主题笔记：猜想-验证系列一<迭代和while循环>

在计算机的各种算法中有一种名为“迭代”（Iteration）的算法。这种算法利用了计算机“一个球落地时能计算10亿次”的特性，不断地对问题进行循环验证。这又被抽象为“猜想-验证"（Guess and Check）方法。

About Guess and Check Method：

• Guess and check methods can work on problems with a finite number of possibilities

进一步，猜想-验证方法的本质是穷举法（Exhaustive enumeration）。人脑的特性决定了在计算方面我们使用穷举法的代价非常大，可是计算机却可以轻易地实现。

About Exhaustive Enumeration:

• Exhaustive enumeration is a good way to generate guesses in an organized manner

• literally walk through all possible values of some parameter, some elements of the computation

• test everything until find the right answer

那么这些思想反映到计算机编程内体现出什么样子呢？并且教学语言为Python，更为准确的说，是反映到Python语言里是什么样子呢？答案：循环（loop）

about loop characteristics:

• Need a loop variable

- Initialized outside loop 
- Change within loop 
- Test for termination depends on variable 

• Useful to think about a decrementing function

- Maps set of program variables into an interger
- When loop is entered, value is non-negative (use absolute <abs>)
- When value is <= 0, loop terminates 
- Value is decreased every time through loop

Looping structure compares to branching structure:

• Branching structure (conditionals) let us jump to different pieces of code based on a test

- program are constant time

• Looping structure (e.g. while) let us repeat pieces of code until a condition is satisfied (be false)

• programs now take time depends on values of varibles as well as length of program

Instances of while loop:

num = 10
while True:
    if num < 7:
        print ('Breaking out of loop')
        break
    print (num)
    num -= 1
print ('Outside of loop')

num = 0
while num <= 5:
    print (num)
    num += 1

print ("Outside of loop")
print (num)

num = 2
while num < 12:
    print (num)
    num += 2
print ('Goodbye!')

num = 10
print ('Hello!')
while num >0:
    print (num)
    num -= 2

total = 0
current =1
end = int(input('enter your postive num:'))
while current <= end:
    total += current
    current += 1
print(total)