- Mine programerings prosjekter
Quick sort in Python
def sort(A):
if len(A) <= 1:
return A
small = []
middle = []
big = []
temp = int((A[0][0]+A[len(A)-1][0])/2)
for x in A:
if x[0] < temp:
small.append(x)
elif x[0] == temp:
middle.append(x)
elif x[0] > temp:
big.append(x)
A = sort(small)
A.extend(middle)
A.extend(sort(big))
return A
Nim is a two-player game in which players take turns removing objects from distinct heaps. On each turn, a player must remove at least one object. The player who take the last object loses.
A number chain is created by continuously adding the square of the digits in a number to form a new number until it has been seen before.
For example,
44 -> 32 -> 13 -> 10 -> 1 -> 1
85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89
Therefore any chain that arrives at 1 or 89 will become stuck in an endless loop. What is most amazing is that EVERY starting number will eventually arrive at 1 or 89.
How many starting numbers below ten million will arrive at 89?
Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:
1634 = 14 + 64 + 34 + 44
8208 = 84 + 24 + 04 + 84
9474 = 94 + 44 + 74 + 44
As 1 = 14 is not a sum it is not included.
The sum of these numbers is 1634 + 8208 + 9474 = 19316.
Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
Starting in the top left corner of a 2*2 grid, there are 6 routes (without backtracking) to the bottom right corner.
How many routes are there through a 20*20 grid?
The following iterative sequence is defined for the set of positive integers:
n ->n/2 (n is even)
n ->3n + 1 (n is odd)
Using the rule above and starting with 13, we generate the following sequence:
13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.
Which starting number, under one million, produces the longest chain?
NOTE: Once the chain starts the terms are allowed to go above one million.
The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …
Let us list the factors of the first seven triangle numbers:
1: 1
3: 1,3
6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28
We can see that the 7th triangle number, 28, is the first triangle number to have over five divisors.
Which is the first triangle number to have over five-hundred divisors?
The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
Find the sum of all the primes below one million.
A Pythagorean triplet is a set of three natural numbers, a<b<c, for which,
a² + b² = c²
For example, 3² + 4² = 9 + 16 = 25 = 5².
There exists exactly one Pythagorean triplet for which a + b + c = 1000.
Find the product abc.
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.
What is the 10001st prime number?
