PE-008 Largest product in a series

Tìm tích của 13 số liên tiếp lớn nhất.

Problem 8: Largest product in a series

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?

Đề bài

Cho một số lớn

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

Tích lớn nhất của 4 số liên tiếp trong số lớn trên là: 9 × 9 × 8 × 9 = 5832

Hãy tìm tích lớn nhất của 13 số liên tiếp.

Phân tích đề bài:

Với đề bài này…tôi chưa có cách làm nào tối ưu để tìm tích 13 số. Đành dùng cách “trâu bò” vậy.

Thay vì cách dùng kiểm tra so sánh và swap 2 số với nhau để tìm được số lớn nhất, ta có thể dùng function built-in max(iterator) để nhận dữ liệu lớn nhất.

Giống như bài PE-001 đã phân tích dùng list-comprehension nhanh hơn cách thông thường.

NUMBER = "7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450"
ADJACENT = 13


def digit_product(sub_number):
    result = 1
    for number in sub_number:
        result *= int(number)
    return result


def find_largest_product():
    return max(digit_product(NUMBER[index: index + ADJACENT]) for index in range(len(NUMBER) - ADJACENT + 1))

Thời gian chạy cho bài toán này khá ổn:

Nguyens-MacBook-Pro:PE-008 vinh.nguyenquang$ python3 largest_product_in_a_series.py
find_largest_product of result:
23514624000
elapsed time: 0.0036547183990478516s

Source-code: PE-008