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

Source: Dev.to

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

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 its 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

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).

Neighbor helper

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 on:

• Marking nodes as visited.
• Avoiding revisits.
• 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 per level, etc.

Goal of Phase 1
You are comfortable writing BFS/DFS on grids and trees without hesitation and have a clean, reusable traversal template in your notes.

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

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

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

Visual example

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

2C. Cycle detection

• Undirected graphs – DFS with a parent parameter; a visited neighbor that isn’t the parent indicates a cycle.
• Directed graphs – DFS with three colors (unvisited, visiting, visited) or a recursion‑stack set.

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

Phase 3: Topological Sort and Shortest Paths

3A. Topological sort (ordering with prerequisites)

Two common approaches:

• Kahn’s algorithm (BFS‑based using in‑degrees).
• DFS + stack (reverse post‑order).

Typical pattern: nodes = tasks/courses, edge u → v means “u must come before v.” Topological order is any ordering consistent with the dependencies.

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, so BFS from a source naturally yields the minimum number of steps. Example: shortest path in a grid without weights.

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

After mastering BFS/DFS + toposort, learn Dijkstra’s algorithm with a min‑heap. You don’t need every weighted‑shortest‑path variant to pass most interviews, but recognizing when BFS suffices vs. when Dijkstra is required is key.

Weekly Practice Plan for Graph Beginners

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 an 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 help you generate custom problem sets and get instant feedback as you follow this roadmap.