Overview

Recursion

recursion is a process in which a function calls itself as a subroutine. this allows the function to be repeated several times, since it calls itself during its execution. Functions that incorporate recursion are called recursive functions.

Definition

Recursion

Recursion is used for big problems that can be broken into multiple, smaller pieces.

Why do we use recursion?

Factorial: The product of an integer and all the integers below it.

var tenFactorial = 4 * 3 * 2 * 1;

console.log(tenFactorial) // 24

Recursion

Let's take a look at what this looks like in code.

Why do we use recursion?

var factorial = function(num){
	if (num <= 1){
		return 1;
	} else {
		return num * factorial(num-1);
	}
}

big problem

smaller pieces

Recursion

1. Base Case: The condition that triggers the end of the current recursive branch. Goes at the top of your function. Code inside always returns, but does not have to return a value.​
2. Recursive Call: If the base-case does not trigger, we will invoke our recursive function passing in a new value. The new value will move must move us closer to our base case.
3. Return statement: You must provide a return statement somewhere outside of your base case. If not, your program will run infinitely.

Recursion Rules

Recursion

See them in action.

Recursion Rules

var factorial = function(num){
	if (num <= 1){
		return 1;
	} else {
		return num * factorial(num-1);
	}
}

base case 

action step/recursive call

return statements

Recursion

Recursion and iteration are very similar and can sometimes be used interchangeably.

Recursion vs Iteration

Recursion

Iteration is best when you'd like to search through mostly linear data.

Linear Search

var linearArray = [1, 2, 3, 4, 5, 6, 7];

for (var i = 0; i <= linearArray.length; i++){
    // looping straight through the array.
    console.log(linearArray[i]);
};

11

12

13

14

15

16

17

Recursion

Iteration is also good for simply nested data.

Nested Data Search

var nestedArray = [1, 2, [3, 4, 5] 6, 7];

for (var i = 0; i <= nestedArray.length; i++){
    if (Array.isArray(nestedArray[i]){
       for (var j = 0; j <= nestedArray[i].length; j++){
           console.log(nestedArray[i][j];
       }
    } else {
        console.log(nestedArray[i]);
    }
};

11

12

13

14

15

1[ ]

17

16

Recursion

var treeOfNumbers = [
    [1, 2, [3, [4, [5]], 6]],
    [7, [8, 9]],
    [10, [11, [12]]],
];

A tree is a collection of data with many embedded data structures. The internal data structures are called branches.

Tree Data Structure

branches

tree structure

Recursion

var countEvens = function(tree){
 // base case?
 // action step?
 // return statement?
};

var treeOfNumbers = [
    [1, 2, [3, [4, [5]], 6]],
    [7, [8, 9]],
    [10, [11, [12]]],
];

Recursion is the best method to use when it comes to tree structures.

Recursion!

big problem: looping through tree of arrays.

Recursion

var countEvens = function(tree){
 // base case?
 // action step?
 // return statement?
};

Solve it yourself! Pause the video and give yourself ~15 minutes to solve this function.

Recursion!

Recursion

Recursion is the best method to use when it comes to tree structures.

Recursion!

var countEvens = function(tree){
 var count = 0;
 for (var i = 0; i < tree.length; i++){
    if (Array.isArray(tree[i])){
                // action step/recursive call
        count += countEvens(branch[i]);
    } else {
        if(tree[i] % 2 === 0){
          //action step
          count += 1;
        }
    }
    
 }
 // base case & return statement
 return count;
};

Recursion

Test your understanding!

// Refactor this contains function into a recursive function.
// contains takes a collection and a value and returns true 
// if the value exists within the collection
// and false if it does not.
var contains = function(collection, inputValue){
	var state = false;
	collection.forEach(function(element){
		if (element === inputValue){
			state = true;
		}
	});
	return state;
};