codejam 1a

a.py

def sqrt(n): 
    if n == 0:
        return 0 
    a, b = divmod(n.bit_length(), 2)
    x = 2 ** (a + b)
    while True:
        y = x + n // x
        y //= 2
        if y >= x:
            return x
        x = y

def find_it(r, t):
    pr = 2 * r - 1
    rt = sqrt(pr**2 + 8 * t)
    a1 = -pr + rt
    a2 = -pr - rt
    return (a1 if a1 > 0 else a2) // 4

for case in range(int(input())):
    r, t = [int(n) for n in input().split()]
    answer = find_it(r, t)
    print('Case #{}: {}'.format(case+1, answer))

b.py

def rerere(v, vs, e, E, R, t=0):
    if not vs:
        return t+v*e
    u, us = vs[0], vs[1:]
    return max(rerere(u, us, e-r+R, E, R, t+v*r) for r in range(R, e+1))
            
def find_it(E, R, values):
    v, vs = values[0], values[1:]
    return rerere(v, vs, E, E, R)
            
for case in range(int(input())):
    E, R, _ = [int(n) for n in input().split()]
    if R > E:
        R = E
    values = [int(n) for n in input().split()]
    answer = find_it(E, R, values)
    print('Case #{}: {}'.format(case+1, answer))

c.py

from mathapi import factorized
from collections import Counter

def supcase(kset, N, M):
    r = Counter()
    for k in [factorized(k) for k in kset]:
        r |= Counter(k)
    while 1 in r:
        r.pop(1)
    nset = sorted(p for p, e in r.items() for _ in range(e))
    while len(nset) > N:
        a, b, *rem = nset
        if a * b > M:
            nset = sorted([a, b] + rem)
        else:
            nset = sorted(rem + [a * b])
    while len(nset) != N:
        nset += [2]
    return nset


for case in range(int(input())):
    R, N, M, K = [int(n) for n in input().split()]
    print('Case #{}:'.format(case+1))

    for _ in range(R):
        kset = [int(n) for n in input().split()]
        answer = supcase(kset, N, M)
        if not answer:
            answer = [2] * N
        print(''.join(map(str, answer)))