I don't get the range concept - Math.random() * (max - min + 1)) + min

JavaScript
1

I’ve RSAd a few things around the net including this one and this one.

I’m nearly there but need one more push over the mind hurdle.

I understand how:

Math.random() * (max - min + 1)

… creates the distance between the min and max.

What makes no sense to me is how adding min at the end of :

Math.floor(Math.random() * (max - min + 1)) + min

… lets the computer know that it needs to shift that distance down or increase the min value.

My thinking goes:

Math.random( ) * (6 - 2 + 1)
Math.random( ) * 5
= 1.5 …(for example)
Math.floor(1.5) + 2
1 + 2

Where has my understanding of this gone wrong?

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2

You’re right. We multiply by the size of the range to scale the random number. We then add the minimum value to “shift” our scaled random number into the range.

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3

I hate to bump older posts but I flat out just do not understand this at all. I do have ADHD so it’s hard to follow, so pls be kind :slight_smile:

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4

No worries!

Math.random() gives us a random number between 0 and 1.

But we don’t want a random decimal; we want a random number. We can get that by multiplying our Math.random() result by the size of the range. For example, if we want a random number between 0 and 10, we need to multiply by 10. A result of 0.4 would become 4. If we want random numbers from 7 to 11, that is 5 possible numbers (7, 8, 9, 10, 11).
This is where we get Math.random() * (max - min + 1)

We don’t want decimal numbers though, we want whole numbers. Math.floor() just chops off the decimal. 3.14159 becomes 3.
That’s where we get Math.floor(Math.random() * (max - min + 1)).

Now we’re getting a number from 0 to whatever our range size was. If we wanted a number from 7 to 11, it’s a random number from 0 to 5. To make that be a number from 7 to 11, we just need to add 7 to whatever number we got. 7 is our minimum value.
This leads us to Math.floor(Math.random() * (max - min + 1)) + min

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You’re a total hero. Exactly what I needed and thank you so much!

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6

I know it’s been a while, but here I am & I thought I’d throw in my 2 cents just in case it helps someone else. Combined with ArielLeslie’s description above it helped me.

I don’t think verbally, so this is how I had to work it out:

Math.floor(Math.random() * (max - min + 1)) + min;

// max = 15; min = 5
Math.floor(Math.random() * (15 - 5 + 1)) + 5;
Math.floor(0 * (15 - 5 + 1)) + 5;
Math.floor(0) + 5;
0 + 5;
5

// max = 15; min = 5
Math.floor(Math.random() * (15 - 5 + 1)) + 5;
Math.floor(0.9999999999 * (15 - 5 + 1)) + 5;
Math.floor(0.9999999999 * (11)) + 5;
Math.floor(10.9999999989) + 5;
10 + 5;
15
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Perfect explanation, I was struggling until I read this.

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8

I’m glad it helped. Happy coding!

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9

hey, you seem to understand it better than me.
Should below code not produce the very same result as the one suggested in the solution?

function randomRange(myMin, myMax) {

var result = Math.round(Math.random()* (myMax - myMin)) + myMin;

return result;
}

10

you need to +1 to (myMax - myMin).

What we’re trying to achieve with the above is to gather the range of numbers between myMax and myMin, to be later multiplied by a decimal between 0 and 1(non-inclusive).

Imagine this;
if myMax = 10, myMin = 5

per your formula,
10 - 5 = 5

However,
the numbers between 5 and 10 inclusive are as follows:
5, 6, 7, 8 ,9 ,10
there are a total of 6 numbers.

This is why we add 1 to (myMax - myMin).

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11

I do not understand what the “+1” on (max-min+1) is for…

12

I see. They’re comparable to arrays with zero indexing?

1 Like
13

Correct me if I’m wrong but the 1+ seems to just be the part where it counts up the array.

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14

There is no array involved here.
The +1 is needed if we have an inclusive range. Remember that Math.random() is non-inclusive of 1. If our min is 2 and our max is 5, we want to include 2, 3, 4, 5. That’s four numbers. But 5-2 is 3. That’s why we add 1.

31 Likes
15

Sorry once again this is a little old, but I just wanted to add to this (maybe others can benefit from different wording):

This was how I would explain why add 1 (similar to the explanation by @ArielLeslie) :

When the range is first found, this value is an exclusive range (doesn’t include the min and max ). However, due to the way Math.random() works, this becomes a half-inclusive range, where it includes the min but not the max (refer to previous exercise). Thus, to make this an inclusive range, you add 1 to it to compensate for the missing spot of the max .

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This is a good answer,

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17

hope this helps someone, I did the math for both the minimum and maximum cases to understand the formula better

let’s say Math.random() = 0.99 (maximum case)
example input: min = 5, max = 10

formula with the 1 added :
Math.floor(Math.random() * (max - min + 1)) + min
Math.floor(Math.random() * (10 - 5 + 1)) + 5
Math.floor(Math.random() * (6 )) + 5
Math.floor(0.99 * (6 )) + 5
Math.floor(5.94) + 5
5 + 5
10

formula without the 1 added :
Math.floor(Math.random() * (max - min )) + min
Math.floor(Math.random() * (10 - 5 )) + 5
Math.floor(Math.random() * (5 )) + 5
let’s say Math.random() = 0.99
Math.floor(0.99 * (5 )) + 5
Math.floor(4.95) + 5
4 + 5
9

10, the maxium input, will not be inclusive/never be reached in the formula without the 1

now let’s say Math.random() = 0.00 (minimum case)

formula with the 1 added :
Math.floor(Math.random() * (max - min + 1)) + min
Math.floor(Math.random() * (10 - 5 + 1)) + 5
Math.floor(Math.random() * (6 )) + 5
Math.floor(0.00* (6 )) + 5
Math.floor(0) + 5
0 + 5
5

formula without the 1 added :
Math.floor(Math.random() * (max - min )) + min
example input: min = 5, max = 10
Math.floor(Math.random() * (10 - 5 )) + 5
Math.floor(Math.random() * (5 )) + 5
Math.floor(0.00 * (5 )) + 5
Math.floor(0) + 5
0 + 5
5

TL;DR
without the 1 added to the formula, the minimum number within the range will be included/reached, but never the maximum number
minimum was 5, maximum was 10
via https://www.freecodecamp.org/learn/javascript-algorithms-and-data-structures/basic-javascript/generate-random-whole-numbers-within-a-range
we want to be inclusive of the minimum and the maximum number

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18

Just replying to say I’m doing this in 2020 and did not understand this at all until I saw your explanation. Your explanation is still helping people out, 2.5 years later!! How awesome is that? Thank you! :smile:

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19

I’m really glad that I could help! Thanks for letting me know.

Happy coding!

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This was an awesome explanation, thanks!

1 Like