Problem 8

Problem

The four adjacent digits in the \(1000\)-digit number that have the greatest product are \(9 \times 9 \times 8 \times 9 = 5832\).

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?

Julia

function p8()
  big_string = "73167176531330624919225119674426574742355349194934
      96983520312774506326239578318016984801869478851843
      85861560789112949495459501737958331952853208805511
      12540698747158523863050715693290963295227443043557
      66896648950445244523161731856403098711121722383113
      62229893423380308135336276614282806444486645238749
      30358907296290491560440772390713810515859307960866
      70172427121883998797908792274921901699720888093776
      65727333001053367881220235421809751254540594752243
      52584907711670556013604839586446706324415722155397
      53697817977846174064955149290862569321978468622482
      83972241375657056057490261407972968652414535100474
      82166370484403199890008895243450658541227588666881
      16427171479924442928230863465674813919123162824586
      17866458359124566529476545682848912883142607690042
      24219022671055626321111109370544217506941658960408
      07198403850962455444362981230987879927244284909188
      84580156166097919133875499200524063689912560717606
      05886116467109405077541002256983155200055935729725
      71636269561882670428252483600823257530420752963450" |> filter(isnumeric) # keep only numeric characters
  
  biggest_product = 0
  winner_string = ""
  amount_of_digits = 12
  
  for i in (amount_of_digits + 1):length(big_string)
    current_string = collect(big_string[i-amount_of_digits : i])
    
    p = map(x -> parse(Int32, x), current_string) |> prod
    if p > biggest_product
      biggest_product = p
      winner_string = current_string
    end
  end
  
  return reduce(*, winner_string), biggest_product
end;

p8()

("5576689664895", 23514624000)

using BenchmarkTools;
@benchmark p8()

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  112.113 μs …  1.657 ms  ┊ GC (min … max): 0.00% … 91.25%
 Time  (median):     115.619 μs              ┊ GC (median):    0.00%
 Time  (mean ± σ):   123.760 μs ± 89.008 μs  ┊ GC (mean ± σ):  5.25% ±  6.65%
   ▂▇█▇▅▄▃▃▃▂▂▁▁                                               ▂
  ▆████████████████▇▇▇▅▆▁▅▁▄▄▄▁▁▁▃▁▃▁▁▄▃▁▃▁▁▁▁▁▁▃▁▃▃▄▆▆▅▄▄▇▇██ █
  112 μs        Histogram: log(frequency) by time       167 μs <
 Memory estimate: 249.22 KiB, allocs estimate: 3000.