Way to go from recursion to iteration

Usually, I replace a recursive algorithm by an iterative algorithm by pushing the parameters that would normally be passed to the recursive function onto a stack. In fact, you are replacing the program stack by one of your own.

var stack = [];
stack.push(firstObject);

// while not empty
while (stack.length) {

    // Pop off end of stack.
    obj = stack.pop();

    // Do stuff.
    // Push other objects on the stack as needed.
    ...

}

Note: if you have more than one recursive call inside and you want to preserve the order of the calls, you have to add them in the reverse order to the stack:

foo(first);
foo(second);

has to be replaced by

stack.push(second);
stack.push(first);

Edit: The article Stacks and Recursion Elimination (or Article Backup link) goes into more details on this subject.

Really, the most common way to do it is to keep your own stack. Here's a recursive quicksort function in C:

void quicksort(int* array, int left, int right)
{
    if(left >= right)
        return;

    int index = partition(array, left, right);
    quicksort(array, left, index - 1);
    quicksort(array, index + 1, right);
}

Here's how we could make it iterative by keeping our own stack:

void quicksort(int *array, int left, int right)
{
    int stack[1024];
    int i=0;

    stack[i++] = left;
    stack[i++] = right;

    while (i > 0)
    {
        right = stack[--i];
        left = stack[--i];

        if (left >= right)
             continue;

        int index = partition(array, left, right);
        stack[i++] = left;
        stack[i++] = index - 1;
        stack[i++] = index + 1;
        stack[i++] = right;
    }
}

Obviously, this example doesn't check stack boundaries... and really you could size the stack based on the worst case given left and and right values. But you get the idea.