Which is a better way of finding the max of no.s?

Question

Which is a better way to write a program to find the max of 4 no.s in c/C++:

using a fifth variable & comparing it to all inputs
using max() function
and comparing the inputs using if

or suggest any other, if it has a better approach(in terms of space & time complexity) of solving the problem

Would the same algorithmic approach would still be the best in case of more than 4 variables?

If you know that it's four inputs, the fewest comparisons is `max(max(a,b), max(c,d))`. — rlbond, Sep 17 '15 at 19:25
the comparisons would be few, but wouldn't the space- in terms of the max() function being called repeatedly be more? — dj1, Sep 17 '15 at 19:27
@rlbond: Huh? `max(a, max(b, max(c, d)))` has the same number of comparisons. It just has a longer dependency chain. — EOF, Sep 17 '15 at 19:28
@dj1 What _"space"_ you're talking about?? Meant the "shwitz" or what? — πάντα ῥεῖ, Sep 17 '15 at 19:29
complexity is usual meant as *asymptotic* complexity, i.e. large `N` — TemplateRex, Sep 17 '15 at 19:30

TemplateRex · Accepted Answer · 2015-09-17T19:53:41.417

For a large number of elements, the Standard Library has the std::max_element algorithm which does max(N-1, 0) comparisons for N elements, which his the theoretical minimum, even for 4 elements.

In practice, it loops over all elements as does your method 1., but it could do an "elimination tournament" of nested max if N is a power of 2 (your method 2). Some optimizing compiler might even unroll the loop and produce a complicated chain of if statements (your method 3).

In the comments, the C++11 style solution max({a,b,c,d}) was given by @NathanOliver (which only works in constexpr contexts). But in C++1z, the std::max_element will also become constexpr so that it will be the fully general solution, small or large, runtime or compile-time.

TL;DR: don't overthink this, use the Standard Library which does provably minimal amount of work.

score 0 · Answer 2 · answered Sep 17 '15 at 19:32

0

Better is a lose term. As pointed out in the comments

max(max(a,b), max(c,d));

is very concise however there are 3 function calls. It is slightly faster code wise but a lot more coding to write something like:

if (a>b)
{ 
  if (a>c)
  {
     if (a>d)
     {
         return (a);
     }
  }
}

if (b>a)
{ 
  if (b>c)
  {
     if (b>d)
     {
         return (b);
     }
  }
}
if (c>a)
{ 
  if (c>b)
  {
     if (c>d)
     {
         return (c);
     }
  }
}

if (d>a)
{ 
  if (d>b)
  {
     if (d>c)
     {
         return (d);
     }
  }
}

answered Sep 17 '15 at 19:32

ojblass

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1

`std::max({a,b,c,d})` – NathanOliver Sep 17 '15 at 19:34
2

`max` is commonly implemented as a macro, and even if it isn't, it's probably inlined by modern compilers. – EOF Sep 17 '15 at 19:35
This code may do more than twice as many comparisons as `std::max` and for some values this code won't reach any of the `return` statements. Just use `std::max` unless profiling shows it's a bottleneck (and it probably isn't). – Blastfurnace Sep 18 '15 at 01:15

Which is a better way of finding the max of no.s?

2 Answers2