hello-algo/en/codes/rust/chapter_computational_complexity/recursion.rs

/*
 * File: recursion.rs
 * Created Time: 2023-09-02
 * Author: night-cruise (2586447362@qq.com)
 */

/* Recursion */
fn recur(n: i32) -> i32 {
    // Base case
    if n == 1 {
        return 1;
    }
    // Recurse: make a recursive call
    let res = recur(n - 1);
    // Unwind: return the result
    n + res
}

/* Simulate recursion using iteration */
fn for_loop_recur(n: i32) -> i32 {
    // Use an explicit stack to simulate the system call stack
    let mut stack = Vec::new();
    let mut res = 0;
    // Recurse: make a recursive call
    for i in (1..=n).rev() {
        // Simulate recursive calls by pushing onto the stack
        stack.push(i);
    }
    // Unwind: return the result
    while !stack.is_empty() {
        // Simulate unwinding by popping from the stack
        res += stack.pop().unwrap();
    }
    // res = 1+2+3+...+n
    res
}

/* Tail recursion */
fn tail_recur(n: i32, res: i32) -> i32 {
    // Base case
    if n == 0 {
        return res;
    }
    // Tail-recursive call
    tail_recur(n - 1, res + n)
}

/* Fibonacci sequence: recursion */
fn fib(n: i32) -> i32 {
    // Base cases: f(1) = 0, f(2) = 1
    if n == 1 || n == 2 {
        return n - 1;
    }
    // Recursive calls: f(n) = f(n-1) + f(n-2)
    let res = fib(n - 1) + fib(n - 2);
    // Return the result
    res
}

/* Driver code */
fn main() {
    let n = 5;
    let mut res;

    res = recur(n);
    println!("\nSum from the recursive function: res = {res}");

    res = for_loop_recur(n);
    println!("\nSum from simulating recursion using iteration: res = {res}");

    res = tail_recur(n, 0);
    println!("\nSum from the tail-recursive function: res = {res}");

    res = fib(n);
    println!("\nTerm {n} of the Fibonacci sequence is {res}");
}