I have written a function for partitioning a number:
var combinations = function (i) {
var mem = [];
function inner(n, r, m) {
for (var k = m; k <= n; k++) {
if (k == n) {
r.push(k);
mem[r] = 1;
return mem;
}
else {
var copy = r.slice(0);
copy.push(k);
inner(n - k, copy, k);
}
}
}
return inner(i, [], 1);
}
In second step I would like to add a memoization to this algorithm, but can't think of implementing it the right way, beause there is no return statement until the very end (when return is specified e.g. in faactorial or fibbinacci I can add the memoization).
Can anybody drive me to the right direction?
[edit]
I need this algorithm to be as fast as possible. This is a competition for a kata at codewars: link
There is a requirement it must be executed under 6000ms for input up to 330.
That's the best algorithm I can think of, except how to store the partial results.
Here's a much simpler code that works:
function nr_partitions(n) { return p(n, n); }
function p(sum,largest) {
if (largest == 0) { return 0; }
if (sum == 0) { return 1; }
if (sum < 0) { return 0; }
return p(sum, largest-1) + p(sum-largest, largest);
}
It uses a well-known recurrence, p(n,k) = p(n,k-1) + p(n-k, k), where p(n.k) denotes the number of partitions of n where the largest part is at most k (e.g. p(3, 2)=2 because we only count 1+1+1,1+2, but not 3). For k=n we get the number of all partitions of n.
Adding memozation involves storing dictionary mapping pairs (sum, largest) to p(sum, largest).
I would go along the lines of:
var cache = {};
var combinations = function (i) {
if ( cache[i] ){
return cache[i];
};
var mem = [];
function inner(n, r, m) {
for (var k = m; k <= n; k++) {
if (k == n) {
r.push(k);
mem[r] = 1;
return mem;
}
else {
var copy = r.slice(0);
copy.push(k);
inner(n - k, copy, k);
}
}
}
cache[i] = inner(i, [], 1);
return cache[i];
}
But you'll have to modify your algorithm to make use of that cache (compute the biggest terms first ?)
Depending on your other requirements, you might want to consider using underscore.js which has its own _.memoize function.
The secret of memoization is that it exploits how closures work. When you define a function inside another scope, it has access to everything in that scope. When you return that function to somewhere outside the scope, it carries references to everything it can see inside the scope.
So to implement memorization, you need to make a function that returns another function, one that does the memorization check before calling the inner one.
Your code will look something like this:
/**
* Because we'll be returning "a function that returns a function" below,
* this needs to be executed immediately so combinations() is just
* a standalone function.
*/
var combinations = (function(i) {
/**
* mem needs to stay outside the scope of your inner function.
* If it's in a closure like this, JavaScript will keep its value
* around as long as combinations still exists.
*/
var mem = [];
/**
* A memoization wrapper should return a memoized function
*/
return function(i) {
/**
* Check if mem[i] is set and return it if it has been
*/
if(mem[i] !== undefined) {
console.log('returning memoized value');
return mem[i];
}
function inner(n, r, m) {
for (var k = m; k <= n; k++) {
if (k == n) {
r.push(k);
mem[r] = 1;
return mem;
}
else {
var copy = r.slice(0);
copy.push(k);
inner(n - k, copy, k);
}
}
}
/**
* If the value needs to be computed, we can set it at the same time
* as we return it instead of putting it in a temporary variable.
*/
console.log('computed');
return mem[i] = inner(i, [], 1);
}
}()); /** <--- That's the rest of the automatic execution */
console.log(combinations(5));
console.log(combinations(5));
Related
I have an exercise about JavaScript. This exercise requires me to use higher-order functions. I have managed to specify some of the functions so far, but when I try to execute the code, the result does not seem to work properly. I have some images to give you an idea, hopefully, you can help me correct this.
The thread is: Write the function loop(loops, number, func), which runs the given function the given number of times. Also write the simple functions halve() and square().
This is my code:
function loop(loops, number, func) {
var loops = function(n) {
for (var i = 0; i < n; i++) {
if (i < 0) {
console.log('Programme ended')
}
if (i > 0) {
return n;
}
}
}
}
var halve = function(n) {
return n / 2
}
var square = function(n) {
return n ** 2;
}
console.log(halve(50));
console.log(loop(5, 200, halve));
console.log(loop(3, 5, square));
console.log(loop(-1, 99, halve));
Your current loop function declares an inner function and then exits. Ie, nothing actually happens -
function loop(loops,number,func){
// declare loops function
var loops= function(n){
// ...
}
// exit `loop` function
}
One such fix might be to run the supplied func a number of times in a for loop, like #code_monk suggest. Another option would be to use recursion -
function loop (count, input, func) {
if (count <= 0)
return input
else
return loop(count - 1, func(input), func)
}
function times10 (num) {
return num * 10
}
console.log(loop(3, 5, times10))
// 5000
so first things first: Higher-Order functions are functions that work on other functions.
The reason why you get undefined is because you are calling a function which doesn't return anything.
function x(parameter){
result = parameter + 1;
}
// -> returns undefined every time
console.log(x(5));
// -> undefined
function y(parameter){
return parameter+1;
}
// -> returns a value that can be used later, for example in console.log
console.log(y(5));
// -> 6
Second, you are using n for your for loop when you should probably use loops so it does the intended code as many times as "loops" indicates instead of the number you insert (i.e. 200, 5, 99).
By having the "console.log" inside a loop you may get a lot of undesired "programme ended" in your output so in my version I kept it out of the loop.
The other two answers given are pretty complete I believe but if you want to keep the for loop here goes:
function loop(loops, number, func){
if(loops>0){
for(let i = 0; i< loops; i++){ // let and const are the new ES6 bindings (instead of var)
number = func(number)
}
return number
}
else{
return "Programme ended"
}
}
function halve(n) { // maybe it's just me but using function declarations feels cleaner
return n / 2;
}
function square(n) {
return n ** 2;
}
console.log(halve(50));
console.log(loop(5, 200, halve));
console.log(loop(3, 5, square));
console.log(loop(-1, 99, halve));
Here's one way
const loop = (loops, n, fn) => {
for (let i=0; i<loops; i++) {
console.log( fn(n) );
}
};
const halve = (n) => {
return n / 2;
};
const square = (n) => {
return n ** 2;
};
loop(2,3,halve);
loop(4,5,square);
I have prepared 2 Javascript functions to find matching integer pairs that add up to a sum and returns a boolean.
The first function uses a binary search like that:
function find2PairsBySumLog(arr, sum) {
for (var i = 0; i < arr.length; i++) {
for (var x = i + 1; x < arr.length; x++) {
if (arr[i] + arr[x] == sum) {
return true;
}
}
}
return false;
}
For the second function I implemented my own singly Linked List, in where I add the complementary integer to the sum and search for the value in the Linked List. If value is found in the Linked List we know there is a match.
function find2PairsBySumLin(arr, sum) {
var complementList = new LinkedList();
for (var i = 0; i < arr.length; i++) {
if (complementList.find(arr[i])) {
return true;
} else {
complementList.add(sum - arr[i]);
}
}
return false;
}
When I run both functions I clearly see that the Linked List search executes ~75% faster
var arr = [9,2,4,1,3,2,2,8,1,1,6,1,2,8,7,8,2,9];
console.time('For loop search');
console.log(find2PairsBySumLog(arr, 18));
console.timeEnd(‘For loop search’);
console.time('Linked List search');
console.log(find2PairsBySumLin(arr, 18));
console.timeEnd('Linked List search');
true
For loop search: 4.590ms
true
Linked List search: 0.709ms
Here my question: Is the Linked List approach a real linear search? After all I loop through all the nodes, while my outer loop iterates through the initial array.
Here is my LinkedList search function:
LinkedList.prototype.find = function(data) {
var headNode = this.head;
if(headNode === null) {
return false;
}
while(headNode !== null) {
if(headNode.data === data) {
return true;
} else {
headNode = headNode.next;
}
}
return false;
}
UPDATE:
It was a good idea to go back and have another think of the problem based the comments so far.
Thanks to #nem035 comment on small datasets, I ran another test but this time with 100,000 integers between 1 and 8. I assigned 9 to the first and last position and searched for 18 to make sure the entire array will be searched.
I also included the relatively new ES6 Set function for comparison thanks to #Oriol.
Btw #Oriol and #Deepak you are right. The first function is not a binary search but rather a O(n*n) search, which has no logarithmic complexity.
It turns out my Linked List implementation was the slowest of all searches. I ran 10 iterations for each function individually. Here the result:
For loop search: 24.36 ms (avg)
Linked List search: 64328.98 ms (avg)
Set search: 35.63 ms (avg)
Here the same test for a dataset of 10,000,000 integers:
For loop search: 30.78 ms (avg)
Set search: 1557.98 ms (avg)
Summary:
So it seems the Linked List is really fast for smaller dataset up to ~1,000, while ES6 Set is great for larger datasets.
Nevertheless the For loop is the clear winner in all tests.
All 3 methods will scale linearly with the amount of data.
Please note: ES6 Set is not backward compatible with old browsers in case this operation has to be done client side.
Don't use this. Use a set.
function find2PairsBySum(arr, sum) {
var set = new Set();
for(var num of arr) {
if (set.has(num)) return true;
set.add(sum - num);
}
return false;
}
That's all. Both add and has are guaranteed to be sublinear (probably constant) in average.
You can optimize this substantially, by pre-sorting the array and then using a real binary search.
// Find an element in a sorted array.
function includesBinary(arr, elt) {
if (!arr.length) return false;
const middle = Math.floor(arr.length / 2);
switch (Math.sign(elt - arr[middle])) {
case -1: return includesBinary(arr.slice(0, middle - 1), elt);
case 0: return true;
case +1: return includesBinary(arr.slice(middle + 1), elt);
}
}
// Given an array, pre-sort and return a function to detect pairs adding up to a sum.
function makeFinder(arr) {
arr = arr.slice().sort((a, b) => a - b);
return function(sum) {
for (let i = 0; i < arr.length; i++) {
const remaining = sum - arr[i];
if (remaining < 0) return false;
if (includesBinary(arr, remaining)) return true;
}
return false;
};
}
// Test data: 100 random elements between 0 and 99.
const arr = Array.from(Array(100), _ => Math.floor(Math.random() * 100));
const finder = makeFinder(arr);
console.time('test');
for (let i = 0; i < 1000; i++) finder(100);
console.timeEnd('test');
According to this rough benchmark, one lookup into an array of 100 elements costs a few microseconds.
Rewriting includesBinary to avoid recursion would probably provide a further performance win.
first of all find2PairsBySumLog function is not a binary search, it's a kind of brute force method which parses all the elements of array and it's worst case time complexity should be O(n*n), and the second function is a linear search that' why you are getting the second method to run fastly, for the first function i.e. find2PairsBySumLog what you can do is initialize binary HashMap and check for every pair of integers in array kind of like you are doing in the second function probably like
bool isPairsPresent(int arr[], int arr_size, int sum)
{
int i, temp;
bool binMap[MAX] = {0};
for (i = 0; i < arr_size; i++)
{
temp = sum - arr[i];
if (temp >= 0 && binMap[temp] == 1)
return true;
binMap[arr[i]] = 1;
}
}
I have the following code
var utils = require(`${__dirname}/../../utils/utils.js`);
...
let object = utils.parse(input);
if (object === undefined){
let helper = utils.recognize(input);
msg.channel.sendMessage("\"" + input + "\" not recognized. Did you mean \"" + helper[0] + "\"?");
object = utils.parse(helper[0]);
}
//code related to object
console.log(object.strLength);
where "parse" tries to match the input to an object in a database, and "recognize" tries to find the best match if the input is spelled incorrectly (Levenshtein) (along with additional info such as how close the match was).
Currently the issue is that the code is ran asynchronously; "object.strLength" returns an undefined before utils.recognize() returns a value. If I copy/paste the recognize() and parse() functions into the file, then the code is run synchronously and I do not run into any issues. However I would rather keep those functions in a separate file as I reuse them in other files.
Is there a way to specify that the functions in utils must be synch? I know that there are libraries that convert asynch into synch but I prefer to use as few libraries as I can help it. I tried to have the recognize functions return a Promise but it ended up as a jumbled mess
edit: here's parse. I did not think it was necessary to answer this question so I did not include it initially:
var db = require(`${__dirname}/../data/database.js`);
...
var parse = (input) => {
let output = db[output];
if (output === null) {
Object.keys(db).forEach((item) => {
if (db[item].num === parseInt(input) || (db[item].color + db[item].type === input)){
output = db[item];
return false;
}
});
}
return output;
}
I solved the issue, thanks everyone. Here's what was wrong, it was with recognize(). It was my mistake to not show the code for it initially.
Original recognize:
var recognize = (item) => {
//iterate through our databases and get a best fit
let bestItem = null;
let bestScore = 99999; //arbitrary large number
//let bestType = null;
//found algorithm online by milot-mirdita
var levenshtein = function(a, b) {
if (a.length == 0) { return b.length; }
if (b.length == 0) { return a.length; }
// swap to save some memory O(min(a,b)) instead of O(a)
if(a.length > b.length) {
let tmp = a;
a = b;
b = tmp;
}
let row = [];
for(let i = 0; i <= a.length; i++) {
row[i] = i;
}
for (let i = 1; i <= b.length; i++) {
let prev = i;
for (let j = 1; j <= a.length; j++) {
let val;
if (b.charAt(i-1) == a.charAt(j-1)) {
val = row[j-1]; // match
} else {
val = Math.min(row[j-1] + 1, // substitution
prev + 1, // insertion
row[j] + 1); // deletion
}
row[j - 1] = prev;
prev = val;
}
row[a.length] = prev;
}
return row[a.length];
}
//putting this here would make the code work
//console.log("hi");
Object.keys(db).forEach((key) => {
if (levenshtein(item, key) < bestScore) {
bestItem = key;
bestScore = levenshtein(item, key);
}
});
return [bestItem, bestScore];
}
My solution was to move the levenshtein function outside of the recognize function, so if I wanted to I can call levenshtein from another function
#user949300 and #Robert Moskal, I changed the forEach loop into a let...in loop. There is no functional difference (as far as I can tell) but the code does look cleaner.
#Thomas, I fixed the let output = db[output]; issue, oops.
Again, thanks for all of your help, I appreciate it. And happy New Year too
What is the difference between
settings = {
edit: function (key, value) {
return anotherFunction(key, value) {
return value * 2;
};
}
};
and
settings = {
edit: function edit(key, value) {
return anotherFunction(key, value) {
return value * 2;
};
}
};
?
There's no difference when executing.
However, in the second case (named function), you can call the function recursively easier because it has a name.
For example, with a named function you can do:
fact: function factorial(n) {
if(n == 0) return 1;
return n * factorial(n-1); //You can do this with a named function easily
}
Without a name, this would be tricky.
Cheers
The essential difference is better debugging. In your developer tools, the named function in your second example will appear as edit in a backtrace; your first example will appear as anonymous. This can be extremely confusing when you're 10 function deep, and they are all called anonymous.
There are three reasons to give a function an inherent name. The first is that everyone does it. It's what everyone is used to.
function factorial(n) {
var accum = 1, i;
for (i = 1; i <= n; i++) {
accum *= i;
}
return accum;
}
The second is to understand stack traces better, as #meagar wrote.
The third is to let you write call functions recursively.
var factorial = function(n) {
var a = 1;
return (function factRecursive(k, a) {
if (k >= 2) {return factRecursive(k - 1, k * a)}
else {return a;}
})(n, a);
}
In JavaScript, is it possible to insert a line into a function that already exists? I want to create a function that inserts a line at a specific position in a function:
function insertLine(theFunction, lineToInsert, positionToInsert){
//insert a line into the function after the specified line number
}
For example, would it be possible to programmatically insert the line checkParameterTypes(min, "string", max, "string"); before the first line of this function?
function getRandomInteger(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
If you want something to happen at the beginning of a function, you can use the following. You do have access to this and the arguments from your injected function. So it will still work for functions that require a specific context.
function inject(before, fn) {
return function(){
before.apply(this, arguments);
return fn.apply (this, arguments);
}
}
For example
function add(a, b) {
return a + b;
}
function concat(a, b) {
return a + b;
}
/**
* You can repeat index and type to check multiple arguments
*/
function createArgumentChecker(index, type /**index, type, ... */) {
var originalArgs = arguments;
return function() {
for (var i=0; i < originalArgs.length; i+=2) {
var index = originalArgs[i],
requestedType = originalArgs[i+1],
actualType = typeof arguments[index];
if (typeAtIndex != actualType) {
console.log("Invalid argument passed at index " + index +
". Expected type " + requestedType + "but it's " + actualType );
}
}
}
}
function logArguments() {
console.log(this, arguments);
}
// Inject an argument checker
add = inject(add, createArgumentChecker(0,"number", 1, "number"));
concat = inject (concat, createArgumentChecker(0, "string", 1, "string"));
// You can even do it multiple times, inject an argument logger;
add = inject(add, logArguments);
concat = inject(concat, logArguments);
JSfiddle
This can be handy when debugging websites that you can't modify the source code, I wouldn't use it do parameter checking unless you can strip it our for the production version.
Yes you can but using eval is always evil ;)
function insertInbetween (arr, value, index) {
var inserted, i, newarr = [];
for (i = 0; i < arr.length; i++) {
if(i == index && !inserted) {
newarr[i] = value;
inserted = true;
}
newarr.push(arr[i]);
}
return newarr;
}
function test (a, b) {
console.log(a,b);
}
var fstrarr = test.toString().split('\n');
eval(insertInbetween(fstrarr, "console.log('injected!');", 1).join('\n'));
Edit:
As mentioned in the comments to your question you'll loose scope by doing so.