# Project Euler: #8 - Largest product in a series

### **Problem**

The four adjacent digits in the `1000`\-digit number that has the greatest product is `9 × 9 × 8 × 9 = 5832`.

73167176531330624919225119674426574742355349194934  
96983520312774506326239578318016984801869478851843  
85861560789112949495459501737958331952853208805511  
12540698747158523863050715693290963295227443043557  
66896648950445244523161731856403098711121722383113  
62229893423380308135336276614282806444486645238749  
30358907296290491560440772390713810515859307960866  
70172427121883998797908792274921901699720888093776  
65727333001053367881220235421809751254540594752243  
52584907711670556013604839586446706324415722155397  
53697817977846174064955149290862569321978468622482  
83972241375657056057490261407972968652414535100474  
82166370484403199890008895243450658541227588666881  
16427171479924442928230863465674813919123162824586  
17866458359124566529476545682848912883142607690042  
24219022671055626321111109370544217506941658960408  
07198403850962455444362981230987879927244284909188  
84580156166097919133875499200524063689912560717606  
05886116467109405077541002256983155200055935729725  
71636269561882670428252483600823257530420752963450

Find the `thirteen adjacent digits` in the `1000`\-digit number that has the greatest product. What is the value of this product?

---

### **Problem Description**

Well, a `1000`\-digit number is given to us.

The `4` adjacent digits with the greatest product are `9 × 9 × 8 × 9 = 5832`.

We need to find the product of a `13` adjacent digits in this number and to top it off, it is the greatest product of any `13` adjacent digits in this `1000`\-digit number.

---

### **Approach**

To solve this problem, first, we are going to convert this `1000`\-digit number to an array of length `1000`. We use `String.prototype.split()` function to convert the number to an array.

Then, we loop through the array till we reach the last `13` digits.

Slice the array for every 13 digits using the Array `slice()` method and then calculate the product using the Array `reduce()` method.

Push this product to a new array.

Once all the digits are handled, then using `Math.max()`, return the greatest of the calculated product.

Slicing the array and calculating its product is a much better solution compared to looping through every digit and calculating its product in terms of time complexity.

---

### **Solution**

```javascript
const givenNumber = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450';

const gvnNumArr = givenNumber.trim().split('').map(Number);

const largestProduct = n => {
    let prod = 0,
        prodArray = [];

    for (let i = 0; i <= gvnNumArr.length - n; i++) {
        const last = i + n;
        
        prod = gvnNumArr.slice(i, last).reduce((acc, curr) => acc * curr, 1);
        prodArray.push(prod);
    }

    return Math.max(...prodArray);
}

console.log(largestProduct(13));
```

You can find my solution on GitHub [08](https://github.com/sansk/project-euler-solutions-javascript/tree/main/08)

This particular solution was executed with a better complexity in Hacker rank. If you have another solution, please leave it in the comments below.

For the other Project Euler Solutions, please follow the series [**Project Euler Solutions in JS.**](https://theintrovertcoder.hashnode.dev/series/project-euler)

Thank you!