring
    [Memoization] [Tabulation]

19. Find longest increasing subsequence (LIS)
    [Memoization] [Tabulation]

20. Longest palindromic subsequence (LPS)
    [Memoization] [Tabulation]

21. Maximum size of square sub-matrix with all 1s
    [Memoization] [Tabulation]

22. Min cost path
    [Memoization] [Tabulation]

23. Minimum insertions to form a palindrome
    [Memoization] [Tabulation]

24. Find the minimum number of edits
    [Memoization] [Tabulation]

25. Number of unique BST with N keys
    [Memoization] [Tabulation]

26. Maximize number segments of cutted in length x, y and z
    [Memoization] [Tabulation]

27. Find number of ways paint a fence with n posts and k colors
    [Memoization] [Tabulation]

28. Partition a set into two subsets of equal sum
    [Memoization] [Tabulation]

29. Pascal's Triangle
    [Memoization] [Tabulation]

30. Regular expression wildcard pattern matching
    [Memoization] [Tabulation]

31. Find number of permutation with K inversions
    [Memoization] [Tabulation]

32. Print maximum number of A’s using given four keys
    [Memoization] [Tabulation]

33. Stacking box
    [Memoization] [Tabulation]

34. Subsequence with difference of 1
    [Memoization] [Tabulation]

35. Subset sum
    [Memoization] [Tabulation]

36. Maximize total tips
    [Memoization] [Tabulation]

37. Find Nth Tribonacci number
    [Memoization] [Tabulation]

38. Count unique paths in matrix from top left to bottom right
    [Memoization] [Tabulation]

39. Weighted interval job scheduling
    [Memoization] [Tabulation]

40. Word Break
    [Memoization] [Tabulation]

Branch and bound

Greedy

A greedy algorithm is a problem-solving technique that chooses the best option at each step, with the goal of finding a globally optimal solution. Greedy algorithms are simple and easy to implement, but they don't always produce the best solution.

1. Fractional Knapsack