Origami reaches the height of Mount Everest (for&while loop, closed function loop)

How many times do you fold a paper with a thickness of 0.1mm in half to reach a height of 8848180mm, the height of Mount Everest.

_{(This note is suitable for coders who are familiar with loops and lists)}

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How many times to fold 0.1mm thick paper in half

Origami reaches the height of Mount Everest

(Height can reach 8848180mm, the height of Mount Everest)

Quality score of this article:

【 97 】
This article address:
https://blog.csdn.net/m0_57158496/article/details/134168298

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Directory

◆?Origami reaches the height of Mount Everest
- 1. Topic description
- - 1.1 Screenshot of the problem
  - 1.2 Screenshot “Defects”
- 2. Algorithm analysis
- - 2.1 Question Analysis
  - 2.2 Python code (for & amp;power of 2)
  - 2.3 Loop×2
  - 2.4 Python bit operations<<1 instead of ×2
  - 2.5 Simple while
  - 2.6 Function self-calling (closure) loop

◆?Origami reaches the height of Mount Everest

1. Title description

1.1 Screenshot of the problem

Screenshot of question description

How many times can a paper with a thickness of 0.1mm be folded in half to reach a height of 8848180mm, the height of Mount Everest

1.2 Screenshot “Defect”

[The question comes from the CSDN Q&A community question “Origami reaches the height of Mount Everest”]

The questioner is not familiar with loops yet, so he needs to read more books.

?
The number of loops in this question is “uncertain”. For loops with an uncertain number of times, it is most suitable to use the while keyword to construct a loop body.

Back to table of contents

2. Algorithm analysis

Screenshot of code running effect

This topic is a loop × 2, and there is no algorithm discussion. I tried to talk about using for and while to solve it through various code forms.

2.1 Question Analysis

Analyze the question and “dig” the meaning of the question. For programming problem solving, after “understanding” the problem, you have to carry out data design (structured data) and code expression according to the determined algorithm, and finally organize the statements to output the expected conclusion.
?
1. When the paper in this question is folded in half, each increase in height is an increase in the power of 2.
?
2. Another point is, pay attention to the description in parentheses “fold it in half again and it will exceed”. If the exit loop condition we set is h >= 8848180, the return value will be one less than the current number of loops, that is, print(k-1 ).
?
3. Another point is that the initial value of paper thickness is 0.1 instead of 0. Why do you have to be so serious? Because it is possible that 0.1 may affect the result by folding in half.

Back to table of contents

2.2 Python code (for & amp;power of 2)

Python code (for)

mountQomolangma = 8848180

for i in range(1, int(1e8)): # For an uncertain number of loops, if you have to use for, just get a large value that you can think of. It is just a decoration anyway. I set 1 million here.
    paperHigh = 0.1*2**i + 0.1
    
    if paperHigh >= mountQomolangma:
        break #

print(f"\
Paper with a thickness of 0.1mm, folded in half {<!-- -->i} times, height {<!-- -->paperHigh}mm, folded in half {<!-- -->i-1 }can reach the height of Mount Everest {<!-- -->mountQomolangma}mm.")

The efficiency of writing code in this way will be low. Each loop is calculating the power of 2. You can use loop × 2 instead, which will be more efficient.

Back to table of contents

2.3 Loop×2

Loop×2 code

mountQomolangma = 8848180
paperHigh = 0.1

for i in range(1, int(1e8)): # For an uncertain number of loops, if you have to use for, just get a large value that you can think of. It is just a decoration anyway. I set 1 million here.
    paperHigh *= 2
    
    if paperHigh >= mountQomolangma:
        break #Exit the loop.

print(f"\
Paper with a thickness of 0.1mm, folded in half {<!-- -->i} times, height {<!-- -->paperHigh}mm, folded in half {<!-- -->i-1 }can reach the height of Mount Everest {<!-- -->mountQomolangma}mm.")

Every time it is ×2, it will be faster to use bit operations. If the binary number is shifted left by one bit <<1, the value it represents is doubled, thus completing the ×2 operation.

Back to table of contents

2.4 Python bit operations<<1 instead of ×2

Bit operation<<1 replaces ×2 code

mountQomolangma = 8848180
paperHigh = 1

for i in range(1, int(1e8)): # For an uncertain number of loops, if you have to use for, just get a large value that you can think of. It is just a decoration anyway. I set 1 million here.
    paperHigh <<= 1
    
    if paperHigh/10 >= mountQomolangma:
        break #Exit the loop.

print(f"\
Paper with a thickness of 0.1mm, folded in half {<!-- -->i} times, height {<!-- -->paperHigh}mm, folded in half {<!-- -->i-1 }can reach the height of Mount Everest {<!-- -->mountQomolangma}mm.")

Back to table of contents

2.5 Concise while

Or while loop, the code should be simpler, just put the while keyword in the if condition and then make the switch.

Concise while code

mountQomolangma = 8848180
paperHigh = 1
k = 0

while paperHigh/10 < mountQomolangma:
    k+=1
    paperHigh <<= 1

print(f"\
Paper with a thickness of 0.1mm, folded {<!-- -->k} times in height {<!-- -->paperHigh/10}mm, folded in half {<!-- -->k} -1} can reach the height of Mount Everest {<!-- -->mountQomolangma}mm.")

Back to table of contents

2.6 Function self-calling (closure) loop

Can a loop be implemented without using the for and while keywords? The answer is yes. In python, there is a "package" called "closure", which can implement data transfer like recursion. "Closure" is actually an encapsulated cyclic space structure formed by the self-invocation of a function, that is, a layer of "scopes", and data "penetrates" between each layer of scope through function parameters. Just like the cycle, the focus is on reasonable switch settings so that the "closure" can be "broken", narcissistic and "reversed" in a timely manner. Otherwise, we will really "enter the reincarnation of eternal destruction."

For the understanding of closures, I feel a little uncomfortable when looking at for and while. Regarding fundamental weaknesses in programming, coders with smaller coding capabilities are slightly less readable. But the code structure is still rigorous and concise.

Closure function implements loop

def fold(h, paper, k):
    
    if (paper + 1)/10 < h:
        return fold(h, paper<<1, k + 1)
    else:
        print(f"\
A paper with a thickness of 0.1mm, folded in half {<!-- -->k} times, the height is {<!-- -->(paper + 1)/10}mm, folded in half {<!-- -->k-1} can reach the height of Mount Everest {<!-- -->mountQomolangma}mm.")


if __name__ == '__main__':
    mountQomolangma = 8848180
    fold(mountQomolangma, 1, 0)

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