Construction and interpretation of computer programs> 1. Construction Process abstraction> 1.2. Process and the computation they produce

Linear recursion:

Function Factorial (n ){
Return N = 1? 1: N * factorial (n-1 );
}

 

Linear iteration:

Function Factorial (n ){
Return Fact_iter (1, 1, n );
}
Function Fact_iter (product, counter, max_count ){
Return Counter> max_count? Product:
Fact_iter (counter * product), (counter + 1), max_count );
}

The shape of a linear recursive computing process is first expanded and then shrunk. The interpreter also saves the linear recursive calculation steps.

The linear iteration saves the computing results without the need to explain the Save calculation steps.

Therefore, linear iteration prevails in terms of speed. However, in terms of understanding, linear recursion prevails.

 

Tree recursion:

Function FIB (n ){
Return N = 0? 0: N = 1? 1:
FIB (n-1) + fib (n-2 );
}

 

estimate the time and space of the algorithm .