<gh_stars>0
# Solution of;
# Project Euler Problem 430: Range flips
# https://projecteuler.net/problem=430
# 
# N disks are placed in a row, indexed 1 to N from left to right. Each disk 
# has a black side and white side. Initially all disks show their white side. 
# At each turn, two, not necessarily distinct, integers A and B between 1 and 
# N (inclusive) are chosen uniformly at random. All disks with an index from A 
# to B (inclusive) are flipped. The following example shows the case N = 8. At 
# the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6. Let 
# E(N, M) be the expected number of disks that show their white side after M 
# turns. We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5. 157 
# and E(100, 10) ≈ 51. 893. Find E(1010, 4000). Give your answer rounded to 2 
# decimal places behind the decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 430
    timed.caller(dummy, n, i, prob_id)

# Solution of;
# Project Euler Problem 430: Range flips
# https://projecteuler.net/problem=430
# 
# N disks are placed in a row, indexed 1 to N from left to right. Each disk 
# has a black side and white side. Initially all disks show their white side. 
# At each turn, two, not necessarily distinct, integers A and B between 1 and 
# N (inclusive) are chosen uniformly at random. All disks with an index from A 
# to B (inclusive) are flipped. The following example shows the case N = 8. At 
# the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6. Let 
# E(N, M) be the expected number of disks that show their white side after M 
# turns. We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5. 157 
# and E(100, 10) ≈ 51. 893. Find E(1010, 4000). Give your answer rounded to 2 
# decimal places behind the decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 430
    timed.caller(dummy, n, i, prob_id)
# Solution of; # Project Euler Problem 430: Range flips # https://projecteuler.net/problem=430 # # N disks are placed in a row, indexed 1 to N from left to right. Each disk # has a black side and white side. Initially all disks show their white side. # At each turn, two, not necessarily distinct, integers A and B between 1 and # N (inclusive) are chosen uniformly at random. All disks with an index from A # to B (inclusive) are flipped. The following example shows the case N = 8. At # the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6. Let # E(N, M) be the expected number of disks that show their white side after M # turns. We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5. 157 # and E(100, 10) ≈ 51. 893. Find E(1010, 4000). Give your answer rounded to 2 # decimal places behind the decimal point. # # by lcsm29 http://github.com/lcsm29/project-euler