Can every recursion be changed to iteration?

Question

Is every recursive function convertible to iteration? What characteristic should a recursive function have in order for it to be implemented using iteration?

I've been trying to define the following function using iteration but seems like a no-go! It is supposed to explore all the paths (nodes) in a maze. Can anyone rewrite this using iterations? If it is not possible, why not?

typedef int[0,99] id_t;
bool visited[id_t];
int path[id_t];
int pathCounter = 0;

struct { 
    id_t id;
    bool free;
    int neighborNode[4];
} nodeMap[id_t];

void findPath(int current){
    visited[current] = true;
    for (i : int[0, 3]){
        if(nodeMap[nodeMap[current].neighborNode[i]].free == true && visited[nodeMap[current].neighborNode[i]] == false && nodeMap[current].neighborNode[i] != -1){
        path[pathCounter] = nodeMap[nodeMap[current].neighborNode[i]].id;
        pathCounter++;
        findPath(nodeMap[current].neighborNode[i]);
        path[pathCounter] = nodeMap[current].id;
        pathCounter++;      
        }
    }
    path[0] = current;
}

Extension: Is it possible to convert the mentioned recursive function to iteration without implementing my own stack? One of the answers suggested that every tail recursive function can be converted to iteration without using a stack structure...if that's so, is every recursive function convertible to tail recursion? How?

Answer 1

Yes, every recursive function can be converted to an iterative one by following a rather mechanical process.

Recall that compilers implement recursion by using a stack, which is typically implemented in the CPU's hardware. You can build a software stack of your own, make it suitable for keeping the state of your function (i.e. its local variables), push the initial state onto that stack, and write a while loop that pushes new state onto the stack instead of making a recursive call, popping the stack instead of returning, and continuing the process while the stack is not empty.

Answer 2

It is generally possible to convert any recursive algorithm into loop. The method is simple: we can imitate how the compiler generate code for function call: entering function, returning from function, and continue execution.

To turn a recursive function into an iterative loop, you can:

• Define a record, which stores the arguments to the function and the local variables. This is equivalent to stack frame.
• Define a stack, to which records a pushed. This is analogy to the program stack.
• When a function is called, create a record of the current value of the arguments and local variables and push to stack.
• When you return from the function, pop out from stack and overwrite the current value with that from the record.

The whole process above is done in a while loop, which will exit when the stack is empty,