We Keep Coding

How to calculate what is probability of getting same result 8 times in a row, when flipping coin 1000 times?

I've tried to use this code:
function calc (n, c) {
let a = 0
const omega = Math.pow(2, n)
let search1 = ''
let search2 = ''
for (let i = 0; i < c; i++) {
search1 += '0'
}
for (let i = 0; i < c; i++) {
search2 += '1'
}
for (let i = 0; i < omega; i++) {
if (i.toString(2).includes(search1) || i.toString(2).includes(search2)) {
a++
}
}
const prob = a * 100 / omega
console.log({ a: a, omega: omega, prob: prob.toFixed(2) })
}
calc(1000, 8)
Which works, but is slow when it comes to big numbers. How can I optimize my code to make it faster? Or maybe there exists a Mathematical solution, that doesn't require to code at all? I just want to know the solution for this problem.

First a Monte Carlo simulation answer:
You can find a confidence interval for this simulation by doing some statistical inference on the Bernoulli distribution which I won't do here.
function doesItHappen(l,r){
var lastValue = null;
var lastN = 0;
for(var i = 0; i < l; i++){
var currentValue = Math.random() > 0.5 ? 1 : 0;
if(lastValue === currentValue) {
lastN++;
} else {
lastValue = currentValue;
lastN = 1;
}
if(lastN === r) return true;
}
return false;
}
function rep(n,l,r){
var t = 0;
for(var i = 0; i < n; i++) {
if(doesItHappen(l,r)) t++;
}
return t/n;
}
console.log(rep(100000,1000,8))
Finally the actual Mathematical answer
I couldn't find a solution to this question online so I came up with my own method to calculate this in o(n) time and space complexity, you can even get it down to o(1) space complexity by discarding valueStore objects older than the length of consecutive sequence you want. The key thing is to recognise you have to computer all the combinations prior to the current length, similar to a Fibonacci sequence.
function calculateProbability(l,r) {
var valueStore = [
{ // Initialize it
totalNumberOfCombinations: 2,
numberOfCombinationsWithSequence: 0
}
];
function getValues(index) {
// combinations with the sequence in it
// There are two ways a consecutive sequence of r length can occur, it either occured in the previous combination and we flipped a new heads or tails(doesn't matter)
// Or this flip resulted in a new consecutive sequence of r length occuring (let's say theres k combinations of this)
// Heres the genius, k must end in a sequence of heads or tails so theres 2 possible endings, the beginnings of k cannot contain the sequence of r consecutive flips
// If this previous combination ends in a head then the new sequence is all tails and vice versa
// So k = the combinations of flips without the consective flips before the current sequence
// k = the totalNumberOfCombinations 8 flips ago - numberOfCombinationsWithSequence 8 flips ago
if (index === r - 1) {
// All heads or all tails
var numberOfCombinationsWithSequence = 2;
} else if(index < r) {
var numberOfCombinationsWithSequence = 0;
} else {
var numberOfCombinationsWithSequence = valueStore[index - 1].numberOfCombinationsWithSequence * 2 + (valueStore[index - r].totalNumberOfCombinations - valueStore[index - r].numberOfCombinationsWithSequence)
}
return {
// total possible combinations
// this is just the previous number of combinations but times 2 since we flip again
totalNumberOfCombinations: valueStore[index - 1].totalNumberOfCombinations * 2,
numberOfCombinationsWithSequence: numberOfCombinationsWithSequence
}
}
for(var i = 1; i < l; i++) {
var values = getValues(i);
valueStore.push(values);
}
return valueStore[valueStore.length - 1].numberOfCombinationsWithSequence / valueStore[valueStore.length - 1].totalNumberOfCombinations;
}
console.log(calculateProbability(1000,8));
The 100% accurate answer is 0.9817098435878764 or 98.17%

how about a simulation?
function simulate(throws, streak, runs) {
let win = "".padStart(streak, "1")
let win2 = "".padStart(streak, "0")
let hits = 0
for (let n = 0; n < runs; n++) {
let res = "";
for (let i = 0; i < throws; i++) {
let val = Math.round(Math.random())
res += val
}
if (res.includes(win) || res.includes(win2)) {
hits++
}
}
console.log({
hits,
runs,
prob: ((hits / runs) * 100).toFixed(2)
})
}
simulate(1000, 8, 10000)

Multiplying N positive odd numbers

I'm trying to get the product of N positive odd numbers
function multOdd(n) {
var mult = 1;
var counter=[];
for (var i = 1; i <= 2*n-1; i += 2){
counter.push(i);
}
console.log(counter);
return mult=mult*counter[i];
}
console.log(multOdd(10));
I pushed the numbers into an array and attempted to get the product from them but I can't get it to work.

When you return mult=mult*counter[i] you're only returning the multipication once. It should return mult = 1 * counter[lastElement+2] which will be wrong. In your case, the last element of counter is 19, before exiting for loop i value is i= 19 + 2 = 21. You're returning mult = 1 * 21 = 21.
You can instead return the multipication value by for loop with no need for an array:
function multOdd(n) {
var mult = 1;
for (var i = 1; i <= 2*n-1; i += 2){
mult = mult * i;
}
return mult;
}

If you just want the result for n, use:
function multOdd(n) {
var result = 1;
for (var i = 1; i <= 2*n-1; i += 2){
result = result * i;
}
console.log(result);
return result;
}
console.log(multOdd(4));
If you want an array that has an array indexed by the number of odd numbers up to n you could use:
function multOdd(n) {
let result = 1;
let results = [];
for (let i = 1; i <= 2*n-1; i += 2){
result = result * i;
results[(i+1) / 2] = result;
}
console.log(results);
return results;
}
console.log(multOdd(10));

There are a few ways to get the product of an array of numbers. Here are two easy ones:
Relevant MDN
// Using `Array.prototype.reduce`
[3, 5, 7, 9].reduce((acc, val) => acc * val)
// Using a `for ... of` loop
let product = 1
for (const val of [3, 5, 7, 9]) {
product *= val
}

You could separate out the two steps of your current code into two functions:
const getFirstNOddNums = (n) => {
let oddNums = []
for (let i = 1; i <= 2*n-1; i+=2) {
oddNums.push(i)
}
return oddNums
}
const productOfArray = (arr) => {
return arr.reduce((a, b) => a * b)
}
const N = 5
const firstNOddNums = getFirstNOddNums(N)
console.log(`The first ${N} odd numbers are: ${JSON.stringify(firstNOddNums)}`)
console.log(`The product of the first ${N} odd numbers is: ${productOfArray(firstNOddNums)}`)

let multOdd = (n) => {
let total = 1;
for (let i = 1; i<= 2*n; i+=2){
total *= i;
}
return total;
}
console.log(multOdd(10));

Instead of recursion, We should use the standard mathematical formula for the product of first n positive odd integers which is
Can also be written as (in the form of pi notation)
For this latex image, I used https://codecogs.com/latex/eqneditor.php.
Factorial is
n! = n(n-1)(n-2)(n-3) ... and so on
So we can use Array(n).fill() to get an array of 10 elements and reduce them to get a factorial by
Array(n).fill().reduce((v,_,i) => (i+1) * v || 2)
Then we divide it by 2 to the power n times the n!. Which is what we want. The advantage here is that, this makes your solution, a one liner
let n = 10
let answer = Array(2*n).fill().reduce((v,_,i) => (i+1) * v || 2) / (Math.pow(2,n) * Array(n).fill().reduce((v,_,i) => (i+1) * v || 2))
console.log(answer)

JavaScript neglecting the else statement

I created a function which takes in two values..
Both are numbers represented by n & p. What the function does is that it gets the number n and splits it up then squares it to the value of p and sums them in an increasing order like this: n^p + n^(p+1) + n^(p+2) + ...
Here is the function
function digPow(n, p) {
// ...
let num = n.toString();
let pow = p;
let arrn = [];
let arrp = [];
for (let i = 0; i < num.length; i++) {
arrn.push(JSON.parse(num[i]));
}
let index = arrn.join('');
let sindex = index.split('');
for (let j = 0; j < sindex.length; j++) {
let power = p + j;
let indexs = sindex[j];
let Mathpow = Math.pow(indexs, power);
arrp.push(Mathpow);
}
let total = 0;
for (let m in arrp) {
total += arrp[m]
}
let secondVal = total / n;
let totals = total / secondVal;
let mx = [-1]
if (totals.length == n.length) {
return secondVal
} else {
return -1
}
}
Now i created variables and arrays to store up the values and then the if part is my problem.. The if/else statement is meant to let the program check if a particular variable totals is equal to n which is the input.. if true it should return a variable secondVal and if not it should return -1..
So far its only returning secondVal and i'snt returning -1 in cases where it should like:
digPow(92, 1) instead it returns 0.14130434782608695
What do i do?

totals and n are both numbers. They don't have a .length property, so both totals.length and n.length evaluate to undefined. Thus, they are equal to each other.
There are plenty of other weird things going on in your code, too. I'd recommend finding a good JavaScript tutorial and working through it to get a better feel for how the language (and programming in general) works.

Let's start by stripping out the redundant variables and circular-logic code from your function:
function digPow(n, p) {
let num = n.toString();
// let pow = p; // this is never used again
// let arrn = []; // not needed, see below
// let arrp = []; // was only used to contain values that are later summed; can instead just sum them in the first place
// this does the same thing as num.split(''), and isn't needed anyway:
//for (let i = 0; i < num.length; i++) {
// arrn.push(JSON.parse(num[i]));
//}
// this is the same as the original 'num' variable
// let index = arrn.join('');
// This could have been num.split(), but isn't needed anyway
// let sindex = index.split('');
let total = 0; // moved this line here from after the loop below:
for (let j = 0; j < num.length; j++) { // use num.length instead of the redundant sindex
let power = p + j;
// The only reason for the sindex array was to get individual characters from the string, which we can do with .charAt().
//let indexs = sindex[j];
let indexs = num.charAt(j);
let Mathpow = Math.pow(indexs, power);
//arrp.push(Mathpow); // No need to collect these in an array
total += Mathpow; // do this instead
}
// No need for this loop, since we can sum the total during the previous loop
// let total = 0;
//for (let m in arrp) {
// total += arrp[m]
//}
let secondVal = total / n;
// let totals = total / secondVal;
// The above is the same thing as total / total / n, which is:
let totals = 1/n;
// This is never used
//let mx = [-1]
// This was totals.length and n.length, which for numbers would always be undefined, so would always return true
if (totals == n) {
return secondVal
} else {
return -1
}
}
So the above reduces to this functionally identical code:
function digPow(n, p) {
let num = n.toString();
let total = 0;
for (let j = 0; j < num.length; j++) {
let power = p + j;
let indexs = num.charAt(j);
let Mathpow = Math.pow(indexs, power);
total += Mathpow;
}
let secondVal = total / n;
let totals = 1 / n;
if (totals == n) {
return secondVal
} else {
return -1
}
}
Now let's talk about the logic. The actual output will always be -1, unless the input is 1, due to what's clearly a logic error in the totals variable: the only case where 1/n == n is true is when n==1.
Setting that aside, and looking only at the secondVal variable, some examples of what it's calculating for a given input would be
digPow(123,1) --> (1^1 + 2^2 + 3^3) / 123 --> 14/123
digPow(321,2) --> (3^2 + 2^3 + 1^4) / 321 --> 21/321
digPow(92, 1) --> (9^1 + 2^2) / 92 --> 13/92
I'm pretty sure from your description that that's not what you intended. I'm not at all sure from your description what you did intend, so can't be much help in correcting the function beyond what I've done here.
What I'd suggest is to sit down and think through your algorithm first; make sure you know what you're trying to build before you start building it. There were some syntax problems with your code, but the real issues are with the logic itself. Your original function shows clear signs of "just keep throwing more lines of code at it until something happens" rather than any planned thinking -- that's how you wind up with stuff like "split a string into an array, then join it back into a string, then split that string into another array". Write pseudocode first: break the problem down into steps, think through those steps for some example inputs and make sure it'll produce the output you're looking for. Only then should you bust out the IDE and start writing javascript.

How can I get the sum of all odd fibonacci vales in javaScript?

I am working through this Free Code Camp exercise.
Return the sum of all odd Fibonacci numbers up to and including the
passed number if it is a Fibonacci number. The first few numbers of the Fibonacci sequence are 1, 1, 2, 3, 5 and
8, and each subsequent number is the sum of the previous two numbers.
And here is what I have so far...
Any suggestions?
function sumFibs(num) {
var arr, isFibVal, isEvenVal, sum, i = 0, fibonacci = function (num){
var a, b, result, fibArr = [1];
a=0;
b=1;
result=b;
for(var j = 0; j < num; j++){
result = a + b;
a = b;
b = result;
fibArr.push(result);
}
return fibArr;
},
isFib = function (val){
var prev = 0;
var curr = 1;
while(prev<=val){
if(prev == val){
return true;
} else {
return false;
}
curr = prev + curr;
prev = curr - prev;
}
},
isEven = function(someNumber){
return (someNumber % 2 === 0) ? true : false;
};
function sumArray(array) {
for (
var
index = 0, // The iterator
length = array.length, // Cache the array length
sum = 0; // The total amount
index < length; // The "for"-loop condition
sum += array[index++] // Add number on each iteration
);
return sum;
}
arr = fibonacci(num);
isFibVal = isFib(num);
isEvenVal = isEven(num);
if (isFibVal && !isEvenVal){
sum += sumArray(arr);
}
return sum;
}
All I get back is undefined which seems to be weird because i thought this part of my code was pretty cool—using the function values to check vs. in the if statement.
arr = fibonacci(num);
isFibVal = isFib(num);
isEvenVal = isEven(num);
if (isFibVal && !isEvenVal){
sum += sumArray(arr);
}

I won't give you the answer outright since you're going through FCC, but I'll provide you with some hints as to where to look:
See this segment:
for(var j = 0; j < num; j++){
result = a + b;
a = b;
b = result;
fibArr.push(result);
}
And this one:
function sumArray(array) {
for (
var
index = 0, // The iterator
length = array.length, // Cache the array length
sum = 0; // The total amount
index < length; // The "for"-loop condition
sum += array[index++] // Add number on each iteration
);
return sum;
}
Also, you probably don't need this segment at all:
isFibVal = isFib(num);
isEvenVal = isEven(num);
if (isFibVal && !isEvenVal){
sum += sumArray(arr);
Good luck. As someone who has finished a good chunk of the curriculum, I can say that Free Code Camp is the real deal.

You're pretty close and the other answer is good for pushing you in the right direction, I'll post a different way that does this using native JS functions:
Example of the code below in JSBin
function fibs(n) {
var f = [0, 1];
var extraNumber = 0;
for (var i = 0; i < n; i++) {
f.push(f[f.length - 1] + f[f.length - 2]);
}
// lets check if the passed in number is a fib:
if (f.indexOf(n) > -1) {
extraNumber = n;
}
console.log(f); // just to check we can cut all the logs later...
var filtered = f.filter(function(num) {
// filter out the even numbers
return num % 2 === 1;
});
console.log(filtered);
var sum = filtered.reduce(function(a, b) {
// add up whats left
return a + b;
});
console.log(sum);
return sum + extraNumber;
}

heres my solution, and i find it to be pretty readable:
function sumOddFibs(num) {
// initialize with 2 because
// fib sequence starts with 1 and 1
var sum = 2;
var prev = 1;
var curr = 1;
var next = 2;
while (next <= num) {
prev = curr;
curr = next;
next = prev + curr;
if (curr % 2 !== 0) {
sum += curr;
}
}
return sum;
}

You could start by defining variables for the previous number, current number, and total Fibonacci
To check for odd numbers, you could use an if statement and use %:
if (currNum % 2 !== 0){ }
If current number is odd, then you add it to the total
fibTotal += currNumber;
To determine the next Fibonacci number you, you will need to add the previous and current number:
var nextNumber = prevNumber + currNumber;
You will need to update the previous number to the current one
prevNumber = currNumber;
Set the current number to the next Fibonacci number in the sequence
currNumber = nextNumber;
Hope this helps.

Codility "PermMissingElem" Solution in Javascript

A codility problem asks to find the missing number in zero-indexed array A consisting of N different integers.
E.g.
Arr[0] = 2
Arr[1] = 3
Arr[2] = 1
Arr[3] = 4
Arr[4] = 6
I previously submitted a solution that first sorts the array and then performs a forEach function returning the value +1 where the array difference between elements is more than 1, however this doesn't get the 100 points.
Is there a way to improve this?

Here is 100% javascript solution:
function solution(A) {
if (!A.length) return 1;
let n = A.length + 1;
return (n + (n * n - n) / 2) - A.reduce((a, b) => a + b);
}
We return 1 if the given array is empty, which is the missing element in an empty array.
Next we calculate the 'ordinary' series sum, assuming the first element in the series is always 1. Then we find the difference between the given array and the full series, and return it. This is the missing element.
The mathematical function I used here are series sum, and last element:
Sn = (n/2)*(a1 + an)
an = a1 + (n - 1)*d

Get 100 in correctness and performance using this function
function solution(A) {
// write your code in JavaScript (Node.js 4.0.0)
var size = A.length;
var sum = (size + 1) * (size + 2) / 2;
for (i = 0; i < size; i++) {
sum -= A[i];
}
return sum;
}

Easy if you use the Gauss formula to calculate the sum of the first N consecutive numbers:
function solution(A) {
var np1, perfectSum, sum;
if (!A || A.length == 0) {
return 1;
}
np1 = A.length + 1;
// Gauss formula
perfectSum = np1 * (1 + np1) / 2;
// Sum the numbers we have
sum = A.reduce((prev, current) => prev + current);
return perfectSum - sum;
}

From the sum of first natural numbers formula we have
now since the N item for us in the task is (N+1) we substitue n with n+1 and we get
with the formula above we can calculate the sum of numbers from 1 to n+1, since in between these numbers there is the missing number, now what we can do is we can start iterating through the given array A and subtracting the array item from the sum of numbers. The ending sum is the item which was missing in the array. hence:
function solution(A) {
var n = A.length;
// using formula of first natural numbers
var sum = (n + 1) * (n + 2) / 2;
for (var i = 0; i < n; i++) {
sum -= A[i];
}
return sum;
}

No Gauss formula, only simple and plain separate for loops that give an O(N) or O(N * log(N)) and 100% score:
function solution(A) {
if(!A.length){
return 1; //Just because if empty this is the only one missing.
}
let fullSum = 0;
let sum = 0;
for(let i = 0; i <= A.length; i++){
fullSum += i+1;
}
for(let i = 0; i < A.length; i++){
sum += A[i];
}
return fullSum - sum;
}

Try utilizing Math.min , Math.max , while loop
var Arr = [];
Arr[0] = 2
Arr[1] = 3
Arr[2] = 1
Arr[3] = 4
Arr[4] = 6
var min = Math.min.apply(Math, Arr),
max = Math.max.apply(Math, Arr),
n = max - 1;
while (n > min) {
if (Arr.indexOf(n) === -1) {
console.log(n);
break;
}
--n;
}

This should be work good:
function solution(A) {
// Size of the A array
const size = A.length;
// sum of the current values
const arrSum = A.reduce((a, b) => a + b, 0);
// sum of all values including the missing number
const sum = (size + 1) * (size + 2) / 2;
// return substruction of all - current
return (sum - arrSum);
}

This got me 100%
function solution(A) {
if (A.length === 0 || !A) {
return 1;
}
A.sort((a, b) => a - b);
let count = A[0];
if (count !== 1) { return 1 }
for (let i = 0; i <= A.length; i++) {
if (A[i + 1] === count + 1) {
count ++;
continue
}
return count + 1;
}
}

// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');
function solution(A) {
if (!A.length) return 1;
A = A.sort((a, b) => a - b);
for (let i = 0; i < A.length + 1; i++) {
if (A[i] !== i + 1) {
return i + 1;
}
}
}

My 100% JavaScript solution:
function solution(A) {
const N = A.length;
// use the Gauss formula
const sumNatural = (N + 1) * (N + 2) / 2;
// actual sum with the missing number (smaller than sumNatural above)
const actualSum = A.reduce((sum, num) => sum += num, 0);
// the difference between sums is the missing number
return sumNatural - actualSum;
}

I wonder why there isn't any answer using a hashtable.
It's obvious that we need to iterate this array from start to end.
Therefore, best solution we can have is O(n).
I simply map numbers, and access them with O(1) in another iteration.
If all numbers are tagged as true, it means it's either an empty array, or it doesn't contain missing number. Either way length + 1 returns the expected output.
It returns 1 for [], and it returns 3 for [1,2].
// you can write to stdout for debugging purposes, e.g.
function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
let nums = new Map()
for (let i = 0; i < A.length; i++) {
nums[A[i]] = true;
}
for (let i = 1; i < A.length + 1; i++) {
if (nums[i]) { continue; }
else { return i;}
}
return A.length + 1;
}

function solution(A) {
// write your code in JavaScript (Node.js 8.9.4)
const n = A.length+1
return (n*(n+1)/2) - A.reduce((a, b) => a + b, 0)
}
Explanation:
The formula for sum of natural numbers => n(n+1)/2
where n is the last number or last nth term.
In our case, n will be our array.length. But the question states that exactly one item is missing, meaning the last nth term is array.length +1.
To find the expected sum of all our natural numbers,
We can deduct the total of the available numbers (A.reduce((a, b) => a + b, 0)) from the expected sum n(n+1)/2 to arrive at the missing number.

I had the same problem with my code:
function solution(A) {
var i, next;
A.sort();
next = 1;
for (i=0; i<A.length; i++){
if (A[i] != next) return next;
next++;
}
return next;
}
Altough it scored 100% in correctness, it returned wrong answer in all the performance tests.
The same code in C receives 100% on both:
int cmpfunc (const void * a, const void * b){
return ( *(int*)a - *(int*)b );
}
int solution(int a[], int n) {
int i, next;
qsort(a, n, sizeof(int), cmpfunc);
next = 1;
for (i=0; i<n; i++){
if (a[i] != next) return next;
next++;
}
return next;
}

I got an alternative 100% correctness/performance solution without the Gauss formula, sorting the array first instead:
function solution(A) {
A.sort((a, b) => a-b);
for(let i=0; i<A.length; i++){
if(A[i] != i+1) {
return 0;
}
}
return 1;
}