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Algorithmic Problem Solving: Preparing for a Coding Interview

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Course Overview

Algorithms and Complexity

Introduction to Algorithms and Complexity Correct vs. Incorrect Algorithms Time Complexity of Algorithms

Runtime Algorithms

The Big-O Notation Advantages and Disadvantages of the Big-O Notation Five Common Rules for Analyzing the Runtime Visualize Common Rules for Runtime Analysis Frequently Arising Running Times Quiz: Running Time of Algorithms

Algorithm Design Techniques

Introduction to Algorithm Design Techniques Algorithm Design: Exhaustive Search Algorithms Algorithm Design: Branch-and-Bound Algorithms Algorithm Design: Greedy Algorithms Algorithm Design: Dynamic Programming Algorithms Algorithm Design: Recursive Algorithms Algorithm Design: Divide-and-Conquer Algorithms Algorithm Design: Randomized Algorithms Quiz: Algorithm Design Techniques

Programming Challenges

Introduction to Programming Challenges Challenge: Sum of Two Digits Solution: Sum of Two Digits Challenge: Maximum Pairwise Product Naive Solution: Maximum Pairwise Product Fast Solution: Maximum Pairwise Product Evaluating Solutions to Maximum Pairwise Product Problem Solving a Programming Challenge in Four Easy Steps Quiz: Programming Challenges

Good Programming Practices

Introduction to Good Programming Practices Code Formatting and Naming Guidelines Debugging and Code Optimization C++-Specific C++ Rules For Classes And Numbers Python-Specific Quiz: Good Programming Practices

Algorithmic Warm Up

Introduction to Algorithmic Warm Up Challenge: Fibonacci Number Solution: Fibonacci Number Challenge: Last Digit of the Fibonacci Number Solution: Last Digit of Fibonacci Number Challenge: Huge Fibonacci Number Solution: Huge Fibonacci Number Challenge: Last Digit of the Sum of Fibonacci Numbers Solution: Last Digit of the Sum of Fibonacci Numbers Challenge: Last Digit of the Partial Sum of Fibonacci Numbers Solution: Last Digit of the Partial Sum of Fibonacci Numbers Challenge: Last Digit of the Sum of Fibonacci Numbers’ Squares Solution: Last Digit of the Sum of Fibonacci Numbers’ Squares Challenge: Greatest Common Divisor Solution: Greatest Common Divisor Challenge: Least Common Multiple Solution: Least Common Multiple Quiz: Algorithmic Warm Up

Greedy Algorithms

Introduction to Greedy Algorithms Greedy Strategies Prove the Correctness of Greedy Algorithms Challenge: Money Change Solution: Money Change Challenge: Maximum Value of the Loot Solution: Maximum Value of the Loot Challenge: Car Fueling Solution: Car Fueling Challenge: Maximum Advertisement Revenue Solution: Maximum Advertisement Revenue Challenge: Collecting Signatures Solution: Collecting Signatures Challenge: Maximum Number of Prizes Solution: Maximum Number of Prizes Challenge: Maximum Salary Solution: Maximum Salary Quiz: Greedy Algorithms

Divide and Conquer Algorithm

Introduction to Divide-and-Conquer Algorithms

Guessing a Number

Searching Sorted Data

Finding a White-Black Pair

Multiplying Integers

The Master Theorem

Challenge: Sorted Array Multiple Search

Solution: Sorted Array Multiple Search

Challenge: Multiple Search with Duplicates

Solution: Multiple Search with Duplicates

Challenge: Majority Element

Solution: Majority Element

Challenge: Improving Quicksort

Solution: Improving Quicksort

Challenge: Number of Inversions

Solution: Number of Inversions

Challenge: Organizing a Lottery

Solution: Organizing a Lottery

Challenge: Closest Points

Solution: Closest Points

Quiz: Divide-and-Conquer Algorithms

Dynamic Programming

Introduction to Dynamic Programming Challenge: Money Change Again Solution: Money Change Again Challenge: Primitive Calculator Solution: Primitive Calculator Challenge: Edit Distance Solution: Edit Distance Challenge: Longest Common Subsequence of Two Sequences Solution: Longest Common Subsequence of Two Sequences Challenge: Longest Common Subsequence of Three Sequences Solution: Longest Common Subsequence of Three Sequences Challenge: Maximum Amount of Gold Solution: Maximum Amount of Gold Challenge: Splitting the Pirate Loot Solution: Splitting the Pirate Loot Challenge: Maximum Value of an Arithmetic Expression Solution: Maximum Value of an Arithmetic Expression Quiz: Dynamic Programming

Conclusion

Challenge: Number of Inversions

Solve the Number of Inversions Problem.

We'll cover the following

Problem
Coding exercise

Problem

Number of Inversions Problem

Compute the number of inversions in a sequence of integers.

Input: A sequence of $n$ integers $a_{1},\ldots,a_{n}$ .
Output: The number of inversions in the sequence—that is, the number of indices $i < j$ such that $a_{i} > a_{j}$ .

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