Question

Test your recursion skills.

Given an integer array `a` of size `n`, write a recursive function with prototype
```
int findmin(int a[], int n);
```
that finds the minimum element of the array.

Answer 1

If only there were a “spoilers” style so we could post code that was hidden unless highlighted ;)

Answer 2

I actually asked this question because I wanted to test a way to post code in OS. It turns out to be very cumbersome (or perhaps I'm missing an already-existing code tag somewhere?).

Answer 3

@farmdawgnation was awesome a while back and added triple-backtick delimiting of code, Github-style.

e.g.:

```
int findmin(int a[], int n) {
if (n <= 0)
return // uh-oh, dat bounds checking
else if (n == 1)
return // something?
else {
// what magic goeth here?
}
}
```

Answer 4

You can use single backticks around something to mark it as inline code, or three on either side for blocks.

Answer 5

And I think if you want to give the syntax highlighter a hint, you can put the language name after the three backticks, assuming it recognizes the language. Could be wrong about that part, I haven't used it too much :)

Answer 6

Oh, wow! That looks really nice.

Answer 7

The puzzling question for me is, is there a way to make a tail-recursive min function… Ah-hah, I think I've figured that one out as well.

Answer 8

Backticks have to be on their own line :) The live preview should be highlighting things for you as you go as well.

Answer 9

The triple ones*

Answer 10

`test`

```
#include <iostream>
using namespace std;
int main()
{
return 0;
}
```

Answer 11

You guys are awesome. ;)

Answer 12

I'm just happy I got the tail recursive version. Boom!

Answer 13

Post it! This is the best tail-recursive version I could come up with:
```
int findmin(int a[], int n)
{
static int *min;

if (min == 0)
min = new int(a[n - 1]);
else if (*min > a[n - 1])
*min = a[n - 1];

if (n == 1)
return *min;
else
return findmin(a, n - 1);
}
```

Answer 14

I did this in python in a few different ways.
http://pastebin.com/LZAkS8Ge

btw, what markup code do you use to show code?

Answer 15

Ew statics ;) Tail recursion is of course only really useful if the host language supports tail recursion optimizations. I used a helper function:

```cpp
int findmin(int a[], int n)
{
if (n <= 0)
return -1; // arbitrary “no minimum” value, not really a good idea
else
findmin(a[0], a[1..n - 1], n - 1);
}

int findmin(int lastmin, int a[], int n)
{
if (n <= 0)
return lastmin;
else {
int currentmin = lastmin;
if (a[0] < currentmin)
currentmin = a[0];

findmin(currentmin, a[1..n - 1], n - 1);
}
}
```

You actually did a clever trick I'd forgotten about by using n as an index, avoiding copying the array. Solid goodness there, and here's an update of mine to do that:

```cpp
int findmin(int a[], int n)
{
if (n <= 0)
return -1; // arbitrary “no minimum” value, not really a good idea
else
return findmin(a[n - 1], a, n - 1);
}

int findmin(int lastmin, int a[], int n)
{
if (n <= 0)
return lastmin;
else {
int currentmin = lastmin;
if (a[n - 1] < currentmin)
currentmin = a[n - 1];

return findmin(currentmin, a, n - 1);
}
}
```

Implemented in Scala:

```scala
def findmin(a: List[Int]): Option[Int] = {
a match {
case first :: rest => findmin(first, rest)
case _ => None // otherwise
}
}

@scala.annotation.tailrec
def findmin(currentMin: Int, a: List[Int]): Option[Int] = {
a match {
case first :: Nil if currentMin < first => Some(currentMin)
case first :: Nil => Some(first)
case first :: rest if currentMin < first => findmin(currentMin, rest)
case first :: rest => findmin(first, rest)
case _ => None
}
}
```

The upside of the above is that the `@scala.annotation.tailrec` asks the compiler to double-check that we're tail recursive (we are :p). The Scala compiler will automatically optimize tail recursion regardless of whether the annotation is present. I also think it reads better ;)

Answer 16

Also worth mentioning about the Scala example above, the most basic collection in Scala is a List, which is a linked list. We're unpacking it in the match statements into the first part vs the rest of the List (much like Lisps let you via car/cdr or head/rest).

Answer 17

I see! I had forgotten how helpful helper functions (you don't say?) can be.

Also, I don't think it can get any shorter than this C implementation a friend came up with:

```
int findmin(int a[], int n)
{
if (n == 1)
return a[0];
n--;
return f(a + (a[0] > a[n]), n);
}
```

These guys are monsters. I feel so behind when it comes to programming. T_T

Answer 18

Is this worth considering?

#include <limits.h>

int findmin( int a[], int n )
{
int m;

if( !n )
return( INT_MAX );

m = findmin( a, --n );
return( a[n] < m ? a[n] : m );
}

Answer 19

Succinctness is not the only goal of programming. Indeed, it's often an anti-goal.

@rsmith6559 my only problem with that one is that it seems to attend to edge cases but doesn't (what happens with a negative n?). And that it relies on INT_MAX, which always seems nasty even if technically correct. Then again, there's no good way to deal with a negative n or indeed any invalid entry.

Answer 20

Dealing with a negative n isn't really the responsibility of this function. It should be validated by the calling code. INT_MAX would be the most likely value that would always be eliminated in the comparisons, and it's portable!

Answer 21

That's a good question: is it considered proper coding to implement error-handling procedures in functions, or to have the client file or whoever is using those functions validate the input passed?

Answer 22

FWIW, in the cases of iteration or recursion, having the calling code handle validation will certainly execute faster. One check, instead of however many iterations checks.

IMO, the answer is a very clear interface, and clear documentation/commenting. I don't see any issue, besides the speed, either way, but to be successful the implementer and client programmers need to be pretty much in lock step.

Answer 23

Honestly, in the version with a helper, it's reasonable to only check at the entry point and take the check out of the helper. But in a language like C, where stuff like that is completely unsafe, it's rarely a good idea to eliminate the check altogether. In a language that carries length with the array, it's obviously a different matter.

I agree that INT_MAX is perfectly valid. But the problem with it is that INT_MAX could actually be the minimum, so what does it mean if the function returns INT_MAX? Was there invalid information or was it the minimum value in the list? Most C functions seem to deal with this via a passed in pointer-to-an-error-flag of some sort. It's nasty, but it works.