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Author: je-suis-tm

pascal triangle with memory.py

@@ -0,0 +1,84 @@
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Apr 13 17:06:21 2018
+
+@author: terry.mai
+"""
+import datetime as dt
+
+def row(n): 
+ list=[] 
+ if n==1: 
+#base case
+ return [1] 
+ else: 
+ for i in range(1,len(row(n-1))): 
+#rolling sum all the values with 2 windows from the previous row 
+#but we cannot include two boudary numbers 1 in this list 
+ temp=row(n-1)[i]+row(n-1)[i-1] 
+ list.append(temp) 
+#append 1 for both front and rear of the list 
+ list.insert(0,1) 
+ list.append(1) 
+ 
+ return list 
+ 
+def printit(n): 
+ for j in range(1,n+1): 
+ print(row(j)) 
+ return 
+ 
+#---------------------
+
+#introduce a global dictionary
+#the function is basically the same as the previous one
+#except we add one more if function
+#to see if we can find pas[n] in dictionary
+#if so, we return the output
+#if not, we append it to dictionary for future use
+global dict
+dict={1:[1]}
+def pas(n):
+ if n in dict:
+ return dict[n]
+ else:
+ list=[] 
+ if n==1: 
+#base case
+ return dict[1] 
+ else: 
+ for i in range(1,len(row(n-1))): 
+#rolling sum all the values with 2 windows from the previous row 
+#but we cannot include two boudary numbers 1 in this list 
+ temp=pas(n-1)[i]+pas(n-1)[i-1] 
+ list.append(temp) 
+#append 1 for both front and rear of the list 
+ list.insert(0,1) 
+ list.append(1) 
+ dict[n]=list
+ 
+ return dict[n]
+
+def printit2(n): 
+ for j in range(1,n+1): 
+ print(pas(j)) 
+ return 
+ 
+ 
+#-----------------
+#comparison between recursion with memory and without memory
+#use datetime now to capture the time and take the difference 
+def compare(n):
+ t1=dt.datetime.now()
+ printit(n)
+ t2=dt.datetime.now()
+ 
+ 
+ t3=dt.datetime.now()
+ printit2(n)
+ t4=dt.datetime.now()
+ 
+ print('without memory:',t2-t1,'\nwith memory',t4-t3)
+ return
+
+compare(12)