Climbing stairs

Author: volodimyr

70.climbing_stairs/stairs.py

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+# 70. Climbing stairs
+# Topics: 'Math', 'Dynamic Programming', 'Memoization'
+
+# You are climbing a staircase. It takes n steps to reach the top.
+
+# Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?
+
+ 
+
+# Example 1:
+
+# Input: n = 2
+# Output: 2
+# Explanation: There are two ways to climb to the top.
+# 1. 1 step + 1 step
+# 2. 2 steps
+
+# Example 2:
+
+# Input: n = 3
+# Output: 3
+# Explanation: There are three ways to climb to the top.
+# 1. 1 step + 1 step + 1 step
+# 2. 1 step + 2 steps
+# 3. 2 steps + 1 step
+
+ 
+
+# Constraints:
+
+#     1 <= n <= 45
+
+from typing import List
+
+class Solution:
+   # time and space O(n)
+   def climbStairs(self, n: int) -> int:
+      memo = [0]*(n+1)
+      return self.climb(n, memo)
+   
+   def climb(self, n: int, memo: List[int]) -> int:
+      if n <= 1:
+         return 1
+      if memo[n]:
+         return memo[n]
+      memo[n] = self.climb(n-1, memo) + self.climb(n-2, memo)
+      return memo[n]
+
+   #  bruteforce solution O(2^n)
+   # def climbStairs(self, n: int) -> int:
+   #    if n <= 1:
+   #       return 1
+   #    return self.climbStairs(n-1) +  self.climbStairs(n-2)

70.climbing_stairs/test_stairs.py

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+import unittest
+from stairs import Solution
+
+class TestClimbStairs(unittest.TestCase):
+    def setUp(self):
+        self.s = Solution()
+    def test_small_values(self):
+        self.assertEqual(self.s.climbStairs(1), 1)
+        self.assertEqual(self.s.climbStairs(2), 2)
+        self.assertEqual(self.s.climbStairs(3), 3)
+        self.assertEqual(self.s.climbStairs(4), 5)
+
+    def test_medium_values(self):
+        # Fibonacci sequence logic
+        self.assertEqual(self.s.climbStairs(5), 8)
+        self.assertEqual(self.s.climbStairs(6), 13)
+        self.assertEqual(self.s.climbStairs(7), 21)
+
+    def test_larger_value(self):
+        # Warning: with naive recursion this may run slow!
+        self.assertEqual(self.s.climbStairs(10), 89)
+
+    def test_typical_leetcode_examples(self):
+        self.assertEqual(self.s.climbStairs(2), 2)
+        self.assertEqual(self.s.climbStairs(3), 3)
+
+
+if __name__ == "__main__":
+    unittest.main()