Graph Algorithm Problems in LeetCodeAnimation: Complete BFS and DFS Coverage

The LeetCodeAnimation repository provides animated solutions to seven core LeetCode graph algorithm problems utilizing Breadth-First Search (BFS) and Depth-First Search (DFS), covering tree traversals, island detection, graph cloning, and string state exploration.

The MisterBooo/LeetCodeAnimation repository is a curated collection of visual explanations for fundamental graph algorithm problems. Each markdown article pairs algorithmic theory with C++ implementations to demonstrate how BFS and DFS traversals solve complex interview questions. This guide examines every graph-related problem in the repository, detailing which traversal strategy each employs and where to find the source explanations.

BFS Graph Algorithm Solutions

Breadth-First Search implementations in the repository focus on level-order processing, shortest-path discovery in unweighted state spaces, and iterative graph exploration using queues.

Level Order Traversal (Problem 102)

In 0102-Binary-Tree-Level-Order-Traversal/Article/0102-Binary-Tree-Level-Order-Traversal.md, the solution demonstrates classic BFS on a binary tree. The algorithm uses a queue storing pair<TreeNode*, int> objects to track nodes and their depths, dequeuing in FIFO order to produce level-wise output.

/// BFS
/// Time Complexity: O(n), Space Complexity: O(n)
class Solution {
public:
    vector<vector<int>> levelOrder(TreeNode* root) {
        vector<vector<int>> res;
        if (!root) return res;
        queue<pair<TreeNode*,int>> q;
        q.push({root,0});

        while (!q.empty()){
            auto [node, lvl] = q.front(); q.pop();
            if (lvl == (int)res.size()) res.emplace_back();
            res[lvl].push_back(node->val);
            if (node->left)  q.push({node->left,  lvl+1});
            if (node->right) q.push({node->right, lvl+1});
        }
        return res;
    }
};

Remove Invalid Parentheses (Problem 301)

The solution in notes/LeetCode第301号问题：删除无效的括号.md applies BFS to a string state graph. Starting from the original string, the algorithm generates all possible strings by removing one parenthesis per level, stopping at the first level that yields a valid expression—guaranteeing the minimum removal count.

Clone Graph (Problem 133)

As documented in 0133-Clone-Graph/Article/0133-Clone-Graph.md, the BFS approach traverses the original graph using a queue while maintaining an unordered_map<Node*, Node*> to track cloned nodes. Each neighbor is cloned on first visit and enqueued for subsequent processing.

Node* cloneGraph(Node* node){
    if (!node) return nullptr;
    unordered_map<Node*,Node*> mp;
    queue<Node*> q; q.push(node);
    mp[node] = new Node(node->val);
    while (!q.empty()){
        Node* cur = q.front(); q.pop();
        for (Node* nb : cur->neighbors){
            if (!mp.count(nb)){
                mp[nb] = new Node(nb->val);
                q.push(nb);
            }
            mp[cur]->neighbors.push_back(mp[nb]);
        }
    }
    return mp[node];
}

DFS Graph Algorithm Solutions

Depth-First Search implementations emphasize recursive traversal, flood-fill algorithms, and backtracking for exploring all possible paths or connected components.

Number of Islands (Problem 200)

The 0200-Number-of-Islands/Article/0200-Number-of-Islands.md article implements a flood-fill DFS. Each unvisited '1' triggers a recursive exploration that marks the entire island by changing cell values to '2', effectively counting connected components in a 2D grid.

void dfs(vector<vector<char>>& grid, int r, int c){
    if (r<0 || r>=grid.size() || c<0 || c>=grid[0].size() || grid[r][c]!='1')
        return;
    grid[r][c] = '2';                     // mark visited
    dfs(grid, r-1, c); dfs(grid, r+1, c);
    dfs(grid, r, c-1); dfs(grid, r, c+1);
}
int numIslands(vector<vector<char>>& grid){
    int cnt = 0;
    for (int i=0;i<grid.size();++i)
        for (int j=0;j<grid[0].size();++j)
            if (grid[i][j]=='1'){ dfs(grid,i,j); ++cnt; }
    return cnt;
}

Max Area of Island (Problem 695)

Found in 0695-Max-Area-of-Island/Article/0695-Max-Area-of-Island.md, this solution extends the flood-fill pattern to calculate island area. The DFS returns the size of each connected component, allowing the algorithm to track the maximum area encountered.

Maximum Depth of Binary Tree (Problem 104)

The article at 0104-Maximum-Depth-Of-Binary-Tree/Article/0104-Maximum-Depth-Of-Binary-Tree.md presents DFS as a post-order recursive traversal. The function computes depth by returning 1 + max(left_depth, right_depth) for each node, traversing to leaf nodes before calculating height.

Problems Supporting Both BFS and DFS

Several articles demonstrate both traversal strategies side-by-side, highlighting trade-offs between iterative queue-based and recursive stack-based approaches.

Palindrome Partitioning (Problem 131)

In 0131-Palindrome-Partitioning/Article/0131-Palindrome-Partitioning.md, the repository illustrates both methods: DFS explores all partition possibilities recursively through backtracking, while BFS can build partitions level-by-level, offering alternative perspectives on the state space exploration.

Clone Graph and Maximum Depth (Problems 133 and 104)

Both problems include dual-approach discussions. While the BFS implementations use explicit queues to avoid recursion depth limits, the DFS variants leverage the call stack for more concise code, as noted in 0133-Clone-Graph/Article/0133-Clone-Graph.md and 0104-Maximum-Depth-Of-Binary-Tree/Article/0104-Maximum-Depth-Of-Binary-Tree.md.

Summary

• Seven graph algorithm problems are covered: 102, 104, 131, 133, 200, 301, and 695
• BFS-specific problems: Level Order Traversal (102), Remove Invalid Parentheses (301), and Clone Graph (133) primarily demonstrate queue-based iteration
• DFS-specific problems: Number of Islands (200) and Max Area of Island (695) utilize recursive flood-fill; Maximum Depth (104) uses post-order recursion
• Dual-approach demonstrations: Palindrome Partitioning (131), Clone Graph (133), and Maximum Depth (104) explicitly compare both strategies
• Animation framework: All solutions utilize the anima/ package (anima/base.py, anima/create.py, anima/model.py) to generate visual step-by-step traversals

Frequently Asked Questions

Which LeetCode graph problems in the repository use BFS exclusively?

Problem 102 (Binary Tree Level Order Traversal) and Problem 301 (Remove Invalid Parentheses) utilize BFS as their primary solution strategy. The level order traversal relies on a FIFO queue to process nodes by depth, while the parentheses removal treats each string modification as a level in an implicit state graph, guaranteeing minimal removals by stopping at the first valid level.

How does the repository visualize DFS recursion and BFS queues?

According to the source code structure, the anima/ directory contains the animation engine (anima/base.py, anima/create.py, anima/model.py) which generates visual steps for both traversals. For BFS, it visualizes queue operations and node visits by level; for DFS, it illustrates recursion unwinding, stack depth changes, and visited node marking—particularly evident in the island-flood-fill animations.

Are the implementations language-specific or abstract pseudocode?

While the repository stores concrete C++ implementations for all solutions, each markdown article (such as 0102-Binary-Tree-Level-Order-Traversal/Article/0102-Binary-Tree-Level-Order-Traversal.md) abstracts the algorithm with language-neutral descriptions before presenting the code. This dual-format approach ensures readers understand the graph theory independently of syntax.

What distinguishes the BFS and DFS approaches for cloning a graph in Problem 133?

The BFS approach in 0133-Clone-Graph/Article/0133-Clone-Graph.md uses an explicit queue and an unordered_map to iteratively clone nodes, avoiding stack overflow on deep graphs. The DFS approach uses the call stack to recursively visit neighbors, resulting in more compact code but potentially hitting recursion depth limits on large connected components—trade-offs explicitly discussed in the article.

{
  "mcpServers": {
    "instagit": {
      "command": "npx",
      "args": ["-y", "instagit@latest"]
    }
  }
}