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The Snakes and Ladders board can be seen as a graph where each square is a node, and an edge exists between node i and node j if you can move from square i to square j with a dice roll. Use BFS to efficiently explore this graph, ensuring each move accounts for ladders and snakes.
Time Complexity: O(n^2), where n is the board dimension, as each square is processed once.
Space Complexity: O(n^2), for storing the queue and visited status of squares.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int SnakesAndLadders(int[][] board) {
6 int n = board.Length;
7 int CalculatePosition(int num) {
8 int quot = (num - 1) / n, rem = (num - 1) % n;
9 int row = n - 1 - quot;
10 int col = (quot % 2 == 0) ? rem : (n - 1 - rem);
11 return board[row][col];
12 }
13
14 var visited = new bool[n * n + 1];
15 Queue<(int, int)> queue = new Queue<(int, int)>();
16 queue.Enqueue((1, 0));
17 visited[1] = true;
18
19 while (queue.Count > 0) {
20 var (pos, moves) = queue.Dequeue();
21 for (int i = 1; i <= 6; i++) {
22 int nextPos = pos + i;
23 if (nextPos > n * n) continue;
24
25 int boardValue = CalculatePosition(nextPos);
26 if (boardValue != -1) nextPos = boardValue;
27
28 if (!visited[nextPos]) {
29 if (nextPos == n * n) return moves + 1;
30 visited[nextPos] = true;
31 queue.Enqueue((nextPos, moves + 1));
32 }
33 }
34 }
35
36 return -1;
37 }
38}The C# implementation mirrors other BFS solutions, employing a tuple in the queue for position and moves, navigating the board as per snakes and ladders, and using a helper to calculate current board values.
Dijkstra's Algorithm typically finds shortest paths in weighted graphs. Adapting it for an unweighted snakes and ladders board can ensure the fewest moves to reach the final square by evaluating and using priority. Each move is computed implicitly based on its dice-distance weight.
Time Complexity: O(n^2 log(n^2)), given heap operations for prioritized traversal.
Space Complexity: O(n^2) for heap management.
1
Java's solution focuses on leveraging Dijkstra's structure with priority queue capabilities, minimizing moves cost at each step during navigation of the board.