Create climbing_stairs.py (#1002)

a simple dp problem seen on LeetCode:  https://leetcode.com/problems/climbing-stairs/

dynamic_programming/climbing_stairs.py

@@ -0,0 +1,27 @@
+def climb_stairs(n: int) -> int:
+  """
+  LeetCdoe No.70: Climbing Stairs
+  Distinct ways to climb a n step staircase where
+  each time you can either climb 1 or 2 steps. 
+
+  Args:
+      n: number of steps of staircase
+
+  Returns:
+      Distinct ways to climb a n step staircase 
+
+  Raises:
+      AssertionError: n not positive integer
+
+  >>> climb_stairs(3) 
+  3
+  >>> climb_stairs(1)
+  1
+  """
+  assert isinstance(n,int) and n > 0, "n needs to be positive integer, your input {0}".format(0)
+  if n == 1: return 1 
+  dp = [0]*(n+1)
+  dp[0], dp[1] = (1, 1)
+  for i in range(2,n+1): 
+      dp[i] = dp[i-1] + dp[i-2]
+  return dp[n]