From f67553296ce2a5b8600ae3358c920b187c10e534 Mon Sep 17 00:00:00 2001
From: jackfiled <xcrenchangjun@outlook.com>
Date: Tue, 20 Aug 2024 11:58:29 +0800
Subject: [PATCH] 20240820 Finished

---
 src/problem/mod.rs                            |  3 +-
 ..._number_of_ways_to_reach_the_k_th_stair.rs | 56 +++++++++++++++++++
 2 files changed, 58 insertions(+), 1 deletion(-)
 create mode 100644 src/problem/p3154_find_number_of_ways_to_reach_the_k_th_stair.rs

diff --git a/src/problem/mod.rs b/src/problem/mod.rs
index 6e82130..a0c4841 100644
--- a/src/problem/mod.rs
+++ b/src/problem/mod.rs
@@ -210,4 +210,5 @@ mod p3117_minimum_sum_of_values_by_dividing_array;
 mod p3137_minimum_number_of_operations_to_make_word_k_periodic;
 mod p551_student_attendance_record_i;
 
-mod p552_student_attendance_record_ii;
\ No newline at end of file
+mod p552_student_attendance_record_ii;
+mod p3154_find_number_of_ways_to_reach_the_k_th_stair;
\ No newline at end of file
diff --git a/src/problem/p3154_find_number_of_ways_to_reach_the_k_th_stair.rs b/src/problem/p3154_find_number_of_ways_to_reach_the_k_th_stair.rs
new file mode 100644
index 0000000..f52ace6
--- /dev/null
+++ b/src/problem/p3154_find_number_of_ways_to_reach_the_k_th_stair.rs
@@ -0,0 +1,56 @@
+/**
+ * [3154] Find Number of Ways to Reach the K-th Stair
+ */
+pub struct Solution {}
+
+
+// submission codes start here
+
+impl Solution {
+    pub fn ways_to_reach_stair(k: i32) -> i32 {
+        let mut n = 0;
+        let mut pos = 1;
+        let mut result = 0;
+
+        loop {
+            if pos - n - 1 <= k && k <= pos {
+                result += Self::combine(n + 1, pos - k);
+            }
+            
+            if pos - n - 1 > k {
+                break;
+            }
+            
+            n += 1;
+            pos *= 2;
+        }
+        
+        result
+    }
+
+    /// C_n^k = \frac{n * (n - 1) * .. * (n - k + 1)}{1 * 2 * 3 * ... * k}
+    fn combine(n : i32, k: i32) -> i32 {
+        let mut result: i64 = 1;
+        let (n, k) = (n as i64, k as i64);
+        
+        for i in (n - k + 1..=n).rev() {
+            result *= i;
+            result /= n - i  + 1;
+        }
+        
+        result as i32
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_3154() {
+        assert_eq!(2, Solution::ways_to_reach_stair(0));
+        assert_eq!(4, Solution::ways_to_reach_stair(1));
+    }
+}