Modulo Operation Tricks

When you solve a problem that might result in values beyond integer limits (e.g., Wouldn't fit into a 64bit integer), you're often asked to print the value modulo a significant prime value (e.g. 10^9 + 1).

To be able to use the modulo operation correctly, you need to understand its properties.

Trick #1 Multiplication/Summation of values

For example, if you are multiplying/adding a set of numbers (a, b, c, d) then its useful to know that:

(a*b*c*d)%N = (a%N)*(b%N)(c%N)*(d%N) = ((a*b*c)%N)*d%N

The above is quite useful when you want to always keep calculations to fit into the given limits.

Trick #2 Multiplicative Inverse

For division, it's a little bit tricky though, you can't merely assume that:

(a/b)%N = (a%N/b%N)

Although that would be awesome, it's unfortunately not correct - So to solve this, you have to understand the modular multiplicative inverse of a number A.

So to calculate (a/b)%N, you can convert it to a%N*power(b, N-2) - I will not explain how or why, please refer to the wiki page above for more details.

Trick #3 Negative Numbers

Another problem one would face during programming contests is when you calculate modulo for a negative number, which doesn't really work as intended.

So -1%10 would result in -1 rather than 9 - This really depends on the programming language you use but this trick is useful for Java and C++ but not for Python which produces the right value 😊.

To overcome this, you can calculate it by adding N to the number so, -1%10 = 9%10 = 9 👍.

That's it! I will keep this post up to date with any other tricks I find in the future.

Speak so that others want to listen

How many times were you in a meeting or discussing with a group of people, and was your turn to say something, and someone either interrupted you or waited until you finished and continued talking or just switched the topic?

I'm pretty sure this has happened many times throughout your career and will continue to happen even after you read this article and practice its techniques, but I can promise it will be less often than before.

I've been observing others and myself in meetings and always found out that most of the discussions followed the same scenario I've described above, so I started to look for ways to improve the way I speak and spotting the mistakes I and others often do.

I've found many techniques and suggestions that are helpful for someone to speak effectively and make people more engaged to what he/she says, I've chosen only 3 of them to talk about in this article.

Note: The following techniques are not only useful when speaking, but for example, rule #3 is a handy technique to write persuasive and easy to follow/read content (e.g., Email).

1. The power of the pause

 

This technique is one of the essential methods one could learn and practice to improve the effectiveness of his contributions in discussions and meetings.

Adding a pause before you talk allowing the other person to finish, rather than jumping with the first thing comes to your mind to avoid the risk of interrupting the other person if he wants to continue to add something.

Adding pauses when you jump from one point to the next, grabs your audience full attention to what you are saying.

This technique will make people feel more comfortable talking to you and, of course, actively listening to you and what you say. It will also make you and the others more engaged in the discussion.

2. Speak with clarity and confidence

 

 

How many times have you been asked (or asked someone) to repeat what you/he/she's just said (multiple times)?

One mistake we all do (both native and non-native speakers) is speaking too fast and tend to swallow the endings of some words, which might change the meaning or cause confusion. If the audience lost focus for few seconds to think about what you said or feels difficulty tracking it, then he will either ask you to repeat what you just said or stop focusing because he is still thinking about some words that you mispronounced.

So next time, try to speak at a slower pace and make yourself clear when speaking. You will see the difference in how confident you become and how engaged the audience is - practicing this technique will improve your cadence, and later it will naturally happen when you speak.

One tip I liked is to speak slowly as if you are giving your phone number to someone and want to make sure he gets it right and able to write it down.

 

 

3. The rule of three

 

Structuring your content, for example, when writing an Email or in a presentation in three parts, makes it very easy for your audience to follow and remember and makes you (the author) as a speaker or writer appear more knowledgeable, credible, and convincing.

As you can see, I followed this approach in this article, and after reading through it, I genuinely believe that you will be able to memorize all three techniques quickly next time you speak or write about something.

Do you know more techniques? Please comment on the article and share them with other readers and me. And as a little practice, write your review using the above methods about the topic and share it with friends.