add sol3 to project_euler/problem_08 (#1557)

* Add sol3 for project_euler proble_03

* Update sol3.py

add type hint 
remove unused variable

* Format code with psf/black

* add sol3 to project_euler/problem_08, modify the stepsize of the loop,will be faster than sol1

project_euler/problem_08/sol3.py

@@ -0,0 +1,83 @@
+# -*- coding: utf-8 -*-
+"""
+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?
+"""
+import sys
+
+N = """73167176531330624919225119674426574742355349194934\
+96983520312774506326239578318016984801869478851843\
+85861560789112949495459501737958331952853208805511\
+12540698747158523863050715693290963295227443043557\
+66896648950445244523161731856403098711121722383113\
+62229893423380308135336276614282806444486645238749\
+30358907296290491560440772390713810515859307960866\
+70172427121883998797908792274921901699720888093776\
+65727333001053367881220235421809751254540594752243\
+52584907711670556013604839586446706324415722155397\
+53697817977846174064955149290862569321978468622482\
+83972241375657056057490261407972968652414535100474\
+82166370484403199890008895243450658541227588666881\
+16427171479924442928230863465674813919123162824586\
+17866458359124566529476545682848912883142607690042\
+24219022671055626321111109370544217506941658960408\
+07198403850962455444362981230987879927244284909188\
+84580156166097919133875499200524063689912560717606\
+05886116467109405077541002256983155200055935729725\
+71636269561882670428252483600823257530420752963450"""
+
+
+def streval(s: str) -> int:
+    ret = 1
+    for it in s:
+        ret *= int(it)
+    return ret
+
+
+def solution(n: str) -> int:
+    """Find the thirteen adjacent digits in the 1000-digit number n that have
+    the greatest product and returns it.
+ 
+    >>> solution(N)
+    23514624000
+    """
+    LargestProduct = -sys.maxsize - 1
+    substr = n[:13]
+    cur_index = 13
+    while cur_index < len(n) - 13:
+        if int(n[cur_index]) >= int(substr[0]):
+            substr = substr[1:] + n[cur_index]
+            cur_index += 1
+        else:
+            LargestProduct = max(LargestProduct, streval(substr))
+            substr = n[cur_index : cur_index + 13]
+            cur_index += 13
+    return LargestProduct
+
+
+if __name__ == "__main__":
+    print(solution(N))