Iteration vs Recursion

Staying out of the loop with recursion.

Iteration​

• Imperative looping stateful.
• Using loops to do Iteration.

Example​

function sum(numbers) {
  let total = 0;
  for (i = 0; i < numbers.length; i++) {
    total += numbers[i];
  }
  return total;
}

sum([0, 1, 2, 3, 4]); // 10

Problem: Find the factorial of number using Iteration

Example 5! = 5 x 4 x 3 x 2 x 1

Factorial(1)                      = 1; // base condition
Factorial(2) = 2 * 1              = 2 * Factorial(1);
Factorial(3) = 3 * 2 * 1          = 3 * Factorial(2);
Factorial(4) = 4 * 3 * 2 * 1      = 4 * Factorial(3);
Factorial(5) = 5 * 4 * 3 * 2 * 1  = 5 * Factorial(4);
Factorial(n) = n * Factorial(n-1) // recursive condition

function factorial(n) {
  let fact = 1;
  for (let i = 5; i > 0; i--) {
    fact *= i;
  }
  return fact;
}
console.log(factorial(5)); // return 120

Fanocci Number find usign Iterative

function iterativeFabnocci(n) {
  if (n === 0) return 0;
  if (n === 1) return 1;
  let previous = 0;
  let current = 1;
  for (let i = n; i > 1; i--) {
    let next = previous + current;
    previous = current;
    current = next;
  }
  return current;
}
console.log(iterativeFabnocci(6));

Recursion​

• functional self-referential stateless.
• When a function is recursive, it continues to call itself until a non-recursive base case is reached.

Example​

A recursive function has two parts:

1. Base Case : stop the execution by calling it self if the length is 1. if we not added it, it goes to infit loop.

• It is condition(s) under which the function returns an output without making a recursive call.
• Base condition is the one which doesn’t require fo call the same function again and it helps in stopping the recursion.

1. Recursive Case: calling itself function until the last element.It is condition(s) under which the function calls itself to return the output.

function sum(numbers) {
  if (numbers.length === 1) {
    // base case
    return numbers[0];
  } else {
    // recursive case
    return numbers[0] + sum(numbers.slice(1));
  }
}

sum([0, 1, 2, 3, 4]); // 10

Problem: Find the factorial of number using recursive

function factorial(n) {
  if (n === 1) {
    return 1;
  } else {
    return n * factorial(n - 1);
  }
}
console.log(factorial(5)); // return 120

Fabnocci Number using Recursive Func

function recursiveFabnocci(n) {
  if (n === 0) return 0;
  if (n === 1) return 1;
  return recursiveFabnocci(n - 1) + recursiveFabnocci(n - 2);
}
console.log(recursiveFabnocci(6));

Are recursive functions more expensive than iterative functions?

Exercise​

• Iteration vs Recursion Exercise

Comparing performance​

• Recursive has less performance then iterative the reason is that Recursive call again and again itself.
• Another reason is that call stack, it call too much recursion.
• Recursion throw error "Internal Error: too much recursion" in Firefox if we adding the 10,000. to solve this error using Trail call Optimization.

• Using memorization(cache) in the recursion the result that can help to re-again calculate the computation in the recursion.