Problem: Takahashi is standing on a multiplication table with infinitely many rows and columns.  The square (i,j) contains the integer i \times j. Initially, Takahashi is standing at (1,1).  In one move, he can move from (i,j) to either (i+1,j) or (i,j+1).  Given an integer N, find the minimum number of moves needed to reach a square that contains N.

Submission attempts (in order):
import itertools
from itertools import combinations, chain
import copy 

# def powerset(L):
#   pset = set()
#   for n in range(len(L) + 1):
#     for sset in itertools.combinations(L, n):
#       pset.add(sset)
#   return pset
def powerset(iterable):
    "powerset([1,2,3]) --> () (1,) (2,) (3,) (1,2) (1,3) (2,3) (1,2,3)"
    s = list(iterable)
    return chain.from_iterable(combinations(s, r) for r in range(len(s)+1))
    
def list_diff(first, second):
        first = copy.copy(first)
        for s in second:
            first.remove(s)
        return first

def prod(lst):
    ret = 1
    for a in lst:
        ret *= a
    return ret

def sup(x):
    return [sorted(x[:i]+x[i+s:]) for i in range(len(x)) for s in range(len(x))]

def main():
    N = int(input())
    facs = factors(N)
    
    st=sup(facs)

    mn_ij = 10**12
    for i in st:
        i = list(i)
        j = list_diff(facs, i)
        i, j = prod(i), prod(j)

        mn_ij = min(mn_ij, i+j)

    # print(list(map(len,[ st, facs]) ))
    print(int(mn_ij-2))

if __name__ == "__main__":
    main()


import itertools
import numpy as np

def powerset(L):
  pset = set()
  for n in range(len(L) + 1):
    for sset in itertools.combinations(L, n):
      pset.add(sset)
  return pset
    
def list_diff(first, second):
        first = first.copy()
        for s in second:
            first.remove(s)
        return first

def main():
    N = int(input())
    facs = factors(N)
    st = powerset(facs)

    mn_ij = 10**12
    for i in st:
        i = list(i)
        j = list_diff(facs, i)
        i, j = np.prod(i), np.prod(j)

        mn_ij = min(mn_ij, i+j)

    print(int(mn_ij-2))

if __name__ == "__main__":
    main()


for line in sys.stdin:
    A, B = list(map(int, line.split(' ')))


import itertools
import numpy as np

def powerset(L):
  pset = set()
  for n in range(len(L) + 1):
    for sset in itertools.combinations(L, n):
      pset.add(sset)
  return pset
    
def list_diff(first, second):
        first = first.copy()
        for s in second:
            first.remove(s)
        return first

def main():
    N = int(input())
    facs = factors(N)
    st = powerset(facs)

    mn_ij = 10**12
    for i in st:
        i = list(i)
        j = list_diff(facs, i)
        i, j = np.prod(i), np.prod(j)

        assert i * j == N, f'{i} {j} {N}'
        mn_ij = min(mn_ij, i+j)

    print(int(mn_ij-2))

if __name__ == "__main__":
    main()


import math

def main():
    N = int(input())
    rt_N = math.ceil(math.sqrt(N))

    mn_ij = 10**12
    for i in range(1, rt_N+1):
        if N % i == 0:
            j = N // i

            mn_ij = min(mn_ij, i+j)
        
        mn_ij = min(mn_ij, i+j)

    # print(list(map(len,[ st, facs]) ))
    print(int(mn_ij-2))

if __name__ == "__main__":
    main()


Verdicts: Runtime Error

Runtime Error

Runtime Error

Runtime Error

Accepted