Alex Hunter

Posted on Dec 12 • Originally published at leetcopilot.dev

How to Practice Graph Problems on LeetCode for Beginners: A Structured Roadmap

#leetcode #bfs #dfs #graphs

Originally published on LeetCopilot Blog

Graphs feel overwhelming if you jump in randomly. This roadmap walks LeetCode beginners through a staged, pattern-first way to master graph problems without getting lost.

Arrays and strings were hard at first, but at least they felt familiar. Graphs, on the other hand, can feel like stepping into a different world:

Adjacency lists vs matrices
BFS vs DFS vs Dijkstra
Directed vs undirected, cycles, components, topological order

If you open a random Medium graph problem on LeetCode as a beginner, it’s easy to get discouraged and conclude: “I’m just not good at graphs.”

You’re not the problem. Your practice path is.

This guide gives you a structured roadmap for how to practice graph problems on LeetCode for beginners—what to start with, how to group problems, and how to build confidence step by step.

TL;DR

Don’t start with random graph problems; start with unweighted BFS/DFS on grids and simple trees, then progress to adjacency lists, then to topological sort and shortest paths.
Practice graphs in clusters by pattern (BFS, DFS, connected components, topo sort, shortest paths) instead of jumping around, so your brain can actually see the common structure.
Use visual diagrams (nodes, edges, levels) to reason about graph behavior before coding, especially for BFS levels and cycle detection.
Beginners often skip basic grid/graph modeling, avoid drawing, and jump to Dijkstra/Union-Find too early, which kills confidence and retention.
A simple 3-phase roadmap, supported by a DSA learning path and tools like AI-guided LeetCode practice, can make graph problems feel systematic instead of chaotic.

Phase 0: Get Comfortable with the Mental Model of a Graph

Before touching code, make sure “graph” means something concrete in your head.

What is a graph?

At its core, a graph is:

A set of nodes (vertices).
A set of edges connecting nodes (possibly directed).

Visual example:

   A ---- B
   |      |
   |      |
   C ---- D

You can model many LeetCode problems as graphs:

Grids (each cell is a node connected to neighbors).
Course prerequisites (nodes = courses, edges = “must take before”).
Social networks, city maps, dependency graphs.

Minimal code representation

For most beginner problems, adjacency lists are enough:

from collections import defaultdict

graph = defaultdict(list)
for u, v in edges:
    graph[u].append(v)
    graph[v].append(u)  # if undirected

Once you’re comfortable with this, the rest of graph algorithms become much easier.

Phase 1: Grids and Trees – Your Gentle Graph On-Ramp

Step 1 is to master “graph thinking” in environments that feel familiar: grids and trees.

1A. Grids as implicit graphs

Problems like “Number of Islands” or “Rotting Oranges” are graph problems in disguise:

Each cell (r, c) is a node.
Edges connect it to up/down/left/right neighbors (if valid).

Use BFS or DFS with a simple neighbor loop:

directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]

def neighbors(r, c, rows, cols):
    for dr, dc in directions:
        nr, nc = r + dr, c + dc
        if 0 <= nr < rows and 0 <= nc < cols:
            yield nr, nc

Focus here on:

Marking nodes as visited.
Avoiding revisiting the same cell.
Understanding how BFS explores by layers.

1B. Trees as simpler graphs

Binary tree problems are “graphs with structure and no cycles.”

Practice:

DFS (recursive and iterative) for depth, path sums, subtree checks.
BFS (level-order) for distances, averages by level, etc.

Goal of Phase 1:

You are comfortable writing BFS/DFS on grids and trees without much hesitation.
You have a clean, reusable traversal template in your notes.

Phase 2: Explicit Graphs – Adjacency Lists, Components, and Cycles

Once grids and trees feel okay, graduate to explicit graphs.

2A. Build the graph yourself

Given n nodes and an edges list:

def build_graph(n, edges):
    graph = [[] for _ in range(n)]
    for u, v in edges:
        graph[u].append(v)
        graph[v].append(u)  # if undirected
    return graph

Practice problems that ask:

“How many connected components?”
“Is this graph bipartite?”
“Is there a path between X and Y?”

2B. Connected components with DFS/BFS

Idea:

Iterate over all nodes; if unvisited, start a BFS/DFS and mark everything reachable.
Increment your component count.

Visual:

Component 1: 0 - 1 - 2
Component 2: 3 - 4
Component 3: 5

2C. Cycle detection (undirected vs directed)

For undirected graphs:

DFS with a parent parameter; if you see a visited neighbor that isn't the parent, there's a cycle.

For directed graphs:

DFS with three colors (unvisited, visiting, visited) or recursion stack tracking.

This is your first step into problems that require more than “just traversal.”

Phase 3: Topological Sort and Shortest Paths

With basic BFS/DFS and components in place, you’re ready for:

3A. Topological sort (ordering with prerequisites)

Use:

Kahn’s algorithm (BFS-based with in-degrees), or
DFS + stack reversed at the end.

Classic pattern:

Nodes = tasks/courses.
Edge u → v = "u must come before v."
Topological order is any order consistent with dependencies.

Toposort problems are core to interviews and appear in many curated lists. For more interview prep guidance, see how to run mock coding interviews by yourself.

3B. Shortest paths in unweighted graphs

Use BFS:

Each edge has cost 1.
BFS from a source naturally finds the shortest number of steps.

Example: shortest path in a grid without weights.

3C. Shortest paths with weights (optional for beginners)

Once you’re comfortable:

Learn Dijkstra’s algorithm with a min-heap.
Only after BFS/DFS + toposort feel normal.

You don’t need to master every weighted shortest-path variant to pass most interviews, but recognizing when BFS is enough vs when you need Dijkstra is key.

Weekly Practice Plan for Graph Beginners

Here's a realistic 3–4 week plan that fits into a broader DSA learning path.

Week 1 – Grids & Trees

3–4 “Number of Islands”–style grid problems.
2–3 tree BFS problems (level order, average per level).
2–3 tree DFS problems (max depth, path sum).

Week 2 – Explicit Graphs & Components

3 problems: build adjacency lists and traverse.
2 problems: count connected components.
2 problems: detect cycles in undirected graphs.

Week 3 – Directed Graphs & Toposort

2–3 problems: detect cycles in directed graphs.
2–3 problems: course schedule / task ordering via topological sort.
1–2 problems: BFS shortest path in unweighted graph.

Optional Week 4 – Weighted Graphs

2–3 Dijkstra-style problems (shortest path with weights).
1–2 problems mixing graphs with other patterns.

Tools like AI-guided LeetCode practice can pre-select problems for each phase so you don't waste energy deciding "what next?" every day.

Common Mistakes to Avoid

Mistake 1: Skipping Phase 1 (grids/trees)

Jumping straight into complex graph problems without mastering BFS/DFS on grids and trees is like jumping into calculus without being solid on algebra.

Mistake 2: Not drawing the graph

Many bugs come from misreading edges. A 30-second sketch of nodes and arrows can save you 10–15 minutes of confusion.

Mistake 3: Forgetting visited sets

Missing or misusing visited leads to:

Infinite loops.
Overcounting components.
Incorrect cycle detection.

Mistake 4: Practicing in random order

Solving one BFS, then one Dijkstra, then one toposort, then a tree problem doesn’t give your brain enough repetition to see patterns. Cluster your practice.

FAQ

Q1: Do I need to learn every graph algorithm for interviews?

No. For most roles, solid BFS/DFS, components, cycle detection, and toposort cover a large portion of graph questions. Weighted shortest paths and Union-Find are useful additions but can come later.

Q2: How many graph problems should I solve before interviews?

Quality beats quantity. Solving 25–35 graph problems across the core patterns (grids, trees, adjacency lists, toposort, shortest paths) with good review is better than 80 random attempts.

Q3: I understand the solution but forget it a week later. What should I do?

Use a simple notes system where each problem is tagged by pattern and includes the key idea, a small diagram, and a short pseudocode sketch. Regular review sessions, supported by a DSA learning path, turn those notes into long-term memory.

Q4: Should I focus on BFS or DFS first?

Start with whichever feels more natural, but don’t neglect the other. BFS is essential for shortest paths and levels; DFS is essential for structure, cycles, and backtracking.

Q5: How do I know when I’m “ready” for harder graph problems?

When you can look at a new graph problem and quickly decide “this is BFS/DFS/toposort/shortest path,” you’re ready to tackle more complex variations and company-specific questions.

Conclusion

Learning graphs on LeetCode doesn’t require innate talent—it requires a good sequence.

Start with grids and trees, graduate to adjacency lists and components, then add toposort and shortest paths. Practice each pattern in focused clusters, use diagrams, and review your notes regularly.

With a structured roadmap and deliberate practice, graph problems stop being scary puzzles and start feeling like just another category of patterns you know how to navigate.

If you're looking for an AI assistant to help you master LeetCode patterns and prepare for coding interviews, check out LeetCopilot.

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