[Training] Blue Bridge Cup Day 1264

1264

Enter the number 1 to 10 in the grid 5 in two rows.
Requirements: The number of adjacent grid in the right greater than left, below is greater than the top of.
Two kinds, fill method is qualified as shown in FIG.
Please calculate a total number of possible solutions.

Output
Please output the integer, do not print any extra content

note

Large lower right

algorithm

1. For the convenience of the algorithm, the numbers are -1, then the first 0,9 OK in the upper left and lower right corner.
2. To regard it as a row, i and i + 5 to Comparison
3. array [4] can not handle
4. 0-3, Comparative positions i, i + 1, and i, i + 5 Size
5. 5-8, Comparative positions i, i + 1 Size

answer

Answer: 42

from itertools import permutations
def f(data):
    for i in range(9):
        if i == 4:
            continue
        if not i//5:
            if data[i] < data[i+5] and data[i] < data[i+1]:
                continue
            else:
                break
        else:
            if data[i] < data[i+1]:
                continue
            else:
                break
    if i == 8:
        return True

array = [i for i in range(10)]
res = 0
for i in permutations(array[1:-1]):
    array[1:-1] = i
    if f(array):
        res += 1
print(res)

1276

[Blue Bridge Cup 2015 finals] robot breeding

X galaxies robot can automatically replicate itself. They use a year's time can replicate the two themselves, and then lose the ability to replicate.
X galaxies year will elect a new born robot sent into space. That is, if X 5 Galaxy original robot,
after 1 year Total is: 5 + 9 = 14
Number of 2 years is: 5 + 9 + 17 = 31
If the total number of robots has been detected through s n years later, you initially able to calculate how many robots do?
Input
plurality of sets of test data input
for each set of test data input line and two numbers n s, separated by a space, meaning as above. n is not greater than 100, s is not more than 50 bits.
Output
For each test, the required output line, an integer representing the number of the first robot.
Sample input the Copy
2 31 is
97 2218388550399401452619230609499
sample output the Copy
. 5
. 8

note

Has the maximum value of s 50, Map () can not be used in long, however python2.2 later, when stored int overflow, it is automatically converted into a long type value

algorithm

Forgot year n + x, and remember to make up

Extension: If n is known, s (n is the year, x is the initial number), find the total number of years after the robot n s

1. Recursive well calculated from s

answer

def f(n,s):
    up = s + 2**(n+1)-2-n
    return up//(2**(n+1)-1)
while True:  
    n, s = map(int,input().split())
    print(f(n,s))

Extended Solution:

def f(n,x):
    if n == 0:
        return x
    return f(n-1,2*x-1)+x
while True:  
    n, s = map(int,input().split())
    print(f(n,x))