From 5a4efd75dbbaf4e53306a4f6786143a931243a43 Mon Sep 17 00:00:00 2001
From: Matej Focko <me@mfocko.xyz>
Date: Fri, 26 Jan 2024 13:35:04 +0100
Subject: [PATCH] =?UTF-8?q?rs:=20add=20=C2=AB576.=20Out=20of=20Boundary=20?=
 =?UTF-8?q?Paths=C2=BB?=
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Signed-off-by: Matej Focko <me@mfocko.xyz>
---
 rs/out-of-boundary-paths.rs | 58 +++++++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 rs/out-of-boundary-paths.rs

diff --git a/rs/out-of-boundary-paths.rs b/rs/out-of-boundary-paths.rs
new file mode 100644
index 0000000..5e0f234
--- /dev/null
+++ b/rs/out-of-boundary-paths.rs
@@ -0,0 +1,58 @@
+use std::collections::HashMap;
+
+const CAP: i64 = 1000000007;
+
+struct DPSolver {
+    m: i32,
+    n: i32,
+    max_move: i32,
+    dp: Vec<HashMap<i32, i64>>,
+}
+
+impl DPSolver {
+    pub fn new(m: i32, n: i32, max_move: i32) -> Self {
+        let dp = vec![HashMap::new(); (m as usize) * (n as usize)];
+        Self { m, n, max_move, dp }
+    }
+
+    fn index(&self, y: i32, x: i32) -> usize {
+        (y * self.n + x) as usize
+    }
+
+    fn dfs(&mut self, y: i32, x: i32, moves: i32) -> i64 {
+        if y < 0 || y >= self.m || x < 0 || x >= self.n {
+            // BASE: we got out of the bounds
+            return 1;
+        }
+
+        if moves <= 0 {
+            // BASE: all moves were used or there are no moves left
+            return 0;
+        }
+
+        let idx = self.index(y, x);
+
+        if let Some(paths) = self.dp[idx].get(&moves) {
+            return *paths;
+        }
+
+        let mut options = 0;
+        for (dx, dy) in [(0, 1), (1, 0), (0, -1), (-1, 0)] {
+            options = (options + self.dfs(y + dy, x + dx, moves - 1)) % CAP;
+        }
+
+        self.dp[idx].insert(moves, options);
+        options
+    }
+
+    pub fn get(&mut self, y0: i32, x0: i32) -> i32 {
+        self.dfs(y0, x0, self.max_move) as i32
+    }
+}
+
+struct Solution {}
+impl Solution {
+    pub fn find_paths(m: i32, n: i32, max_move: i32, start_row: i32, start_column: i32) -> i32 {
+        DPSolver::new(m, n, max_move).get(start_row, start_column)
+    }
+}