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Iterative vs. Recursive Approaches

, 5 Nov 2007 CPOL
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Implication of not thinking of iterative solutions over recursive from performance (response time) point of view

Introduction

This article was originally posted at blogs.microsoft.co.il/blogs/Eyal.

Recursive function – is a function that is partially defined by itself and consists of some simple case with a known answer. Example: Fibonacci number sequence, factorial function, quick sort and more.
Some of the algorithms/functions can be represented in an iterative way and some may not.

Iterative functions – are loop based imperative repetitions of a process (in contrast to recursion which has a more declarative approach).

Comparison between Iterative and Recursive Approaches from Performance Considerations

Factorial

//recursive function calculates n!
static int FactorialRecursive(int n)
{
    if (n <= 1) return 1;
    return n * FactorialRecursive(n - 1);
}

//iterative function calculates n!
static int FactorialIterative(int n)
{
    int sum = 1;
    if (n <= 1) return sum;
    while (n > 1)
    {
        sum *= n;
        n--;
    }
    return sum;
}
N Recursive Iterative
10 334 ticks 11 ticks
100 846 ticks 23 ticks
1000 3368 ticks 110 ticks
10000 9990 ticks 975 ticks
100000 stack overflow 9767 ticks

As we can clearly see, the recursive is a lot slower than the iterative (considerably) and limiting (stackoverflow).

The reason for the poor performance is heavy push-pop of the registers in the ill level of each recursive call.

Fibonacci

//--------------- iterative version ---------------------    
static int FibonacciIterative(int n)
{
    if (n == 0) return 0;
    if (n == 1) return 1;
        
    int prevPrev = 0;
    int prev = 1;
    int result = 0;
        
    for (int i = 2; i <= n; i++)
    {
        result = prev + prevPrev;
        prevPrev = prev;
        prev = result;
    }
    return result;
}
    
//--------------- naive recursive version --------------------- 
static int FibonacciRecursive(int n)
{
    if (n == 0) return 0;
    if (n == 1) return 1;
        
    return FibonacciRecursive(n - 1) + FibonacciRecursive(n - 2);
}
    
//--------------- optimized recursive version ---------------------
static Dictionary<int> resultHistory = new Dictionary<int>();

static int FibonacciRecursiveOpt(int n)
{
    if (n == 0) return 0;
    if (n == 1) return 1;
    if (resultHistory.ContainsKey(n)) 
        return resultHistory[n];

    int result = FibonacciRecursiveOpt(n - 1) + FibonacciRecursiveOpt(n - 2);
    resultHistory[n] = result;
        
    return result;
}
N Recursive Recursive opt. Iterative
5 5 ticks 22 ticks 9 ticks
10 36 ticks 49 ticks 10 ticks
20 2315 ticks 61 ticks 10 ticks
30 180254 ticks 65 ticks 10 ticks
100 too long/stack overflow 158 ticks 11 ticks
1000 too long/stack overflow 1470 ticks 27 ticks
10000 too long/stack overflow 13873 ticks 190 ticks
100000 too long/stack overflow too long/stack overflow 3952 ticks

As before, the recursive approach is worse than iterative however, we could apply memorization pattern (saving previous results in dictionary for quick key based access), although this pattern isn't a match for the iterative approach (but definitely an improvement over the simple recursion).

Notes

  1. The calculations may be wrong in big numbers, however the algorithms should be correct.
  2. For timer calculations, I used System.Diagnostics.Stopwatch.

Points of Interest

  1. Try not to use recursion in system critical locations.
  2. Elegant solutions not always the best performing when used in "recursive situations".
  3. If you required to use recursion, at least try to optimize it with dynamic programming approaches (such as memorization).

History

  • Post: November 06, 2007

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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About the Author

Eyal Lantzman
Software Developer (Senior) Taldor
Israel Israel
In the last couple of years I'm working as Microsoft sub contractor in various project types - LOB, applications, CnC applications and Distributed applicaitons all of them considered to be extra large in tems of man power (or brain power), duration and geographic destribution between connected sites.

Comments and Discussions

 
Generalblame C#, not .NET. F# does it better. PinmemberJay R. Wren13-Nov-07 3:00 
GeneralRe: blame C#, not .NET. F# does it better. Pinmemberncarey13-Nov-07 8:29 

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