{{quote {author: "Donald Knuth", chapter: true}
People think that computer science is the art of geniuses but the actual reality is the opposite, just many people doing things that build on each other, like a wall of mini stones.
quote}}
{{index "Knuth, Donald"}}
{{figure {url: "img/chapter_picture_3.jpg", alt: "Picture of fern leaves with a fractal shape", chapter: framed}}}
{{index function, [code, "structure of"]}}
Functions are the bread and butter of JavaScript programming. The concept of wrapping a piece of program in a value has many uses. It gives us a way to structure larger programs, to reduce repetition, to associate names with subprograms, and to isolate these subprograms from each other.
The most obvious application of functions is defining new ((vocabulary)). Creating new words in prose is usually bad style. But in programming, it is indispensable.
{{index abstraction, vocabulary}}
Typical adult English speakers have some 20,000 words in their vocabulary. Few programming languages come with 20,000 commands built in. And the vocabulary that is available tends to be more precisely defined, and thus less flexible, than in human language. Therefore, we usually have to introduce new concepts to avoid repeating ourselves too much.
{{index "square example", [function, definition], [binding, definition]}}
A function definition is a regular binding where the value of the
binding is a function. For example, this code defines square
to
refer to a function that produces the square of a given number:
const square = function(x) {
return x * x;
};
console.log(square(12));
// → 144
{{indexsee "curly braces", braces}} {{index [braces, "function body"], block, [syntax, function], "function keyword", [function, body], [function, "as value"], [parentheses, arguments]}}
A function is created with an expression that starts with the keyword
function
. Functions have a set of ((parameter))s (in this case,
only x
) and a body, which contains the statements that are to be
executed when the function is called. The function body of a function
created this way must always be wrapped in braces, even when it
consists of only a single ((statement)).
{{index "power example"}}
A function can have multiple parameters or no parameters at all. In
the following example, makeNoise
does not list any parameter names,
whereas power
lists two:
const makeNoise = function() {
console.log("Pling!");
};
makeNoise();
// → Pling!
const power = function(base, exponent) {
let result = 1;
for (let count = 0; count < exponent; count++) {
result *= base;
}
return result;
};
console.log(power(2, 10));
// → 1024
{{index "return value", "return keyword", undefined}}
Some functions produce a value, such as power
and square
, and some
don't, such as makeNoise
, whose only result is a ((side effect)). A
return
statement determines the value the function returns. When
control comes across such a statement, it immediately jumps out of the
current function and gives the returned value to the code that called
the function. A return
keyword without an expression after it will
cause the function to return undefined
. Functions that don't have a
return
statement at all, such as makeNoise
, similarly return
undefined
.
{{index parameter, [function, application], [binding, "from parameter"]}}
Parameters to a function behave like regular bindings, but their initial values are given by the caller of the function, not the code in the function itself.
{{indexsee "top-level scope", "global scope"}} {{index "var keyword", "global scope", [binding, global], [binding, "scope of"]}}
Each binding has a ((scope)), which is the part of the program in which the binding is visible. For bindings defined outside of any function or block, the scope is the whole program—you can refer to such bindings wherever you want. These are called global.
{{index "local scope", [binding, local]}}
But bindings created for function ((parameter))s or declared inside a function can be referenced only in that function, so they are known as local bindings. Every time the function is called, new instances of these bindings are created. This provides some isolation between functions—each function call acts in its own little world (its local environment) and can often be understood without knowing a lot about what's going on in the global environment.
{{index "let keyword", "const keyword", "var keyword"}}
Bindings declared with let
and const
are in fact local to the
((block)) that they are declared in, so if you create one of those
inside of a loop, the code before and after the loop cannot "see" it.
In pre-2015 JavaScript, only functions created new scopes, so
old-style bindings, created with the var
keyword, are visible
throughout the whole function that they appear in—or throughout the
global scope, if they are not in a function.
let x = 10;
if (true) {
let y = 20;
var z = 30;
console.log(x + y + z);
// → 60
}
// y is not visible here
console.log(x + z);
// → 40
{{index [binding, visibility]}}
Each ((scope)) can "look out" into the scope around it, so x
is
visible inside the block in the example. The exception is when
multiple bindings have the same name—in that case, code can see only
the innermost one. For example, when the code inside the halve
function refers to n
, it is seeing its own n
, not the global
n
.
const halve = function(n) {
return n / 2;
};
let n = 10;
console.log(halve(100));
// → 50
console.log(n);
// → 10
{{id scoping}}
{{index [nesting, "of functions"], [nesting, "of scope"], scope, "inner function", "lexical scoping"}}
JavaScript distinguishes not just global and local bindings. Blocks and functions can be created inside other blocks and functions, producing multiple degrees of locality.
{{index "landscape example"}}
For example, this function—which outputs the ingredients needed to make a batch of hummus—has another function inside it:
const hummus = function(factor) {
const ingredient = function(amount, unit, name) {
let ingredientAmount = amount * factor;
if (ingredientAmount > 1) {
unit += "s";
}
console.log(`${ingredientAmount} ${unit} ${name}`);
};
ingredient(1, "can", "chickpeas");
ingredient(0.25, "cup", "tahini");
ingredient(0.25, "cup", "lemon juice");
ingredient(1, "clove", "garlic");
ingredient(2, "tablespoon", "olive oil");
ingredient(0.5, "teaspoon", "cumin");
};
{{index [function, scope], scope}}
The code inside the ingredient
function can see the factor
binding
from the outer function. But its local bindings, such as unit
or
ingredientAmount
, are not visible in the outer function.
The set of bindings visible inside a block is determined by the place of that block in the program text. Each local scope can also see all the local scopes that contain it, and all scopes can see the global scope. This approach to binding visibility is called ((lexical scoping)).
{{index [function, "as value"], [binding, definition]}}
A function binding usually simply acts as a name for a specific piece of the program. Such a binding is defined once and never changed. This makes it easy to confuse the function and its name.
{{index [binding, assignment]}}
But the two are different. A function value can do all the things that other values can do—you can use it in arbitrary ((expression))s, not just call it. It is possible to store a function value in a new binding, pass it as an argument to a function, and so on. Similarly, a binding that holds a function is still just a regular binding and can, if not constant, be assigned a new value, like so:
let launchMissiles = function() {
missileSystem.launch("now");
};
if (safeMode) {
launchMissiles = function() {/* do nothing */};
}
{{index [function, "higher-order"]}}
In Chapter ?, we will discuss the interesting things that can be done by passing around function values to other functions.
{{index [syntax, function], "function keyword", "square example", [function, definition], [function, declaration]}}
There is a slightly shorter way to create a function binding. When the
function
keyword is used at the start of a statement, it works
differently.
function square(x) {
return x * x;
}
{{index future, "execution order"}}
This is a function declaration. The statement defines the binding
square
and points it at the given function. It is slightly easier
to write and doesn't require a semicolon after the function.
There is one subtlety with this form of function definition.
console.log("The future says:", future());
function future() {
return "You'll never have flying cars";
}
The preceding code works, even though the function is defined below the code that uses it. Function declarations are not part of the regular top-to-bottom flow of control. They are conceptually moved to the top of their scope and can be used by all the code in that scope. This is sometimes useful because it offers the freedom to order code in a way that seems meaningful, without worrying about having to define all functions before they are used.
{{index function, "arrow function"}}
There's a third notation for functions, which looks very different
from the others. Instead of the function
keyword, it uses an arrow
(=>
) made up of an equal sign and a greater-than character (not to be
confused with the greater-than-or-equal operator, which is written
>=
).
const power = (base, exponent) => {
let result = 1;
for (let count = 0; count < exponent; count++) {
result *= base;
}
return result;
};
{{index [function, body]}}
The arrow comes after the list of parameters and is followed by the function's body. It expresses something like "this input (the ((parameter))s) produces this result (the body)".
{{index [braces, "function body"], "square example", [parentheses, arguments]}}
When there is only one parameter name, you can omit the parentheses around the
parameter list. If the body is a single expression,
rather than a ((block)) in braces, that expression will be returned
from the function. So, these two definitions of square
do the same
thing:
const square1 = (x) => { return x * x; };
const square2 = x => x * x;
{{index [parentheses, arguments]}}
When an arrow function has no parameters at all, its parameter list is just an empty set of parentheses.
const horn = () => {
console.log("Toot");
};
{{index verbosity}}
There's no deep reason to have both arrow functions and
function
expressions in the language. Apart from a minor detail,
which we'll discuss in Chapter ?, they do the same thing.
Arrow functions were added in 2015, mostly to make it possible to
write small function expressions in a less verbose way. We'll be using
them a lot in Chapter ?.
{{id stack}}
{{indexsee stack, "call stack"}} {{index "call stack", [function, application]}}
The way control flows through functions is somewhat involved. Let's take a closer look at it. Here is a simple program that makes a few function calls:
function greet(who) {
console.log("Hello " + who);
}
greet("Harry");
console.log("Bye");
{{index ["control flow", functions], "execution order", "console.log"}}
A run through this program goes roughly like this: the call to greet
causes control to jump to the start of that function (line 2). The
function calls console.log
, which takes control, does its job, and
then returns control to line 2. There it reaches the end of the
greet
function, so it returns to the place that called it, which is
line 4. The line after that calls console.log
again. After that
returns, the program reaches its end.
We could show the flow of control schematically like this:
not in function
in greet
in console.log
in greet
not in function
in console.log
not in function
{{index "return keyword", [memory, call stack]}}
Because a function has to jump back to the place that called it when
it returns, the computer must remember the context from which the call
happened. In one case, console.log
has to return to the greet
function when it is done. In the other case, it returns to the end of
the program.
The place where the computer stores this context is the ((call stack)). Every time a function is called, the current context is stored on top of this stack. When a function returns, it removes the top context from the stack and uses that context to continue execution.
{{index "infinite loop", "stack overflow", recursion}}
Storing this stack requires space in the computer's memory. When the stack grows too big, the computer will fail with a message like "out of stack space" or "too much recursion". The following code illustrates this by asking the computer a really hard question that causes an infinite back-and-forth between two functions. Rather, it would be infinite, if the computer had an infinite stack. As it is, we will run out of space, or "blow the stack".
function chicken() {
return egg();
}
function egg() {
return chicken();
}
console.log(chicken() + " came first.");
// → ??
{{index argument, [function, application]}}
The following code is allowed and executes without any problem:
function square(x) { return x * x; }
console.log(square(4, true, "hedgehog"));
// → 16
We defined square
with only one ((parameter)). Yet when we call it
with three, the language doesn't complain. It ignores the extra
arguments and computes the square of the first one.
{{index undefined}}
JavaScript is extremely broad-minded about the number of arguments you
pass to a function. If you pass too many, the extra ones are ignored.
If you pass too few, the missing parameters get assigned the value
undefined
.
The downside of this is that it is possible—likely, even—that you'll accidentally pass the wrong number of arguments to functions. And no one will tell you about it.
The upside is that this behavior can be used to allow a function to be
called with different numbers of arguments. For example, this minus
function tries to imitate the -
operator by acting on either one or
two arguments:
function minus(a, b) {
if (b === undefined) return -a;
else return a - b;
}
console.log(minus(10));
// → -10
console.log(minus(10, 5));
// → 5
{{id power}} {{index "optional argument", "default value", parameter, ["= operator", "for default value"]}}
If you write an =
operator after
a parameter, followed by an expression, the value of that expression
will replace the argument when it is not given.
{{index "power example"}}
For example, this version of power
makes its second argument
optional. If you don't provide it or pass the value undefined
, it will default to two, and the
function will behave like square
.
function power(base, exponent = 2) {
let result = 1;
for (let count = 0; count < exponent; count++) {
result *= base;
}
return result;
}
console.log(power(4));
// → 16
console.log(power(2, 6));
// → 64
{{index "console.log"}}
In the next chapter, we will see a way in
which a function body can get at the whole list of arguments it was
passed. This is helpful because it makes it possible for a function to
accept any number of arguments. For example, console.log
does
this—it outputs all of the values it is given.
console.log("C", "O", 2);
// → C O 2
{{index "call stack", "local binding", [function, "as value"], scope}}
The ability to treat functions as values, combined with the fact that local bindings are re-created every time a function is called, brings up an interesting question. What happens to local bindings when the function call that created them is no longer active?
The following code shows an example of this. It defines a function,
wrapValue
, that creates a local binding. It then returns a function
that accesses and returns this local binding.
function wrapValue(n) {
let local = n;
return () => local;
}
let wrap1 = wrapValue(1);
let wrap2 = wrapValue(2);
console.log(wrap1());
// → 1
console.log(wrap2());
// → 2
This is allowed and works as you'd hope—both instances of the binding can still be accessed. This situation is a good demonstration of the fact that local bindings are created anew for every call, and different calls can't trample on one another's local bindings.
This feature—being able to reference a specific instance of a local binding in an enclosing scope—is called ((closure)). A function that references bindings from local scopes around it is called a closure. This behavior not only frees you from having to worry about lifetimes of bindings but also makes it possible to use function values in some creative ways.
{{index "multiplier function"}}
With a slight change, we can turn the previous example into a way to create functions that multiply by an arbitrary amount.
function multiplier(factor) {
return number => number * factor;
}
let twice = multiplier(2);
console.log(twice(5));
// → 10
{{index [binding, "from parameter"]}}
The explicit local
binding from the wrapValue
example isn't really
needed since a parameter is itself a local binding.
{{index [function, "model of"]}}
Thinking about programs like this takes some practice. A good mental model is to think of function values as containing both the code in their body and the environment in which they are created. When called, the function body sees the environment in which it was created, not the environment in which it is called.
In the example, multiplier
is called and creates an environment in
which its factor
parameter is bound to 2. The function value it
returns, which is stored in twice
, remembers this environment. So
when that is called, it multiplies its argument by 2.
{{index "power example", "stack overflow", recursion, [function, application]}}
It is perfectly okay for a function to call itself, as long as it
doesn't do it so often that it overflows the stack. A function that calls
itself is called recursive. Recursion allows some functions to be
written in a different style. Take, for example, this alternative
implementation of power
:
function power(base, exponent) {
if (exponent == 0) {
return 1;
} else {
return base * power(base, exponent - 1);
}
}
console.log(power(2, 3));
// → 8
{{index loop, readability, mathematics}}
This is rather close to the way mathematicians define exponentiation and arguably describes the concept more clearly than the looping variant. The function calls itself multiple times with ever smaller exponents to achieve the repeated multiplication.
{{index [function, application], efficiency}}
But this implementation has one problem: in typical JavaScript implementations, it's about three times slower than the looping version. Running through a simple loop is generally cheaper than calling a function multiple times.
{{index optimization}}
The dilemma of speed versus ((elegance)) is an interesting one. You can see it as a kind of continuum between human-friendliness and machine-friendliness. Almost any program can be made faster by making it bigger and more convoluted. The programmer has to decide on an appropriate balance.
In the case of the power
function, the inelegant (looping) version
is still fairly simple and easy to read. It doesn't make much sense to
replace it with the recursive version. Often, though, a program deals
with such complex concepts that giving up some efficiency in order to
make the program more straightforward is helpful.
{{index profiling}}
Worrying about efficiency can be a distraction. It's yet another factor that complicates program design, and when you're doing something that's already difficult, that extra thing to worry about can be paralyzing.
{{index "premature optimization"}}
Therefore, always start by writing something that's correct and easy to understand. If you're worried that it's too slow—which it usually isn't since most code simply isn't executed often enough to take any significant amount of time—you can measure afterward and improve it if necessary.
{{index "branching recursion"}}
Recursion is not always just an inefficient alternative to looping. Some problems really are easier to solve with recursion than with loops. Most often these are problems that require exploring or processing several "branches", each of which might branch out again into even more branches.
{{id recursive_puzzle}} {{index recursion, "number puzzle example"}}
Consider this puzzle: by starting from the number 1 and repeatedly either adding 5 or multiplying by 3, an infinite set of numbers can be produced. How would you write a function that, given a number, tries to find a sequence of such additions and multiplications that produces that number?
For example, the number 13 could be reached by first multiplying by 3 and then adding 5 twice, whereas the number 15 cannot be reached at all.
Here is a recursive solution:
function findSolution(target) {
function find(current, history) {
if (current == target) {
return history;
} else if (current > target) {
return null;
} else {
return find(current + 5, `(${history} + 5)`) ||
find(current * 3, `(${history} * 3)`);
}
}
return find(1, "1");
}
console.log(findSolution(24));
// → (((1 * 3) + 5) * 3)
Note that this program doesn't necessarily find the shortest sequence of operations. It is satisfied when it finds any sequence at all.
It is okay if you don't see how it works right away. Let's work through it, since it makes for a great exercise in recursive thinking.
The inner function find
does the actual recursing. It takes two
((argument))s: the current number and a string that records how we
reached this number. If it finds a solution, it returns a string that
shows how to get to the target. If no solution can be found starting
from this number, it returns null
.
{{index null, "|| operator", "short-circuit evaluation"}}
To do this, the function performs one of three actions. If the current
number is the target number, the current history is a way to reach
that target, so it is returned. If the current number is greater than
the target, there's no sense in further exploring this branch because
both adding and multiplying will only make the number bigger, so it
returns null
. Finally, if we're still below the target number,
the function tries both possible paths that start from the current
number by calling itself twice, once for addition and once for
multiplication. If the first call returns something that is not
null
, it is returned. Otherwise, the second call is returned,
regardless of whether it produces a string or null
.
{{index "call stack"}}
To better understand how this function produces the effect we're
looking for, let's look at all the calls to find
that are made when
searching for a solution for the number 13.
find(1, "1")
find(6, "(1 + 5)")
find(11, "((1 + 5) + 5)")
find(16, "(((1 + 5) + 5) + 5)")
too big
find(33, "(((1 + 5) + 5) * 3)")
too big
find(18, "((1 + 5) * 3)")
too big
find(3, "(1 * 3)")
find(8, "((1 * 3) + 5)")
find(13, "(((1 * 3) + 5) + 5)")
found!
The indentation indicates the depth of the call stack. The first time
find
is called, it starts by calling itself to explore the solution
that starts with (1 + 5)
. That call will further recurse to explore
every continued solution that yields a number less than or equal to
the target number. Since it doesn't find one that hits the target, it
returns null
back to the first call. There the ||
operator causes
the call that explores (1 * 3)
to happen. This search has more
luck—its first recursive call, through yet another recursive call,
hits upon the target number. That innermost call returns a string, and
each of the ||
operators in the intermediate calls passes that string
along, ultimately returning the solution.
{{index [function, definition]}}
There are two more or less natural ways for functions to be introduced into programs.
{{index repetition}}
The first is that you find yourself writing similar code multiple times. You'd prefer not to do that. Having more code means more space for mistakes to hide and more material to read for people trying to understand the program. So you take the repeated functionality, find a good name for it, and put it into a function.
The second way is that you find you need some functionality that you haven't written yet and that sounds like it deserves its own function. You'll start by naming the function, and then you'll write its body. You might even start writing code that uses the function before you actually define the function itself.
{{index [function, naming], [binding, naming]}}
How difficult it is to find a good name for a function is a good indication of how clear a concept it is that you're trying to wrap. Let's go through an example.
{{index "farm example"}}
We want to write a program that prints two numbers: the numbers of
cows and chickens on a farm, with the words Cows
and Chickens
after them and zeros padded before both numbers so that they are
always three digits long.
007 Cows
011 Chickens
This asks for a function of two arguments—the number of cows and the number of chickens. Let's get coding.
function printFarmInventory(cows, chickens) {
let cowString = String(cows);
while (cowString.length < 3) {
cowString = "0" + cowString;
}
console.log(`${cowString} Cows`);
let chickenString = String(chickens);
while (chickenString.length < 3) {
chickenString = "0" + chickenString;
}
console.log(`${chickenString} Chickens`);
}
printFarmInventory(7, 11);
{{index ["length property", "for string"], "while loop"}}
Writing .length
after a string expression will give us the length of
that string. Thus, the while
loops keep adding zeros in front of the
number strings until they are at least three characters long.
Mission accomplished! But just as we are about to send the farmer the code (along with a hefty invoice), she calls and tells us she's also started keeping pigs, and couldn't we please extend the software to also print pigs?
{{index "copy-paste programming"}}
We sure can. But just as we're in the process of copying and pasting those four lines one more time, we stop and reconsider. There has to be a better way. Here's a first attempt:
function printZeroPaddedWithLabel(number, label) {
let numberString = String(number);
while (numberString.length < 3) {
numberString = "0" + numberString;
}
console.log(`${numberString} ${label}`);
}
function printFarmInventory(cows, chickens, pigs) {
printZeroPaddedWithLabel(cows, "Cows");
printZeroPaddedWithLabel(chickens, "Chickens");
printZeroPaddedWithLabel(pigs, "Pigs");
}
printFarmInventory(7, 11, 3);
{{index [function, naming]}}
It works! But that name, printZeroPaddedWithLabel
, is a little
awkward. It conflates three things—printing, zero-padding, and adding
a label—into a single function.
{{index "zeroPad function"}}
Instead of lifting out the repeated part of our program wholesale, let's try to pick out a single concept.
function zeroPad(number, width) {
let string = String(number);
while (string.length < width) {
string = "0" + string;
}
return string;
}
function printFarmInventory(cows, chickens, pigs) {
console.log(`${zeroPad(cows, 3)} Cows`);
console.log(`${zeroPad(chickens, 3)} Chickens`);
console.log(`${zeroPad(pigs, 3)} Pigs`);
}
printFarmInventory(7, 16, 3);
{{index readability, "pure function"}}
A function with a nice, obvious name like zeroPad
makes it easier
for someone who reads the code to figure out what it does. And such a
function is useful in more situations than just this specific program.
For example, you could use it to help print nicely aligned tables of
numbers.
{{index [interface, design]}}
How smart and versatile should our function be? We could write anything, from a terribly simple function that can only pad a number to be three characters wide to a complicated generalized number-formatting system that handles fractional numbers, negative numbers, alignment of decimal dots, padding with different characters, and so on.
A useful principle is to not add cleverness unless you are absolutely sure you're going to need it. It can be tempting to write general "((framework))s" for every bit of functionality you come across. Resist that urge. You won't get any real work done—you'll just be writing code that you never use.
{{id pure}}
{{index "side effect", "pure function", [function, purity]}}
Functions can be roughly divided into those that are called for their side effects and those that are called for their return value. (Though it is definitely also possible to both have side effects and return a value.)
{{index reuse}}
The first helper function in the ((farm example)),
printZeroPaddedWithLabel
, is called for its side effect: it prints a
line. The second version, zeroPad
, is called for its return value.
It is no coincidence that the second is useful in more situations than
the first. Functions that create values are easier to combine in new
ways than functions that directly perform side effects.
{{index substitution}}
A pure function is a specific kind of value-producing function that not only has no side effects but also doesn't rely on side effects from other code—for example, it doesn't read global bindings whose value might change. A pure function has the pleasant property that, when called with the same arguments, it always produces the same value (and doesn't do anything else). A call to such a function can be substituted by its return value without changing the meaning of the code. When you are not sure that a pure function is working correctly, you can test it by simply calling it and know that if it works in that context, it will work in any context. Nonpure functions tend to require more scaffolding to test.
{{index optimization, "console.log"}}
Still, there's no need to feel bad when writing functions that are not
pure or to wage a holy war to purge them from your code. Side effects
are often useful. There'd be no way to write a pure version of
console.log
, for example, and console.log
is good to have. Some
operations are also easier to express in an efficient way when we use
side effects, so computing speed can be a reason to avoid purity.
This chapter taught you how to write your own functions. The
function
keyword, when used as an expression, can create a function
value. When used as a statement, it can be used to declare a binding
and give it a function as its value. Arrow functions are yet another
way to create functions.
// Define f to hold a function value
const f = function(a) {
console.log(a + 2);
};
// Declare g to be a function
function g(a, b) {
return a * b * 3.5;
}
// A less verbose function value
let h = a => a % 3;
A key aspect in understanding functions is understanding scopes. Each
block creates a new scope. Parameters and bindings declared in a given
scope are local and not visible from the outside. Bindings declared
with var
behave differently—they end up in the nearest function
scope or the global scope.
Separating the tasks your program performs into different functions is helpful. You won't have to repeat yourself as much, and functions can help organize a program by grouping code into pieces that do specific things.
{{index "Math object", "minimum (exercise)", "Math.min function", minimum}}
The previous chapter introduced the
standard function Math.min
that returns its smallest argument. We
can build something like that now. Write a function min
that takes
two arguments and returns their minimum.
{{if interactive
// Your code here.
console.log(min(0, 10));
// → 0
console.log(min(0, -10));
// → -10
if}}
{{hint
{{index "minimum (exercise)"}}
If you have trouble putting braces and parentheses in the right place to get a valid function definition, start by copying one of the examples in this chapter and modifying it.
{{index "return keyword"}}
A function may contain multiple return
statements.
hint}}
{{index recursion, "isEven (exercise)", "even number"}}
We've seen that %
(the remainder operator) can be used to test
whether a number is even or odd by using % 2
to see whether it's
divisible by two. Here's another way to define whether a positive
whole number is even or odd:
-
Zero is even.
-
One is odd.
-
For any other number N, its evenness is the same as N - 2.
Define a recursive function isEven
corresponding to this
description. The function should accept a single parameter (a
positive, whole number) and return a Boolean.
{{index "stack overflow"}}
Test it on 50 and 75. See how it behaves on -1. Why? Can you think of a way to fix this?
{{if interactive
// Your code here.
console.log(isEven(50));
// → true
console.log(isEven(75));
// → false
console.log(isEven(-1));
// → ??
if}}
{{hint
{{index "isEven (exercise)", ["if keyword", chaining], recursion}}
Your function will likely look somewhat similar to the inner find
function in the recursive findSolution
example in this chapter, with an
if
/else if
/else
chain that tests which of the three cases
applies. The final else
, corresponding to the third case, makes the
recursive call. Each of the branches should contain a return
statement or in some other way arrange for a specific value to be
returned.
{{index "stack overflow"}}
When given a negative number, the function will recurse again and again, passing itself an ever more negative number, thus getting further and further away from returning a result. It will eventually run out of stack space and abort.
hint}}
{{index "bean counting (exercise)", [string, indexing], "zero-based counting", ["length property", "for string"]}}
You can get the Nth character, or letter, from a string by writing
"string"[N]
. The returned value will be a string containing only one
character (for example, "b"
). The first character has position 0,
which causes the last one to be found at position string.length - 1
.
In other words, a two-character string has length 2, and its
characters have positions 0 and 1.
Write a function countBs
that takes a string as its only argument
and returns a number that indicates how many uppercase "B" characters
there are in the string.
Next, write a function called countChar
that behaves like countBs
,
except it takes a second argument that indicates the character that is
to be counted (rather than counting only uppercase "B" characters).
Rewrite countBs
to make use of this new function.
{{if interactive
// Your code here.
console.log(countBs("BBC"));
// → 2
console.log(countChar("kakkerlak", "k"));
// → 4
if}}
{{hint
{{index "bean counting (exercise)", ["length property", "for string"], "counter variable"}}
Your function will need a ((loop)) that looks at every character in
the string. It can run an index from zero to one below its length (< string.length
). If the character at the current position is the same
as the one the function is looking for, it adds 1 to a counter
variable. Once the loop has finished, the counter can be returned.
{{index "local binding"}}
Take care to make all the bindings used in the function local to the
function by properly declaring them with the let
or const
keyword.
hint}}