added dynamic programming notebook

02-Dynamic-Programming.ipynb

+%% Cell type:markdown id: tags:
+
+# CO202 - Software Engineering - Algorithms
+
+%% Cell type:markdown id: tags:
+
+## Tutorial on Dynamic Programming: Fibonacci
+
+%% Cell type:markdown id: tags:
+
+### Naive Divide-and-Conquer Approach
+
+%% Cell type:code id: tags:
+
+``` python
+def naive_fib(n):
+    if n == 0:
+        return 0
+    elif n == 1:
+        return 1
+    else:
+        return naive_fib(n-1) + naive_fib(n-2)
+
+print(naive_fib(10))
+%timeit naive_fib(10)
+```
+
+%% Cell type:markdown id: tags:
+
+### Bottom-up Dynamic Programming Approach
+
+%% Cell type:code id: tags:
+
+``` python
+def dp_fib(n):
+    if n == 0:
+        return 0
+    f = [0]*(n+1)
+    f[0] = 0
+    f[1] = 1
+    for i in range(2,n+1):
+        f[i] = f[i-1] + f[i-2]
+    return f[n]
+
+print(dp_fib(10))
+%timeit dp_fib(10)
+```
+
+%% Cell type:markdown id: tags:
+
+### Comparison
+
+%% Cell type:markdown id: tags:
+
+#### Timer
+
+%% Cell type:code id: tags:
+
+``` python
+import time
+
+def time_f(f):
+    before = time.clock()
+    f()
+    after = time.clock()
+    return after - before
+```
+
+%% Cell type:markdown id: tags:
+
+#### Test data
+
+%% Cell type:code id: tags:
+
+``` python
+data = range(1,20)
+#data = range(1,30)
+#data = range(1,1000,10)
+#data = range(1,10000,100)
+#data = range(1,100000,1000)
+```
+
+%% Cell type:markdown id: tags:
+
+#### Running Divide-and-Conquer
+
+%% Cell type:code id: tags:
+
+``` python
+tdc = []
+
+for i in data:
+    tdc.append(time_f(lambda: naive_fib(i)))
+```
+
+%% Cell type:markdown id: tags:
+
+#### Running Dynamic Programming
+
+%% Cell type:code id: tags:
+
+``` python
+tdp = []
+
+for i in data:
+    tdp.append(time_f(lambda: dp_fib(i)))
+```
+
+%% Cell type:markdown id: tags:
+
+#### Plot DC vs DP
+
+%% Cell type:code id: tags:
+
+``` python
+%matplotlib inline
+from matplotlib import pyplot as plt
+
+plt.scatter(data, tdc, c='red')
+plt.scatter(data, tdp, c='blue')
+plt.xlabel('n')
+plt.ylabel('time (/s)')
+plt.xlim(0)
+plt.ylim(0)
+```
+
+%% Cell type:code id: tags:
+
+``` python
+```