Unit

Data Structure and Algorithm IV

Advanced Algorithms: Graphs, DP (Dynamic Programming) – Practice with Curated LeetCode Questions

Graph

Graph Algorithm

Dynamic Programming

Duration

6 weeks

Introduction

Welcome to Data Structures and Algorithms IV. This unit covers two powerful problem-solving techniques: graph algorithms and dynamic programming. You'll learn how to break down complex problems into simpler parts and build efficient solutions step by step. Through practice with carefully selected LeetCode questions, you'll develop the skills to recognize common patterns, implement key algorithms, and optimize your code. These techniques are essential for technical interviews at top tech companies and will help you solve challenging programming problems in your career.

Prerequisites

Complete Data Structure and Algorithm III Unit.

Skills Covered

In this unit, we are going to cover the following topics.

Graphs: Master traversals (DFS/BFS), shortest-path (Dijkstra’s, Bellman-Ford), MSTs (Prim’s, Kruskal’s), topological sorting, and Union-Find for dynamic connectivity.

Dynamic Programming: Design optimal substructures (memoization/tabulation) for knapsack, string edits, and sequence alignment.

Recommended Study Material

Graph

Learn the basic of Graph data structure and its representation.

Graph

Data Structure

Duration:

10 minutes

Breath-first search

Learn to use breath first search and its implementation.

Graph

Algorithm

Duration:

30 minutes

Depth-first search

Learn to use breath first search and its implementation.

Graph

Algorithm

Duration:

30 minutes

Topological Sort

Learn about Topological sort and its implementation.

Graph

Algorithm

Sorting

Duration:

1 hour

Dijkstra's Algorithm

Learn to find single source shortest path using Dijkstra algorithm.

Graph

Algorithm

Duration:

1 hour

Bellman-Ford Algorithm

Learn to find single source shortest path using Dijkstra algorithm.

Graph

Algorithm

Duration:

1 hour

Prim's Algorithm

Learn to find minimum spannig tree using Prim’s algorithm.

Graph

Algorithm

Duration:

1 hour

Kruskal's Algorithm

Learn to find minimum spannig tree using Kruskal’s algorithm.

Graph

Algorithm

Duration:

30 minutes

Disjoint Sets

Design disjoint sets which supports makeSet, union and findSet operations.

Graph

Algorithm

Duration:

1 hour

Dynamic Programming

Learn the basics of memoization and dynamic programming.

Dynamic Programming

Duration:

30 minutes

Practice Problems

Status	Bookmark	Problem	Difficulty	Tags	Solution
		Island Perimeter	Easy
		Find the Town Judge	Easy
		Number of Islands	Medium
		Max Area of Island	Medium
		Time Needed to Inform All Employees	Medium
		All Paths From Source to Target	Medium
		Clone Graph	Medium
		Directed Graph Cycle	Medium
		Undirected Graph Cycle	Medium
		Is Graph Bipartite?	Medium
		All Nodes Distance K in Binary Tree	Medium
		Employee Importance	Medium
		Surrounded Regions	Medium
		Pacific Atlantic Water Flow	Medium
		Rotting Oranges	Medium
		01 Matrix	Medium
		Open the Lock	Medium
		Evaluate Division	Medium
		Graph Valid Tree	Medium
		Walls and Gates	Medium
		Course Schedule	Medium
		Course Schedule II	Medium
		Course Schedule IV	Medium
		Find Eventual Safe States	Medium
		Minimum Height Trees	Medium
		Redundant Connection	Medium
		Number of Provinces	Medium
		Number of Connected Components in an Undirected Graph	Medium
		Accounts Merge	Medium
		Network Delay Time	Medium
		Path With Minimum Effort	Medium
		Path with Maximum Probability	Medium
		Min Cost to Connect All Points	Medium
		Cheapest Flights Within K Stops	Medium
		Divide Nodes Into the Maximum Number of Groups	Hard
		Bus Routes	Hard
		Word Ladder	Hard
		Making A Large Island	Hard
		Sort Items by Groups Respecting Dependencies	Hard
		Alien Dictionary	Hard
		Minimize Malware Spread	Hard
		Swim in Rising Water	Hard
		Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree	Hard
		Reconstruct Itinerary	Hard
		Valid Arrangement of Pairs	Hard
		Climbing Stairs	Easy
		Min Cost Climbing Stairs	Easy
		N-th Tribonacci Number	Easy
		House Robber	Medium
		House Robber II	Medium
		Longest Palindromic Substring	Medium
		Palindromic Substrings	Medium
		Decode Ways	Medium
		Coin Change	Medium
		Maximum Product Subarray	Medium
		Word Break	Medium
		Longest Increasing Subsequence	Medium
		Partition Equal Subset Sum	Medium
		Combination Sum IV	Medium
		Integer Break	Medium
		Unique Paths	Medium
		Unique Paths II	Medium
		Minimum Path Sum	Medium
		Longest Common Subsequence	Medium
		Last Stone Weight II	Medium
		Best Time to Buy and Sell Stock with Cooldown	Medium
		Coin Change II	Medium
		Perfect Squares	Medium
		House Robber III	Medium
		Target Sum	Medium
		Interleaving String	Medium
		Stone Game	Medium
		Stone Game II	Medium
		Edit Distance	Medium
		Egg Drop With 2 Eggs and N Floors	Medium
		Super Egg Drop	Hard
		Burst Balloons	Hard
		Maximum Profit in Job Scheduling	Hard
		Word Break II	Hard
		Palindrome Partitioning II	Hard
		Regular Expression Matching	Hard
		Wildcard Matching	Hard

Credit

The problem set is carefully curated from Neetcode and AlgoMaster, supplemented with additional practice questions for comprehensive coverage.

Contributor(s)

John Doe

Founder and Fullstack Developer at freeCodeProject.org

Created this Unit with curated list of questions for practice.