 Expression Tree and Objects 1

Elements of Python  Literals, Strings, Tuples, Lists, …  The order of file reading  The order of execution 2

WHILE Loop 1. I = 0 2. WHILE I < 2: 3. I = I + 1 The order of execution is

IF statement 1. I = 3 2. IF I < 3: 3. PRINT “A” 4. ELIF I == 3: 5. PRINT “B” 6. ELSE: 7. PRINT “C” The order of execution is:

Quiz Time (~ 1:45 pm) 5

Guess what 1I = 0 2for e in get_names(): 3I = I + 1 1) What is the intention of the code writer? 2) What is the return type of get_names()? 3) What is the order of execution? 6

Guess what What is the result of following expressions? 1. “five” – “three” 3. 3 in 7 4. “one” += 1 7

Rules for operators ??? 8

Semantics I will buy a book. I will go to USA. I will go to a book. I will buy USA. 9

Semantics  Close the lid 10

Semantics  Even if a code is syntactically correct, the semantics could be wrong.  The type system determines the correctness of semantics. 1. “five” – “three”  The above examples are semantically wrong. 11

Operators  Algebraic Operator produces a numeric type. OP  OP   Logical Operator produces boolean type (True|False) OP  True or False OP  True of False  Assignment Operator stores a value into a variable. 12

Expression  With the help of the type system, an expression is reduced to another value.  Expression can appear as an input to any operator as long as the type of its evaluation is compatible.  For example +  number | string %  number  Can you guess the type of expression1,2,3, and 4? 13

Expression: more examples I = 0 for n in range(0,3): I = I + 1 What is the type of the evaluation of range(0,3)? 14

Expression: more examples 1.a = if : print “hello” 3.while : i = i + Guess the type of the evaluation result of expression1,2,3,4 15

Expression: more examples 1.if my_function(x): print x 2.while some_func(x,y,z) == 0: print x+y+z 3.if 3 in gen_func(a,b,c): print a,b,c What is the return type of my_function(), some_func(), and gen_func()? 16

The evaluation of Expressions 17

Expression Tree  Expression has a hierarchical structure * 9 n * factorial(n-1) 3 49 * + n factorial(n-1) * 18

Revisiting the summation  Compute … + 10 = ((((((0+1)+2)+3)+4) … ) + 10) 19

Revisiting the summation  Variable 20 SUM1 SUM2

Revisiting the summation (((((0+1)+2)+3)+4) … ) + 10  (((sum1+2)+3+4)…) + 10  (((sum2+3)+4)…+10  ((sum3+4)+…+10  sum9+10  sum10 21

Revisiting the summation  For each summation, we need 1, 2, 3, …, 10 in this order.  Suppose that the variable I will have that value inside a for loop.  Do you have an idea to represent this with FOR or WHILE? 22

Revisiting the summation SUM0 = 0 SUM1 = SUM0 + 1 SUM2 = SUM1 + 2 SUM3 = SUM2 + 3 … SUM10 = SUM Let’s replace with a variable n SUM0 = 0 n = 1 SUM1 = SUM0 + n n = 2 SUM2 = SUM1 + n n = 3 SUM3 = SUM2 + n n = n + 1 SUM4 = SUM3 + n n = n + 1 SUM5 = SUM4 + n … n = n + 1 SUM10 = SUM9 + n

Eureka!  We found a pattern! 24 It was … n = n + 1

Now  The summation is … SUM0 = 0 n = 1 SUM1 = SUM0 + n n = n + 1 SUM2 = SUM1 + n … n = n + 1 SUM10 = SUM9 + n 25 Wait! Do we use SUMx later? Nope! What happen if I overwrite the variable?

More patterns!  The summation is … SUM = 0 n = 1 SUM = SUM + n n = n + 1 SUM = SUM + n n = n + 1 … SUM = SUM + n n = n It is all the same! How many repetitions? I believe you can do with FOR or WHILE.

Revisiting the summation Compute … + 10 = ((((((0+1)+2)+3)+4) … ) + 10) The summation by looping is same as … sum = 0 sum = sum + 1 sum = sum + 2 sum = sum + 3 … 27

Revisiting the summation sum = sum = (0 + 1) + 2 sum = ((0 + 1) + 2) + 3 … sum = (((((0+1)+2)+3)+4) … )

Revisiting the summation sum = 0 for x in [1,2,3,4,5,6,7,8,9,10]: sum = sum + x After the loop unrolling … sum = 0 sum = sum + 1 sum = sum + 2 … sum = sum

Finding the minimum [3,1,2,4]  What is the minimum? Assume that a function min(x,y) returns a minimum between x and y. Then, 1) how do you implement min(x,y); 2) how to compute the minimum? The answer is min(min(min(3,1),2),4) 30

List and its operations, and Object 31

Mapping of a list Suppose a math function f(x). Write a function to create a list of sample values of f(x) where x is between 1 and 10. The input: [ 1, 2, …, 10 ]  range(1, 11) The Output: [ f(1), f(2), …, f(10) ] L = [] for e in range(1,11): L. append(f(e)) print L 32

Object  An object in Python is a combination of data and functions.  An object can be stored in a variable, which means we can use an assignment operator. L = [ 1,2,3 ]  Using ‘.’ operator, we can call the function of a given object; For example, L.append(4) 33

Object and Function  A typical function works only with a given data.  Many functions works with a collection of specific data.  Suppose that we have a function sum(L) that takes a list and return a number; sum( )   It might be simpler for some people to use L.sum() instead of sum(L). 34

Dot Operator The dot operator changes the way of function calling.. ( ) (, ) sum(L)  L.sum() 35

Append() function L = [] for e in range(0,3): L.append(e) produces L = [0,1,2] def my_append(L, e): return L + [e] L = my_append(L, e) +  36

Collecting data with a list  Find all even numbers between 1 and 10.  Two ways are possible: 1. Generation of even numbers: n = 0 n = n Discrimination of any number: test if n % 2 == 0 37

Collecting even numbers L = [] n = 0 while n < 11: n = n + 2 L.append(n) print L L = [] for e in range(1,11): if e%2 == 0: L.append(e) print L 38 Generation of 2’s multiples Testing if it is 2’s multiples

Generation vs. Discrimination  In general, generative methods are faster and clear.  However, those generative methods are not always available.  For example, finding prime numbers! There is no function f(n) where f(n) is the prime number close to a number n.  Discriminative methods are well suited to a computer. 39

40

41 # find_minimum(number,number) ==> number def find_minimum(x,y): if x > y: return y else: return x # (list) ==> number def find_minimum_of_list(L): return 0 print find_minimum(find_minimum(L[0],L[1]),L[2])

42 List Indexing Ordering elements in a list Advanced list handling Finding the minimum and maximum

The inner product The operation between two vectors: 43