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Largest product in a series

36 minutes ago

 27/05/2019


The four adjacent digits in the 1000-digit number that have the greatest product are 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 have the greatest product. What is the value of this product?

We have to find the thirteen adjacent digits in the 1000-digit number that have the greatest product, such as the example with four, 9 × 9 × 8 × 9 = 5832

Let's think of the 1000-digit number as a grid.

  1. We'll loop through the grid and convert every number to a in64 using strconv.Atoi
  2. Then we'll loop through the grid - 12 and make an array of the current 13 adjacent digits
  3. Next we'll loop through the 13-digit array to get the product.
  4. Finally save the product and do the process again, always checking that the new product is greater than the current.

Here's the implementation after a couple of trials.

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package main

import (
    "fmt"
    "strconv"
    "time"
    "strings"
)

var data string = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"

func main() {
    start := time.Now()
    // Get an array of ints
    var grid []int64
    // Split into 1000 slots
    var stringGrid = strings.Split(data, "")
    for i := 0; i < 1000; i++ {
        // Convert string to int
        cell, _ := strconv.Atoi(stringGrid[i])
        grid = append(grid, int64(cell))
    }

    // Find the largest one
    var largest int64
    // Loop through 1000-digit - 12 to avoid overflow
    for i := 0; i < len(grid)-12; i++ {
        // Create a 13-digit array
        a := grid[i : i+13]
        var total int64 = 1
        // Get the product by looping and multiplying
        for b := 0; b < len(a); b++ {
            total *= a[b]
        }
        // Save a new product if current is smaller than new
        if total > largest {
            largest = total
        }
    }
    fmt.Println("Largest 13 digit Product: ", largest)
    fmt.Println("Execution Time: ", time.Since(start))
}
Answer

Largest 13 digit Product: 23514624000

Execution Time: 104.882µs