Add solution 0909

leetcode/0909.Snakes-and-Ladders/909. Snakes and Ladders.go

@@ -0,0 +1,42 @@
+package leetcode
+
+type pair struct {
+	id, step int
+}
+
+func snakesAndLadders(board [][]int) int {
+	n := len(board)
+	visited := make([]bool, n*n+1)
+	queue := []pair{{1, 0}}
+	for len(queue) > 0 {
+		p := queue[0]
+		queue = queue[1:]
+		for i := 1; i <= 6; i++ {
+			nxt := p.id + i
+			if nxt > n*n { // 超出边界
+				break
+			}
+			r, c := getRowCol(nxt, n) // 得到下一步的行列
+			if board[r][c] > 0 {      // 存在蛇或梯子
+				nxt = board[r][c]
+			}
+			if nxt == n*n { // 到达终点
+				return p.step + 1
+			}
+			if !visited[nxt] {
+				visited[nxt] = true
+				queue = append(queue, pair{nxt, p.step + 1}) // 扩展新状态
+			}
+		}
+	}
+	return -1
+}
+
+func getRowCol(id, n int) (r, c int) {
+	r, c = (id-1)/n, (id-1)%n
+	if r%2 == 1 {
+		c = n - 1 - c
+	}
+	r = n - 1 - r
+	return r, c
+}

leetcode/0909.Snakes-and-Ladders/909. Snakes and Ladders_test.go

@@ -0,0 +1,45 @@
+package leetcode
+
+import (
+	"fmt"
+	"testing"
+)
+
+type question909 struct {
+	para909
+	ans909
+}
+
+// para 是参数
+// one 代表第一个参数
+type para909 struct {
+	one [][]int
+}
+
+// ans 是答案
+// one 代表第一个答案
+type ans909 struct {
+	one int
+}
+
+func Test_Problem909(t *testing.T) {
+	qs := []question909{
+		{
+			para909{[][]int{
+				{-1, -1, -1, -1, -1, -1},
+				{-1, -1, -1, -1, -1, -1},
+				{-1, -1, -1, -1, -1, -1},
+				{-1, 35, -1, -1, 13, -1},
+				{-1, -1, -1, -1, -1, -1},
+				{-1, 15, -1, -1, -1, -1},
+			}},
+			ans909{4},
+		},
+	}
+	fmt.Printf("------------------------Leetcode Problem 909------------------------\n")
+	for _, q := range qs {
+		_, p := q.ans909, q.para909
+		fmt.Printf("【input】:%v       【output】:%v\n", p, snakesAndLadders(p.one))
+	}
+	fmt.Printf("\n\n\n")
+}

leetcode/0909.Snakes-and-Ladders/README.md

@@ -0,0 +1,110 @@
+# [909. Snakes and Ladders](https://leetcode.com/problems/snakes-and-ladders/)
+
+
+## 题目
+
+On an N x N `board`, the numbers from `1` to `N*N` are written *boustrophedonically* **starting from the bottom left of the board**, and alternating direction each row.  For example, for a 6 x 6 board, the numbers are written as follows:
+
+
+![](https://assets.leetcode.com/uploads/2018/09/23/snakes.png)
+
+You start on square `1` of the board (which is always in the last row and first column).  Each move, starting from square `x`, consists of the following:
+
+- You choose a destination square `S` with number `x+1`, `x+2`, `x+3`, `x+4`, `x+5`, or `x+6`, provided this number is `<= N*N`.
+    - (This choice simulates the result of a standard 6-sided die roll: ie., there are always **at most 6 destinations, regardless of the size of the board**.)
+- If `S` has a snake or ladder, you move to the destination of that snake or ladder. Otherwise, you move to `S`.
+
+A board square on row `r` and column `c` has a "snake or ladder" if `board[r][c] != -1`.  The destination of that snake or ladder is `board[r][c]`.
+
+Note that you only take a snake or ladder at most once per move: if the destination to a snake or ladder is the start of another snake or ladder, you do **not** continue moving.  (For example, if the board is `[[4,-1],[-1,3]]`, and on the first move your destination square is `2`, then you finish your first move at `3`, because you do **not** continue moving to `4`.)
+
+Return the least number of moves required to reach square N*N.  If it is not possible, return `-1`.
+
+**Example 1:**
+
+```
+Input:[
+[-1,-1,-1,-1,-1,-1],
+[-1,-1,-1,-1,-1,-1],
+[-1,-1,-1,-1,-1,-1],
+[-1,35,-1,-1,13,-1],
+[-1,-1,-1,-1,-1,-1],
+[-1,15,-1,-1,-1,-1]]
+Output:4
+Explanation:
+At the beginning, you start at square 1 [at row 5, column 0].
+You decide to move to square 2, and must take the ladder to square 15.
+You then decide to move to square 17 (row 3, column 5), and must take the snake to square 13.
+You then decide to move to square 14, and must take the ladder to square 35.
+You then decide to move to square 36, ending the game.
+It can be shown that you need at least 4 moves to reach the N*N-th square, so the answer is 4.
+
+```
+
+**Note:**
+
+1. `2 <= board.length = board[0].length <= 20`
+2. `board[i][j]` is between `1` and `N*N` or is equal to `1`.
+3. The board square with number `1` has no snake or ladder.
+4. The board square with number `N*N` has no snake or ladder.
+
+## 题目大意
+
+N x N 的棋盘 board 上，按从 1 到 N*N 的数字给方格编号，编号 从左下角开始，每一行交替方向。r 行 c 列的棋盘，按前述方法编号，棋盘格中可能存在 “蛇” 或 “梯子”；如果 board[r][c] != -1，那个蛇或梯子的目的地将会是 board[r][c]。玩家从棋盘上的方格 1 （总是在最后一行、第一列）开始出发。每一回合，玩家需要从当前方格 x 开始出发，按下述要求前进：选定目标方格：
+
+- 选择从编号 x+1，x+2，x+3，x+4，x+5，或者 x+6 的方格中选出一个目标方格 s ，目标方格的编号 <= N*N。该选择模拟了掷骰子的情景，无论棋盘大小如何，你的目的地范围也只能处于区间 [x+1, x+6] 之间。
+- 传送玩家：如果目标方格 S 处存在蛇或梯子，那么玩家会传送到蛇或梯子的目的地。否则，玩家传送到目标方格 S。
+
+注意，玩家在每回合的前进过程中最多只能爬过蛇或梯子一次：就算目的地是另一条蛇或梯子的起点，你也不会继续移动。返回达到方格 N*N 所需的最少移动次数，如果不可能，则返回 -1。
+
+## 解题思路
+
+- 这一题可以抽象为在有向图上求下标 1 的起点到下标 `N^2` 的终点的最短路径。用广度优先搜索。棋盘可以抽象成一个包含 `N^2` 个节点的有向图，对于每个节点 `x`，若 `x+i (1 ≤ i ≤ 6)` 上没有蛇或梯子，则连一条从 `x` 到 `x+i` 的有向边；否则记蛇梯的目的地为 `y`，连一条从 `x` 到 `y` 的有向边。然后按照最短路径的求解方式便可解题。时间复杂度 O(n^2)，空间复杂度 O(n^2)。
+- 此题棋盘上的下标是蛇形的，所以遍历下一个点的时候需要转换坐标。具体做法根据行的奇偶性，行号为偶数，下标从左往右，行号为奇数，下标从右往左。具体实现见 `getRowCol()` 函数。
+
+## 代码
+
+```go
+package leetcode
+
+type pair struct {
+	id, step int
+}
+
+func snakesAndLadders(board [][]int) int {
+	n := len(board)
+	visited := make([]bool, n*n+1)
+	queue := []pair{{1, 0}}
+	for len(queue) > 0 {
+		p := queue[0]
+		queue = queue[1:]
+		for i := 1; i <= 6; i++ {
+			nxt := p.id + i
+			if nxt > n*n { // 超出边界
+				break
+			}
+			r, c := getRowCol(nxt, n) // 得到下一步的行列
+			if board[r][c] > 0 {      // 存在蛇或梯子
+				nxt = board[r][c]
+			}
+			if nxt == n*n { // 到达终点
+				return p.step + 1
+			}
+			if !visited[nxt] {
+				visited[nxt] = true
+				queue = append(queue, pair{nxt, p.step + 1}) // 扩展新状态
+			}
+		}
+	}
+	return -1
+}
+
+func getRowCol(id, n int) (r, c int) {
+	r, c = (id-1)/n, (id-1)%n
+	if r%2 == 1 {
+		c = n - 1 - c
+	}
+	r = n - 1 - r
+	return r, c
+}
+```