Iterative vs. Recursive Approaches

• Download source - 2.5 KB

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;
}

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;
}

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