How To Solve This PHP Algorithm?

Question

I am trying to create this algorithm with PHP. I want to be able to echo out the result of this operation:

1 - 2 + 3 - 4 + 5 - 6 +...100

I want to get the result of this till I get to 100.

This how I have already started the code, however I am stuck and don't know how to proceed:

<?php

$somme = 0;
$I = 1;

while($I <= 100){

}

?>

How do I go on from this?

All answers are appreciated

This has a simple closed-form solution, there is no need for a loop or an algorithm. Hint: 1+100 is 101. 2+99 is 101. 3+98 is 101. — Jörg W Mittag, Sep 23 '18 at 11:37
The given solution can be broken down to (1 + 3 + ..) - (2 + 4 + ..) which essentially are sums of two arithmetic progression, the value of each of which is (a1 + aN)/2 where a1 and aN are the first and last term of the series — Nilesh, Sep 23 '18 at 12:21

Mitya · Answer 1 · 2018-09-23T11:41:13.530

0

It's a case of knowing, within the loop, when to add and when to subtract. A simple tracker will help us here.

$somme = 0;
$i = 1;
$op = 'sub';

while($i <= 100){
    $somme = $op == 'sub' ? $somme - $i : $somme + $i;
    $op = $op == 'sub' ? 'add' : 'sub';
    $i++;
}

As noted in the comments, you could also decide the operation based on whether $i is even or odd.

edited Sep 23 '18 at 11:41

answered Sep 23 '18 at 11:37

Mitya

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I still have a hard time understanding this... – Thierry Diallo Sep 23 '18 at 11:38
You forgot `$i++;` – Cid Sep 23 '18 at 11:39
@Cid - good spot, thanks! – Mitya Sep 23 '18 at 11:41
@ThierryDiallo - well it's like this: each iteration, EITHER add or subtract the value of `$i` from the present value of `$somme`. Which of these we do is based on the current value of `$op`, which is switched each iteration. – Mitya Sep 23 '18 at 11:42

How To Solve This PHP Algorithm?

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