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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 Finding a Peak 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: Maximum Number of Prizes

Solve the Distinct Summands Problem.

We'll cover the following

Problem
Coding exercise

Problem

Distinct Summands Problem

Represent a positive integer as the sum of the maximum number of pairwise distinct positive integers.

Input: An integer $n$ .
Output: The maximum $k$ such that $n$ can be represented as the sum $a_{1}$ $+ \ldots +$ $a_{k}$ of $k$ distinct integers.

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