Algorithms Tutorial

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Practice Problems on all Algorithms

What is an Algorithm?

The word Algorithm means “A set of rules to be followed in calculations or other problem-solving operations” Or “A procedure for solving a mathematical problem in a finite number of steps that frequently involves recursive operations “.

Therefore Algorithm refers to a sequence of finite steps to solve a particular problem.

Algorithms can be simple and complex depending on what you want to achieve.

Introduction to Algorithms:

• What is Algorithm | Introduction to Algorithms
• Definition, Types, Complexity, Examples of Algorithms
• Algorithms Design Techniques
• Why is analysis of an Algorithm important?

Analysis of Algorithms:

• Asymptotic Analysis
• Worst, Average and Best Cases
• Asymptotic Notations
• Lower and Upper Bound Theory
• Introduction to Amortized Analysis
• What does ‘Space Complexity’ mean?
• Polynomial Time Approximation Scheme
• Accounting Method | Amortized Analysis
• Potential Method in Amortized Analysis

Searching and Sorting:

• Introduction to Searching Algorithms
• Introduction to Sorting Algorithm
• Stable and Unstable Sorting Algorithms
• Lower bound for comparison based sorting algorithms
• Can Run Time Complexity of a comparison-based sorting algorithm be less than N logN?
• Which sorting algorithm makes minimum number of memory writes?

Greedy Algorithms:

• Introduction to Greedy Algorithms
• Activity Selection Problem
• Huffman Coding
• Job Sequencing Problem
• Quiz on Greedy Algorithms
• Minimum Number of Platforms Required for a Railway/Bus Station

Dynamic Programming:

• Introduction to Dynamic Programming
• Overlapping Subproblems Property
• Optimal Substructure Property
• Longest Increasing Subsequence
• Longest Common Subsequence
• Min Cost Path
• Coin Change
• Matrix Chain Multiplication
• 0-1 Knapsack Problem
• Longest Palindromic Subsequence
• Palindrome Partitioning

Pattern Searching:

• Introduction to Pattern Searching
• Naive Pattern Searching
• KMP Algorithm
• Rabin-Karp Algorithm
• Pattern Searching using a Trie of all Suffixes
• Aho-Corasick Algorithm for Pattern Searching
• Z algorithm (Linear time pattern searching Algorithm)

Backtracking:

• Introduction to Backtracking
• Print all permutations of a given string
• The Knight’s tour problem
• Rat in a Maze
• N Queen Problem
• Subset Sum
• m Coloring Problem
• Hamiltonian Cycle
• Sudoku

Divide and Conquer:

• Introduction to Divide and Conquer
• Merge Sort
• Write your own pow(x, n) to calculate x*n
• Count Inversions
• Closest Pair of Points
• Strassen’s Matrix Multiplication

Geometric Algorithm:

• Introduction to Geometric Algorithms
• Closest Pair of Points | O(nlogn) Implementation
• How to check if a given point lies inside or outside a polygon?
• How to check if two given line segments intersect?
• Given n line segments, find if any two segments intersect
• How to check if given four points form a square
• Convex Hull using Jarvis’ Algorithm or Wrapping

Mathematical Algorithms:

• Introduction to Mathematical Algorithms
• Write an Efficient Method to Check if a Number is Multiple of 3
• Write a program to add two numbers in base 14
• Program for Fibonacci numbers
• Average of a stream of numbers
• Multiply two integers without using multiplication, division and bitwise operators, and no loops
• Babylonian method for square root
• Sieve of Eratosthenes
• Pascal’s Triangle
• Given a number, find the next smallest palindrome
• Program to add two polynomials
• Multiply two polynomials
• Count trailing zeroes in factorial of a number

Bitwise Algorithms:

• Introduction to Bitwise Algorithms
• Little and Big Endian
• Detect opposite signs
• Swap bits
• Turn off the rightmost set bit
• Rotate bits
• Next higher number with same number of set bits
• Swap two nibbles in a byte

Graph Algorithms:

• Introduction to Graph Algorithms
• BFS, DFS
• Cycles in Graph
• Shortest paths
• MST
• Topological Sorting
• Connectivity
• Max Flow

Randomized Algorithms:

• Introduction to Randomized Algorithms
• Linearity of Expectation
• Expected Number of Trials until Success
• Randomized Algorithms | Set 0 (Mathematical Background)
• Randomized Algorithms | Set 1 (Introduction and Analysis)
• Randomized Algorithms | Set 2 (Classification and Applications)
• Randomized Algorithms | Set 3 (1/2 Approximate Median)
• Reservoir Sampling

Branch and Bound:

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

Quizzes:

• Analysis of Algorithms
• Sorting
• Divide and Conquer
• Greedy Algorithms
• Dynamic Programming
• Backtracking
• NP Complete
• Searching
• Recursion
• Bit Algorithms