How to turn for loop into a math equation?

Question

I have the following two loops in my program and I am trying to write them out as math equations, but I'm having some difficulty finding a concise way to do so:

// Loop1
for (int i = 0; i < nr; i++) {
    array[i] = nepr;
}

// Loop2
for (int i = 0; i < (nvr % nr); i++) {
    array[i]++;
}

The code is completely function, but I'm trying to express these loops in a document I'm writing.

Any help would be very much appreciated.

So far I have this:

array[i] = nepr, i = 0,...,(nr-1)

but I'm not sure how to incorporate the second loop into the equation, or write a second equation for it.

SirGuy · Answer 1 · 2016-07-06T19:09:49.600

3

Just express it as a piecewise-defined function:

 f(x) = {nepr + 1 if x <  (nvr % xr)}  
        {nepr     if x >= (nvr % xr)}

You can also define it in terms of the Heaviside step function:

 f(x) = nepr + H((nxr % xr) - x)

edited Jul 06 '16 at 19:09

answered Jul 06 '16 at 18:26

SirGuy

10,660
2
36
66

I believe your notation doesn't take into account that x is discretely valued. Your equations are for x being continuous. Correct me if I'm wrong. – Veridian Jul 06 '16 at 18:30
@Veridian That's not directly necessary, the equations are still valid. If you want to express that x must be an integer, just state it separately. – SirGuy Jul 06 '16 at 18:32
@chux It seems likely that nvr is always positive, but I changed it anyway. – SirGuy Jul 06 '16 at 19:10
Yes, assuming `nvr, nr` positive does simplify the problem. Doubt if OP wants a full range `int` solution. – chux - Reinstate Monica Jul 06 '16 at 19:16

dxiv · Accepted Answer · 2016-07-06T19:12:53.183

1

Not entirely clear that's what you are asking, but the following does the same thing in a single loop.

for (int i = 0, j = nvr % nr; i < nr; i++) {
    array[i] = nepr + (i < j);
}

[EDIT] In casual language without any loops the above is equivalent to...

Let j = nvr % nr. Assuming positive nr and nvr, 0 <= j < nr and:

array[i] = nepr + 1 for i = 0 ... j-1

array[i] = nepr for i = j ... nr-1

edited Jul 06 '16 at 19:12

answered Jul 06 '16 at 18:08

dxiv

16,984
2
27
49

Thanks actually, I think I can do this: array[i] = nepr + (i < j); i = 0,...,(nr-1); j = nvr % nr – Veridian Jul 06 '16 at 18:15
Assuming positive is needed. Code does fail with `nvr = 7; nr = -3;` – chux - Reinstate Monica Jul 06 '16 at 19:13
@chux Right. I edited the answer to spell out the positiveness assumption. – dxiv Jul 06 '16 at 19:14

Sourav Ghosh · Answer 3 · 2016-07-06T18:18:12.010

0

In your second loop, the condition check has the nr-1 as abound.

If i understood your problem correctly, you can express it like

array[i] = array[i] + 1 , i = nvr % nr ,...,(nr-2)

edited Jul 06 '16 at 18:18

answered Jul 06 '16 at 18:04

Sourav Ghosh

133,132
16
183
261

The dependency on nvr is missing – Veridian Jul 06 '16 at 18:10
@Veridian what kind of dependency? Ultimately you're going to use `nvr % nr` value, right? – Sourav Ghosh Jul 06 '16 at 18:13

score 0 · Answer 4 · edited Feb 09 '17 at 15:10

0

Here it is in LaTeX. To see or edit the LaTeX, click on the equation.

The := symbol expresses assignment. You could also write it in functional fashion by replacing array_i with array(i), a function defined on an open range of integers.

edited Feb 09 '17 at 15:10

Community

1
1

answered Jul 06 '16 at 18:32

Kuba hasn't forgotten Monica

95,931
16
151
313

Probably you should add i ∈ N – Logman Jul 06 '16 at 18:38
@Logman that seems inherent in the fact that i is used as an index into array – SirGuy Jul 06 '16 at 18:39
@GuyGreer but let's stay formal ;) – Logman Jul 06 '16 at 18:42

score 0 · Answer 5 · edited May 23 '17 at 11:45

0

Thought I would try to post a full int range soukltion base on @dxiv fine answer which works well when nr, nvr are positive - the usual case.

Assume nr, nvr are int.

assert(nr != 0);
assert(nr != -1 || nvr >= -INT_MAX);  // avoid -2147483648 % -1
int j = nvr % nr;
int ij = max(i,j);
for (int i = 0; i < ij; i++) {
    array[i] = nepr + (i < j);
}

edited May 23 '17 at 11:45

Community

1
1

answered Jul 06 '16 at 19:26

chux - Reinstate Monica

143,097
13
135
256

How to turn for loop into a math equation?

5 Answers5

Linked