What signals in a problem statement indicate the Implicit graph / state BFS sub-pattern?

"minimum number of moves / turns / transformations"; a rule for one move: turn one wheel, change one letter, a knight's jump, a dice roll; a set of forbidden states (deadends, word list)

Implicit graph / state BFS (Graph BFS / DFS Sub-pattern)

Q: What makes Implicit graph / state BFS different from other sub-patterns?

**Knight** and **Open the Lock** are the template: neighbours come from a fixed list of moves. **Snakes and Ladders** needs a square → (row, col) mapping and takes a snake or ladder at most once per move. **The Maze** only counts cells where the ball **stops**, not every cell it rolls over. **Word Ladder** builds neighbours by trying all 26 letters at each position and counts words, not changes.

The nodes aren't given; they are states (codes, words, squares) and you generate each state's neighbours when you pop it.

Signals in the problem statement

›
"minimum number of moves / turns / transformations"
›
a rule for one move: turn one wheel, change one letter, a knight's jump, a dice roll
›
a set of forbidden states (deadends, word list)

What makes it different

Knight and Open the Lock are the template: neighbours come from a fixed list of moves. Snakes and Ladders needs a square → (row, col) mapping and takes a snake or ladder at most once per move. The Maze only counts cells where the ball stops, not every cell it rolls over. Word Ladder builds neighbours by trying all 26 letters at each position and counts words, not changes.

Questions

ordered from “learn the idea” to “recognise it without help”

1
Minimum Steps to Reach Target by a Knight
Basic Anchor·GeeksforGeeks
WalkthroughMedium
2
Open the Lock
Basic Reinforcement·LeetCode #752
WalkthroughMedium
3
Snakes and Ladders
Slight Variation·LeetCode #909
WalkthroughMedium
4
The Maze
Medium·LeetCode #490 Premium
WalkthroughMedium
5
Word Ladder
Pattern Transfer·LeetCode #127
WalkthroughHard

Template

state-bfs-template.cpp

// State BFS: nodes are states (strings here), neighbours are generated on the fly.
int minMoves(const string& start, const string& goal, const unordered_set<string>& blocked) {
    if (blocked.count(start)) return -1;
    unordered_map<string, int> dist{{start, 0}};
    queue<string> q;
    q.push(start);
    while (!q.empty()) {
        string s = q.front(); q.pop();
        if (s == goal) return dist[s];
        for (int i = 0; i < (int)s.size(); i++)
            for (int step : {1, 9}) {                       // one wheel up or down (Open the Lock)
                string t = s;
                t[i] = char('0' + (t[i] - '0' + step) % 10);
                if (blocked.count(t) || dist.count(t)) continue;
                dist[t] = dist[s] + 1;
                q.push(t);
            }
    }
    return -1;
}

Remember this · Graph BFS / DFS

Trigger

Grid of cells, islands, regions, "minimum steps", transformations between states, connected components.

Think

What is a node, what is an edge, and do I need the shortest path or just reachability?

Key question

How do I mark visited so I never process a node twice?

Grid shortest path Graph connectivity