From d7b3b2a116e91833f86cadc69e6bfc80acbd5341 Mon Sep 17 00:00:00 2001
From: jackfiled <xcrenchangjun@outlook.com>
Date: Sat, 7 Dec 2024 12:17:37 +0800
Subject: [PATCH] 20241207 finished.

---
 src/problem/mod.rs                            |  2 +
 .../p688_knight_probability_in_chessboard.rs  | 62 +++++++++++++++++++
 2 files changed, 64 insertions(+)
 create mode 100644 src/problem/p688_knight_probability_in_chessboard.rs

diff --git a/src/problem/mod.rs b/src/problem/mod.rs
index bcf1d52..afd8daa 100644
--- a/src/problem/mod.rs
+++ b/src/problem/mod.rs
@@ -354,3 +354,5 @@ mod p2056_number_of_valid_move_combinations_on_chessboard;
 mod p3001_minimum_moves_to_capture_the_queen;
 
 mod p999_available_captures_for_rook;
+
+mod p688_knight_probability_in_chessboard;
diff --git a/src/problem/p688_knight_probability_in_chessboard.rs b/src/problem/p688_knight_probability_in_chessboard.rs
new file mode 100644
index 0000000..8e19d7c
--- /dev/null
+++ b/src/problem/p688_knight_probability_in_chessboard.rs
@@ -0,0 +1,62 @@
+/**
+ * [688] Knight Probability in Chessboard
+ */
+pub struct Solution {}
+
+// submission codes start here
+
+const DIRECTIONS: [(i32, i32); 8] = [
+    (-1, -2),
+    (1, -2),
+    (-1, 2),
+    (1, 2),
+    (-2, -1),
+    (2, -1),
+    (-2, 1),
+    (2, 1),
+];
+
+impl Solution {
+    pub fn knight_probability(n: i32, k: i32, row: i32, column: i32) -> f64 {
+        let (n, k) = (n as usize, k as usize);
+        let (row, column) = (row as usize, column as usize);
+
+        let mut dp = vec![vec![vec![0f64; n]; n]; k + 1];
+
+        for step in 0..=k {
+            for x in 0..n {
+                for y in 0..n {
+                    if step == 0 {
+                        dp[step][x][y] = 1f64;
+                    } else {
+                        for &(dx, dy) in DIRECTIONS.iter() {
+                            let nx = x as i32 + dx;
+                            let ny = y as i32 + dy;
+
+                            if nx >= 0 && nx < n as i32 && ny >= 0 && ny < n as i32 {
+                                let (nx, ny) = (nx as usize, ny as usize);
+
+                                dp[step][x][y] += dp[step - 1][nx][ny] / 8f64;
+                            }
+                        }
+                    }
+                }
+            }
+        }
+
+        dp[k][row][column]
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_688() {
+        assert_eq!(0.0625, Solution::knight_probability(3, 2, 0, 0));
+        assert_eq!(1.0, Solution::knight_probability(1, 0, 0, 0));
+    }
+}