feat: add initial implementation of minimum path sum solution

64_minimum_path_sum/Cargo.lock

@@ -0,0 +1,7 @@
+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
+
+[[package]]
+name = "minimum_path_sum"
+version = "0.1.0"

64_minimum_path_sum/Cargo.toml

@@ -0,0 +1,6 @@
+[package]
+name = "minimum_path_sum"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]

64_minimum_path_sum/src/main.rs

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+use std::cmp::Reverse;
+
+fn main() {
+    println!("Hello, world!");
+}
+
+struct Solution;
+
+impl Solution {
+    pub fn min_path_sum(grid: Vec<Vec<i32>>) -> i32 {
+        let directions: Vec<(usize, usize)> = vec![(1, 0), (0, 1)];
+        let rows = grid.len();
+        let cols = grid[0].len();
+
+        let mut visited = vec![vec![false; cols]; rows];
+
+        let mut distances = vec![vec![i32::MAX; cols]; rows];
+        distances[0][0] = grid[0][0];
+
+        let mut priority_queue = std::collections::BinaryHeap::<Reverse<Point>>::new();
+        priority_queue.push(Reverse(Point {
+            distance: distances[0][0],
+            loc: (0, 0),
+        }));
+
+        while !priority_queue.is_empty() {
+            let current = priority_queue.pop().unwrap().0;
+
+            visited[current.loc.0][current.loc.1] = true;
+
+            if current.loc == (rows - 1, cols - 1) {
+                return current.distance;
+            }
+
+            for &direction in &directions {
+                let new_loc = (current.loc.0 + direction.0, current.loc.1 + direction.1);
+                if new_loc.0 >= rows || new_loc.1 >= cols {
+                    continue;
+                }
+                if visited[new_loc.0][new_loc.1] {
+                    continue;
+                }
+
+                let new_distance = current.distance + grid[new_loc.0][new_loc.1];
+                if new_distance < distances[new_loc.0][new_loc.1] {
+                    distances[new_loc.0][new_loc.1] = new_distance;
+                    priority_queue.push(Reverse(Point {
+                        distance: new_distance,
+                        loc: new_loc,
+                    }));
+                }
+            }
+        }
+
+        0
+    }
+}
+
+#[derive(PartialEq, Eq, PartialOrd)]
+struct Point {
+    distance: i32,
+    loc: (usize, usize),
+}
+
+impl Ord for Point {
+    fn cmp(&self, other: &Self) -> std::cmp::Ordering {
+        self.distance
+            .cmp(&other.distance)
+            .then(self.loc.cmp(&other.loc))
+    }
+}