练习解决问题技巧的最好方法是什么(一)
2022-08-16 汤沐之邑 5812
正文翻译

What is the best way to practice problem solving skills?

练习解决问题技巧的最好方法是什么?

评论翻译
Ara Mambreyan
I have solved thousands of problems in physics during my high school when I was preparing for International Physics Olympiads and a few hundred at University of Cambridge.
Last summer, I started preparing for Software Engineering internship applications. I solved a few hundred questions on HackerRank and, in a few weeks, I managed to get to a level necessary for good performance in interviews.
(I am telling you these so you would know that I am not BSing and actually know what I am talking about.)
When I first started problem-solving, I was bad. I was nowhere close to even a regional-Olympiads, let alone International!
I started solving problems during my physics club. It took me dozens of problems before I could up my level. I remember one day how I happily approached my teacher and told her: “I solved a National Olympiad question yesterday!”
Fast forward, two years and I was solving international Olympiad problems in ease!
How? What did I do? What’s the secret?

我在高中为国际物理奥林匹克竞赛做准备时,解决了数千个物理问题,在剑桥大学也解决了几百个。
去年夏天,我开始准备软件工程实习申请。我在竞赛算法练习方面解决了几百个问题,在几周内,我已经达到了在面试中取得好成绩所必需的水平。
(我告诉你这些,是为了让你知道我不是在说谎,也知道我在说什么。)
当我第一次开始解决问题时,我很差劲。我甚至连地区奥运会都没参加过,更别提国际奥运会了!
我在我参加物理俱乐部期间开始解决问题。我做了几十道题才提高了水平。我记得有一天,我高兴地走近我的老师,告诉她:“我昨天解决了一个全国奥林匹克运动会的问题!”
很快,两年过去了,我轻松地解决了国际奥林匹克竞赛的问题!
怎么做到了?我做了什么?有什么秘密吗?

The secret is…
JUST KEEP GOING.
Honestly, just keep solving problems and I guarantee that you would get better in this.
But DON’T just look up the solutions, and think that you solved the problem without understanding it and move on.
You need to think about the problems but most importantly you have to get value from it. When you look up the solution, do not just read it, say “yeah, whatever” in your mind and skip.
Instead, ask yourself, “why couldn’t I solve it? How could I have solved this?”

秘密是:坚持就好
老实说,只要继续解决问题,我保证你会做得更好。
但是,不要只是查找解决方案,在没有理解问题的情况下认为你就解决了问题,然后继续前进。
你需要思考问题,但最重要的是,你必须从中获得价值。当你查找解决方案时,不要只是阅读,在你的脑海里说“是啊,随便吧”,然后跳过。
相反,问问自己,“为什么我不能解决它?我怎么能解决这个问题?”

Maybe it’s lack of knowledge (e.g. you do not understand how the law of Mechanics works). If it’s knowledge, don’t problem-solve, but learn theory first.
Maybe you had to think out of the box. Learn from this experience. Note this down in your mind.
On and on, you do this, and your problem solving would increase. And not only it would be good in physics, but in math, in computer science, and in life.
The key point, however, is this:
EVERYONE STARTS FROM THE BOTTOM.
Nobody is born solving complex problems. Like any skill, problem-solving is developed.
Just keep doing it and you WILL get there. Believe me.

也许是因为缺乏知识(例如,你不了解力学定律是如何工作的)。如果是知识,不要去解决问题,而是先学习理论。
也许你需要打破常规。从这次经历中学习后把这些记在脑子里。
不断地重复做,你解决问题的能力就会提高。它不仅在物理方面会很好,在数学、计算机科学和生活方面也会很好。
然而,关键是:
每个人都从底层开始。
没有人天生就是解决复杂问题的。像任何技能一样,解决问题的能力也在发展。
相信我,只要坚持下去,你就会成功。

Bubba Yakoza
Problem solving requires deep or new thinking and it’s a hard job because brain has to deal with complexity.
Problem solving is as old skill as human themselves. Computers are just tools used in the process of problem solving.
Now focus following quotes of Einstein:
“The world as we have created it is a process of our thinking. It cannot be changed without changing our thinking.”
and
“We can not solve our problems with the same level of thinking that created them”
How new thinking comes to mind?
Again Einstein answers it.
“If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.”
The key to solving problem is understanding the problem better.
Simple problems are easy to solve but dealing with complex problems may be mind boggling.
Then how to solve complex problems?
There is set of techniques for it.

解决问题需要深入思考或采用新的思考方向,这是一项艰巨的工作,因为如此一来大脑必须处理复杂性。
解决问题的技能和人类自身一样古老。电脑只是解决问题过程中使用的工具。
下面是爱因斯坦的名言:
“我们创造的世界是我们思考的过程。如果不改变我们的思维,它就无法改变。”和“我们不能用创造问题的思维水平来解决问题”
新思维是如何浮现在脑海中的?
爱因斯坦再次回答了这个问题。
“如果我有一个小时来解决问题,我会花55分钟思考问题,5分钟思考解决方案。”
解决问题的关键是更好地理解问题。
简单的问题很容易解决,但处理复杂的问题(过程)可能令人难以置信。
那么如何解决复杂的问题呢?
这有一套技能。

Whenever you face a complex problem decompose it to smaller problems. In other words, it’s same as saying divide-and-rule or the same philosophy as eating one bite at a time to eat an elephant.
Now solve each smaller problem one by one so that the solution to complex problem becomes visible.
When solving problems, often patterns are looked for. It’s same as “One size fits all”. You won’t write a program to add 1 + 2, rather you would program a pattern so that any two integers x and y could be added. Otherwise, the solution would be too rigid and fail to solve a similar problem like 1 + 3 (without making change to the code)
Abstraction is an important concept in problem solving that most people understand hardly. Let me explain it.

当你面对一个复杂的问题时,把它分解成更小的问题。换言之,这与“分而治之”或“一次咬一口就吃掉一头大象”的理念是一样的。
现在一个接一个地解决每个小问题,这样复杂问题的解决方案就变得可见了。
在解决问题时,通常会寻找模式。这和“一刀切”是一样的。你不会编写一个程序来加“1+2”,而是编写一个模式,以便可以将任意两个整数x和y相加。否则,解决方案将过于僵化,无法解决类似的问题,如“1+3”在不修改代码的情况下就无法解决。
抽象化是解决问题中的一个重要概念,大多数人都很难理解。让我解释一下。

Do you focus on alphabets when writing an email to your friend or you focus on words or sentences or more importantly on the message being sent? Perhaps you focus on message because alphabets, words and sentences were the problems when you were a primary school kid and not anymore. Now you abstract them while solving other problems such as sending a meaningful message.
Let’s explore the abstraction from another angle. Suppose you want to represent a river in computer, how would you do it? Fill water in your computer? No. Computer is just an information representation, information manipulation, information storing and or information exchange machine. All information in computer has to be represented as text, image, sound, video or in some hybrid format. We can abstract river either with text (number, letter or symbol), an image or a sound or a video with some other hybrid format of these four. In this context abstraction works as a code.

在给朋友写邮件时,你是关注字母表,还是关注单词或句子,更重要的是关注发送的信息?也许你关注的是信息,因为当你还是个小学生时,字母表、单词和句子是问题所在,现在不是了。现在,你可以在解决其他问题(如发送有意义的消息)的同时对它们进行抽象化。
让我们从另一个角度探讨抽象化。假设你想在计算机中表示一条河,你会怎么做?给你的电脑注水?不,计算机只是一个信息表示、信息处理、信息存储和/或信息交换的机器。计算机中的所有信息都必须以文本、图像、声音、视频或某种混合格式表示。我们可以用文本(数字、字母或符号)、图像或声音或视频等四种混合格式来抽象化河流。在这种情况下,抽象化就像代码一样工作。

Once we have decomposed problem, recognized patterns and done necessary abstraction, we are ready to write algorithm. Algorithm is a sequence of steps to solve a problem.
If you understand this answer and someone asks you, “Can you grow a tree in computer?”
Just answer that computers can only deal with information and inside a computer you can make a computational model of information of a tree which renders and give you the abstraction of a real tree planted in ground.
You can write a graphical program where you may represent tree with a vector image and change its co-ordinates to show growth of tree and rate of growth could be set the same at which real tree on ground grows.
You can write a command line program where you may represent tree with a number and then change that number to show growth of tree and rate of growth could be set the same at which real tree on ground grows.
It all depends how you abstract things.
In short, you can solve any problem by better understanding it, decomposing it to smaller problems (to deal with complexity), make it as generic as possible through pattern recognition and off course abstracting things at each stage of problem solving.
To solve riddles is a good practice for stretching thinking capabilities of your mind.

一旦我们分解了问题,识别了模式并完成了必要的抽象化,我们就可以编写算法了。算法是解决问题的通用步骤。
如果你理解了这个答案,有人问你:“你能在电脑里种一棵树吗?”
你只需回答,计算机只能处理信息,在计算机中,你可以为树的信息建立一个计算模型,从而呈现并给你一棵种植在地下的真正的树的抽象概念。
你可以编写一个图形程序,在该程序中,你可以用矢量图像表示树,并更改其坐标以显示树在生长,并且可以将生长速率设置为地面上真实树的生长速率。
你可以编写一个命令行程序,在该程序中,你可以用一个数字表示树,然后更改该数字以显示树的生长,并且可以将生长速率设置为地面上真实树的生长速率。
这完全取决于你如何抽象化事物。
简而言之,你可以通过更好地理解问题,将其分解为更小的问题(以处理复杂性),通过模式识别和在问题解决的每个阶段对事物进行抽象化,使其尽可能一般化。
解谜是拓展思维能力的好方法。

Sudha
Honestly, I will tell you something very simple which always helps me a lot.
Go back to your basics.
Instead of directly jumping to a conclusion, read it when you look at a problem. Reread it once you are done reading it, with a mindset that this problem is made for you to solve.
Now look at all the concepts in your head, visualize those and then try to apply those.
Believe me, you are already more than halfway there, even if you think you are not.
You start to read that problem, trying to solve it, remembering all the steps; that’s the most challenging part. Other than that, just that one step varies from problem to problem. You will start realizing those tricks as you practice them more.

老实说,我要告诉你一件非常简单的方法,它对我一直很有帮助。
回去学习基础。
与其直接得出结论,不如在看问题时阅读(基础知识)。一旦你读完了,就重读一遍,抱着这样一种心态:这个问题就是为你而设的。
现在看看你头脑中的所有概念,将它们形象化,然后尝试应用它们。
相信我,即使你认为自己还没有完成,你已经完成了一半以上。
你开始阅读这个问题,试图解决它,记住所有步骤;这是最具挑战性的部分。除此之外,这一步就因问题而异。随着你的练习,你会开始意识到这些技巧。

Rae Joudain
Problem solving is a learned life skill. It’s a process. The ability to make choices, large and small is also a learned skill and one most parents teach their children from a young age. Making choices is part and parcel problem solving. The more confident and sure you are about the choices you make, the better you success overall. However, there is a another group……
There’s an old saying, “Not to decide is to decide.” Unfortunately, I’ve met more than one young person this applies to. There is a disturbing trend in some places, including right here in America, in which young people enter the world alone for the first time through college, traveling, out of state/country job opportunities, etc.. and the second they hit a bump in the road, they freeze. Literally. Because they have no idea how to make a choice beyond the underwear and socks they put on each morning. Seriously. These kids reach the age of consent and have yet to make any personal choices of consequence at all. Throw a complex algebra problem of a complicated physics question at them and they’re good. But ask them to make choices concerning anything more complicated and don’t know how to handle it.

解决问题是一种后天的生活技能,这是一个过程。做出大大小小的选择的能力也是一种后天习得的技能,也是大多数父母在孩子很小的时候就教给他们的技能。做选择是解决问题的一部分。你对自己所做的选择越自信、越确定,你就越容易成功。然而,还有另一个群体。
有句老话,“不做决定就是做决定”。不幸的是,我遇到了不止一个这样的年轻人。在一些地方有一种令人不安的趋势,包括在美国,年轻人第一次独自进入世界是通过大学、旅行、州外/国家的工作机会等。一旦他们遇到困境,他们就会呆住。因为除了每天早上穿的内衣和袜子,他们不知道如何做出选择。认真来说,这些孩子到了法定年龄,根本不会做出任何重大的个人选择。把复杂的代数问题和复杂的物理问题扔给他们,他们能很好摆平。但是让他们对更复杂的事情做出选择,他们就不知道如何处理。

It’s not until they’re away from that influence that they realize this. I’m thinking of two young women in particular, both of whom I met through my business/their college connections. It became quickly apparent both had a problem making the simplest choice the first couple days they were working with me. Despite the clear guidelines I gave them on multiple projects ,and their apparent levels of intelligence, neither could make even the tiniest move without first asking me to decide if it was the right one.(as in “do you want me to add this post-it note with the color change to XX file?) And then there was the “who’s turn is it to get our morning coffee?” And one day, I kinda, sorta blew up. OK, I was in a total snit at this point. I told them if I was meant to deal with every client and their file, they wouldn’t be here and as for coffee, I didn’t give a HOOT who went to the shop next door, just pick one already and do it. like YESTERDAY.

直到他们摆脱这种影响,他们才意识到这一点。我特别想到了两位年轻女性,她们都是我通过工作/大学的关系认识的。很快就发现,在和我一起工作的头几天,他们都无法做出最简单的选择。尽管我在多个项目上都给了他们明确的指导方针,他们的智力水平也明显是够的,但在没有先问我决定这是否是正确的做法之前,他们连最微小的行动都做不出来。(比如“你想让我把这个有颜色变化的便利贴添加到XX文件中吗?”?)然后是“轮到谁来买早上的咖啡呢?”困境每一个仅有一个的那天…我被要求选择一个或另一个。有一天,我有点,有点失控了。好吧,我当时很生气。我告诉他们,如果要我处理每个客户和他们的文件的话,那就不在需要她们呢。至于咖啡,我根本不在乎谁去了隔壁的商店,就像昨天直接挑一杯就行了。
原创翻译:龙腾网 https://www.ltaaa.cn 转载请注明出处


The more they opened up, the more I learned about their family lives. Everything was done and chosen for them.. From how their bedrooms were decorated to the clothes they wore, the school they attended and the people they were allowed to associate with, they had no voice and in fact didn’t realize until they left home they ever had one at all. Regarding college and career choices, both were told they weren’t old enough or mature enough to make such decisions. Any thoughts they expressed were dismissed as childish fantasies. About their own futures….
I told them I was 56(at the time), was quite certain I still wasn’t “grown up” and was currently considering options for my next careerAnd BTW, exactly what does “grown up” or “mature enough” look like? I wanted tangible examples or else these were yet two more ridiculous, disparaging cliches I was kicking to the curb. And that rocked their world because questioning their parent’s attitudes wasn’t in their wheelhouse.

他们越敞开心扉,我就越了解他们的家庭生活。一切都是为他们准备和选择的。从他们的卧室如何装饰,到他们穿的衣服,他们上的学校,他们被允许交往的人,他们没有发言权,事实上,直到他们离开家,他们才意识到他们曾经有过发言权。在大学和职业选择方面,他们都被告知自己还不够成熟,无法做出这样的决定。他们表达的任何想法都被认为是幼稚的幻想。关于自己的未来....
我告诉他们我当时56岁,很确定自己还没有“长大”,目前正在考虑下一个职业选择,顺便问一句,“长大”或“足够成熟”到底是什么样子的?我想要的是具体的例子,否则这只是我被我踢到路边的两个更荒谬的、贬低性的陈词滥调。这震惊了他们的世界,因为质疑父母的态度不是他们的专长。

Our little office “discussion” upset me more than they knew. I started spending time with them, both together and one-on-one. I introduced the idea of independent thinking, critical thinking skills and the value of making one’s own choices. (privately, I could have cried)I’ve mentioned my father before and the amazing things he taught me from an early age, such as the value of thinking for myself and the skills to do it. Every statement or story I came to him with was met with a “How” and/or “Why”. Usually both. When I asked him what his choice would be on a matter, he’d respond by saying, “What would YOU choose?” He challenged me in the best of ways. Best. Gift. Ever.
I did the same with them. Sometimes our conversations were much like a Mad Hatter’s merry-go-round. Round and round we went. Her: what would you do? Me: I’d make the choice best for me, personally, but what would YOU do and WHY? And then, why would you NOT do this or that, if that’s your dream/passion? It was a process, but over time, they both started growing more confident in making choices, expressing their beliefs. Eventually, they went from becoming confident enough to express their personalities through fashion to making BIG choices about their futures. One’s father had his own law firm and had told her since she could toddle, someday it would all be hers. Except, she HATED law and had been interested in medicine for years. Her announcement to switch majors didn’t go over well.

我们在办公室的小规模“讨论”比他们想象的更让我心烦。我开始花时间和他们在一起或单独相处。我介绍了独立思考的理念,批判性思维技能和做出自己选择的价值。(私下里,我都想哭了)我之前提到过我的父亲,以及他从小教我的那些令人惊叹的事情,比如独立思考的价值和做事的技巧。关于每一个陈述或故事都会遇到“如何”和/或“为什么”。通常两者都有。当我问他对某件事的选择时,他回答说:“你会如何选择?”他用最好的方式向我挑战。这永远是最好的礼物。
我也对他们做了同样的事。有时我们的谈话就像疯帽匠的旋转木马。我们转了一圈又一圈。她:你会怎么做?我:就我个人而言,我会做出最适合自己的选择,但你会怎么做?为什么?然后,如果这是你的梦想/激情,你为什么不做这个或那个?这是一个过程,但随着时间的推移,他们都开始在做选择、表达自己的信仰方面变得更加自信。最终,他们从足够自信地通过做事的方式表达自己的个性,到对自己的未来做出重大选择。有一个人的父亲有自己的律师事务所,从她会走路起,他就告诉她,总有一天这一切都会是她的。除此之外,她讨厌法律,多年来一直对医学感兴趣。她宣布转学专业,结果并不顺利。

The other girl decided to switch from an old, conservative Ivy League school(her parent’s alma mater) and a business major to pursuing her dream of architectural engineering at a liberal school, Her reception was pretty much like the other’s, except her parents did pay basic tuition for her undergrad degree. Everything else, both women have PAID for themselves. The first earned her nursing degree and is set to enter med school and the other is currently finishing her Masters, with plans to start her PhD as soon as she can. They’re AMAZING young women who are strong and self-directed today, not because of me, but because each made a CHOICE to take control of their lives, by first becoming their own best friend and making choices that both authenticated them and made them even stronger.
I’ve seen games and puzzles mentioned quite a bit and yep, I enjoy them too. They challenge and intrigue me. But I’ve also learned there’s no one set of rules for problem solving, sometime situations and the people involved are fluid and while I my basic process is simple, after that, it’s sometimes fitting the method of problem solving specifically to the situation that gets the best results.

另一个女孩决定从一所古老、保守的常春藤盟校(她父母的母校)和一个商科专业转为文科学校学梦想中的建筑工程专业。除了她的父母为她的本科学位支付基本学费外,她的待遇与其他人非常相似。其他的一切,两个女人都是自己付的。第一名学生获得了护理学位,即将进入医学院学习,另一名学生正在完成硕士学位,并计划尽快开始攻读博士学位。她们是令人惊叹的年轻女性,今天她们变得坚强和自主,不是因为我,而是因为她们每个人都做了一个控制自己生活的选择,首先成为自己最好的朋友,做出的选择既认证了她们,也让她们变得更强大。
我看过很多提到的游戏和拼图,是的,我也很喜欢。她们对我提出了挑战,也激发了我的兴趣。但我也认识到,解决问题没有一套规则,有时情况和所涉及的人都是不固定的,虽然我的基本过程很简单,但在此之后,有时需要将解决问题的方法专门用于获得最佳结果的情况。

Before we can solve any problem, we must first indentify it. In detail. Others have said it and I whole heartedly agree. It’swhat I do. When I’m facing a business problem, I next collect all the facts, data and consider all the variables. I have a notebook I carry with me, I’m constantly making notes as I go because sometimes the best ideas pop up at the most unexpected times, like during that lunch with my great Aunt Bernice Oh come on, I’m not the only one this happens to Sometimes I do a Ben Franklin list, separating pros from cons. It’s an exercise as old as Benhimself and seen as outdated and to simple by some , but by separatingthe pros from the cons, making actual lists, it brings a certain clarity. Clarity, like the ability to choose, is essential to effective problem solving. ‘Band-aid” or quick fix solutions might be attractive now, but they’re almost always a recipe for disaster in the future. Believe me, I know. Even have the certificate to prove it. :) Sometimes it’s in the numbers, other times it’s by process of elemination, and now and then it’s the wildest, outlandish idea I first dismissed, but my mind takes everything it knows and kind of focuses in on the best solution for me and the minute I get it’s going to work, it’s like I hear a little “click” in my brain. It’s answers most, if not all questions, and I know it’s the right one, including the ones I don’t like. Not every solution is a booyah! moment. Doesn’t have to be. It only happens because I’m confident in my instincts, my ability to make the best choice possible, at least most of the time.

在我们能够解决任何问题之前,我们必须首先确定它。其他人都这么说了详细方面,我真的同意其他人所说的,我就是这么做的。当我面临业务问题时,我接下来会收集所有事实、数据并考虑所有变量。我随身携带着一本笔记本,我一边走一边不断地做笔记,因为有时最好的想法会在最意想不到的时候冒出来,比如和我曾祖母共进午餐的时候(冒出那些想法)。有时我会列出本·富兰克林的名单,把优缺点分开。这个方法和其本人一样古老,在一些人看来已经过时了,它很简单,但通过把优点和缺点区分开来,列一个清单,让人有清晰的认识。清晰,就像选择的能力一样,是有效解决问题的关键。“创可贴”或“快速修复方案”可能很有吸引力,但它们几乎总是未来灾难的导火索。相信我,我知道。甚至有证明书 来证明它。有时是数字,有时是元素分解,有时是我第一次摒弃的最疯狂、最古怪的想法但我的大脑会把它知道的一切都集中在对我最好的解决方案上,当我找到最佳解决方式的时候,它就会起作用,就好像我听到了脑子里的咔嚓声。这即使不是所有问题,也是大多数问题的答案,我知道这是正确的答案,包括我不喜欢的问题。并不是所有的解决方案都是如此来的!这个时间可不一定。这只是因为我对自己的直觉有信心,我有能力做出最好的选择,至少大多数时候是这样。

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