Update README.md and factorial.py

Author: maliknaik16

README.md

@@ -0,0 +1,20 @@
+
+# Dynamic Programming
+
+## Optimal Substructure Property
+
+It means that the optimal solution to the problem can be formulated from the optimal solution to smaller instances of the same problem.
+Example: `f(n) = f(n - 1) + f(n - 2)`. Problem of size n reduced to `n - 1` and `n - 2`.
+
+
+
+## Overlapping Subproblems
+
+The smaller problems, which are needed to solve the bigger problem, are called multiple times while solving.
+
+Example: `f(n) = f(n - 1) + f(n - 2)`, `f(n - 1) = f(n - 2) + f(n - 3)`. `f(n - 2)` is required at least twice to solve this.
+
+
+# References
+* https://www.hackerrank.com/topics/dynamic-programming
+* https://www.geeksforgeeks.org/dynamic-programming/

factorial.py

@@ -1,12 +1,24 @@
 
 # Bottom-up and Top-down Dynamic Programming example for Factorial program.
+from utils import *
+import time
 
 # Initialize factorial list with all -1's
-factorial = [-1 for _ in range(30)]
+factorial = [-1 for _ in range(901)]
 
 # Set 0! to 1
 factorial[0] = 1
 
+def classic_factorial(n):
+ """
+ Factorial function without Dynamic Programming
+ """
+
+ if n <= 1:
+ return 1
+ else:
+ return n * classic_factorial(n - 1)
+
 def bottom_up_factorial(n):
  """
  Tabulation or Bottom-up approach to finding factorial of a number.
@@ -39,12 +51,25 @@ def top_down_factorial(n):
 
  return factorial[n]
 
+def print_time(func_name):
 
-if __name__ == '__main__':
-
- print(bottom_up_factorial(7))
- print(bottom_up_factorial(8))
+ start = get_current_time()
+ print('Running %s function to compute 900!' % (func_name.__name__, ))
+ answer = func_name(900)
+ diff = get_time_diff_ms(start)
+ print('Execution taken: %f ms' % (diff, ))
 
- print(top_down_factorial(7))
- print(top_down_factorial(6))
+if __name__ == '__main__':
 
+ print_time(classic_factorial)
+ print_time(bottom_up_factorial)
+ print_time(top_down_factorial)
+
+# Results
+#
+# Running classic_factorial function to compute 900!
+# Execution taken: 1.060247 ms
+# Running bottom_up_factorial function to compute 900!
+# Execution taken: 0.600815 ms
+# Running top_down_factorial function to compute 900!
+# Execution taken: 0.008583 ms