Merge pull request #694 from 7saheelahmed/7dev

Added new coding problem

Author: matthewsamuel95

DP/Recursive_Staircase_Problem/recursive_staircase_problem_python_steps_DP.py

@@ -0,0 +1,49 @@
+# There's a staircase with N steps, and you can climb 1 or 2 steps at a time. Given N, write a function that returns the number of unique
+# ways you can climb the staircase. The order of the steps matters.
+
+# For example, if N is 4, then there are 5 unique ways:
+
+# 1, 1, 1, 1
+# 2, 1, 1
+# 1, 2, 1
+# 1, 1, 2
+# 2, 2
+
+# What if, instead of being able to climb 1 or 2 steps at a time, you could climb any number from a set of positive integers X? 
+# For example, if X = {1, 3, 5}, you could climb 1, 3, or 5 steps at a time. Generalize your function to take in X.
+
+# Solution using Dynamic Programming
+
+# TC : O(N*|x|)
+# SC : O(N)
+
+def num_ways_X(n):
+    if n==0:
+        return 1
+    total = 0
+    for i in x:
+        if n-i>=0:
+            total+=num_ways_X(n-i)
+    
+    return total
+
+def num_ways_dp(n):
+    if n==0:
+        return 1
+    temp = [0]*(n+1)
+    temp[0] = 1
+    i = 1
+    while i<n+1:
+        total=0
+        for j in x:
+            if i-j>=0:
+                total+=temp[i-j]
+        temp[i]=total        
+        i+=1        
+    return temp[n]
+
+x = [1,3,5]
+for i in range(1,40):
+    print(num_ways_dp(i))
+   
+