Tail Call Elimination - GeeksforGeeks

17 May, 2021
We have discussed (in tail recursion) that a recursive function is tail recursive if the recursive call is the last thing executed by the function. 
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// An example of tail recursive functionvoid print(int n){    if (n < 0)        return;    cout << " " << n;     // The last executed statement is recursive call    print(n-1);}
// An example of tail recursive functionstatic void print(int n){    if (n < 0)        return;             System.out.print(" " + n);     // The last executed statement    // is recursive call    print(n - 1);} // This code is contributed by rutvik_56
# An example of tail recursive functiondef print(n):         if (n < 0):       return        print(" ", n)      # The last executed statement is recursive call    print(n - 1) # This code is contributed by sanjoy_62
// An example of tail recursive functionstatic void print(int n){    if (n < 0)        return;             Console.Write(" " + n);     // The last executed statement    // is recursive call    print(n - 1);} // This code is contributed by pratham76
<script>  // An example of tail recursive functionfunction print(n){    if (n < 0)        return;    document.write( " " + n);     // The last executed statement is recursive call    print(n-1);}  </script>
We also discussed that a tail-recursive is better than a non-tail recursive as tail-recursion can be optimized by modern compilers. Modern compiler basically does tail call elimination to optimize the tail-recursive code. 
If we take a closer look at the above function, we can remove the last call with goto. Below are examples of tail call elimination.
C++
// Above code after tail call eliminationvoid print(int n){start:    if (n < 0)       return;    cout << " " << n;     // Update parameters of recursive call    // and replace recursive call with goto    n = n-1    goto start;}
QuickSort : One more example QuickSort is also tail recursive (Note that MergeSort is not tail recursive, this is also one of the reasons why QuickSort performs better) 
C++
/* Tail recursive function for QuickSort arr[] --> Array to be sorted,  low  --> Starting index,  high  --> Ending index */void quickSort(int arr[], int low, int high){    if (low < high)    {        /* pi is partitioning index, arr[p] is now           at right place */        int pi = partition(arr, low, high);         // Separately sort elements before        // partition and after partition        quickSort(arr, low, pi - 1);        quickSort(arr, pi + 1, high);    }}// See below link for complete running code// http://geeksquiz.com/quick-sort/
The above function can be replaced by following after tail call elimination. 
C++
/* QuickSort after tail call elimination  arr[] --> Array to be sorted,  low  --> Starting index,  high  --> Ending index */void quickSort(int arr[], int low, int high){start:    if (low < high)    {        /* pi is partitioning index, arr[p] is now           at right place */        int pi = partition(arr, low, high);         // Separately sort elements before        // partition and after partition        quickSort(arr, low, pi - 1);         // Update parameters of recursive call        // and replace recursive call with goto        low = pi+1;        high = high;        goto start;    }}// See below link for complete running code// https://ide.geeksforgeeks.org/dbq4yl
Therefore job for compilers is to identify tail recursion, add a label at the beginning and update parameter(s) at the end followed by adding the last goto statement.
Function stack frame management in Tail Call Elimination : Recursion uses a stack to keep track of function calls. With every function call, a new frame is pushed onto the stack which contains local variables and data of that call. Let’s say one stack frame requires O(1) i.e, constant memory space, then for N recursive call memory required would be O(N). 
Tail call elimination reduces the space complexity of recursion from O(N) to O(1). As function call is eliminated, no new stack frames are created and the function is executed in constant memory space. 
It is possible for the function to execute in constant memory space because, in tail recursive function, there are no statements after call statement so preserving state and frame of parent function is not required. Child function is called and finishes immediately, it doesn’t have to return control back to the parent function. 
As no computation is performed on the returned value and no statements are left for execution, the current frame can be modified as per the requirements of the current function call. So there is no need to preserve stack frames of previous function calls and function executes in constant memory space. This makes tail recursion faster and memory-friendly.
Next Article: QuickSort Tail Call Optimization (Reducing worst case space to Log n )This article is contributed by Dheeraj Jain. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above 
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