igorvanloo

def delta(x):
    if x == 0:
        return 1
    return 0 

def Ulam(v, t):
    # See S. R. Finch, Patterns in 1-additive sequences, Experimental Mathematics 1 (1992), 57-63.
    a = 2
    e2 = 2*v + 2
    #Finding the starting part of the sequence

igorvanloo

def find_next(curr):
    #Helper function to find cycles
    t = bin(curr)[2:][::-1]
    b = [int(x) for x in t + '0'*(6 - len(t))]
    nb = b[1:] + [b[0] ^ (b[1] & b[2])]
    snb = ''.join([str(x) for x in nb])
    curr = int(snb[::-1], 2)
    return curr

def lucas(n):

igorvanloo

def c(x, k, d):
    x1 = [int(x) for x in str(x)] + [0]
    x1 = x1[::-1]
    Y = (x//pow(10, k)) *pow(10, k - 1)
    if d > 0:
        if x1[k] > d:
            return Y + pow(10, k - 1)
        elif x1[k] == d:
            return Y + (x % pow(10, k - 1)) + 1
        else:

igorvanloo

import random, fractions

def monte_carlo(trials, n):
    total = 0
    for _ in range(trials):
        painted = 0
        pts = sorted([random.random() for _ in range(n)])
        prev = 1
        for i, x in enumerate(pts):
            if i == 0:

igorvanloo

from functools import cache

@cache
def a(n):
    if n == 0:
        return 0 
    if n == 1:
        return 1
    if n % 2 == 0:
        return a(n//2)

igorvanloo

def compute(p, number = 524487):
    S = [0]
    #V keeps tracks of which connected component vertex i is in
    V = [i for i in range(10**6)]
    #These are the connected components of the graph, initially every vertex is in its own connected component
    #The head of the connected component is itself
    cc = {i:set([i]) for i in range(10**6)}
    k = 1
    calls = 0 
    while True:

igorvanloo

import math
import decimal as dc

def is_sq(x):
    sq = (x ** (1 / 2))
    if round(sq) ** 2 == x:
        return True
    return False

def compute(N):

igorvanloo

def MaxContiguousSubarray(A):
    currMax = 0 
    currSum = 0
    for i in range(len(A)):
        currSum = max(currSum + A[i], A[i])
        currMax = max(currMax, currSum)
    return currMax

def MaxsumSubseq(M):
    currMax = 0

igorvanloo

def is_sq(x):
    sqrt = (x ** (1 / 2))
    if round(sqrt) ** 2 == x:
        return True
    return False

def compute():
    for b in range(1, 1000):
        for a in range(b + 2, 1000, 2):
            x = (a*a + b*b)//2

igorvanloo

def solve(part, j, S, S_set, S_all_sets, P):
    if j == len(part):
        S_all_sets.append(S_set)
        return S_set
    for x in P[part[j]]:
        if all(S[int(i)] + 1 != 2 for i in str(x)):
            SS = [S[k] for k in range(10)]
            for i in str(x):
                SS[int(i)] += 1
            if x == max(S_set + [x]):