Marathon (Codeforces 404B)
Tags: Implement, math

Valera takes part in the Berland Marathon. The marathon race starts at the stadium that can be represented on the plane as a square whose lower left corner is located at point with coordinates (0, 0) and the length of the side equals a meters. The sides of the square are parallel to coordinate axes.As the length of the marathon race is very long, Valera needs to have extra drink during the race. The coach gives Valera a bottle of drink each d meters of the path. We know that Valera starts at the point with coordinates (0, 0) and runs counter-clockwise. That is, when Valera covers a meters, he reaches the point with coordinates (a, 0). We also know that the length of the marathon race equals nd + 0.5 meters. Help Valera's coach determine where he should be located to help Valera. Specifically, determine the coordinates of Valera's positions when he covers d, 2·d, ..., n·d meters.

Input: The first line contains two space-separated real numbers a and d (1 ≤ a, d ≤ 105), given with precision till 4 decimal digits after the decimal point. Number a denotes the length of the square's side that describes the stadium. Number d shows that after each d meters Valera gets an extra drink.The second line contains integer n (1 ≤ n ≤ 105) showing that Valera needs an extra drink n times.

Output: Print n lines, each line should contain two real numbers xi and yi, separated by a space. Numbers xi and yi in the i-th line mean that Valera is at point with coordinates (xi, yi) after he covers i·d meters. Your solution will be considered correct if the absolute or relative error doesn't exceed 10 - 4.Note, that this problem have huge amount of output data. Please, do not use cout stream for output in this problem.


Sample Inputs:
2 5
2

4.147 2.8819
6

Sample Outputs:
1.0000000000 2.0000000000
2.0000000000 0.0000000000

2.8819000000 0.0000000000
4.1470000000 1.6168000000
3.7953000000 4.1470000000
0.9134000000 4.1470000000
0.0000000000 2.1785000000
0.7034000000 0.0000000000

Solution (Python):
import sys

def main():
    (a, d) = map(lambda x: int(round(float(x) * 10000)), input().split(' '))
    ans = []
    for i in range(1, int(input()) + 1):
        cur_round_pos = d * i % (a * 4)
        if cur_round_pos <= a:
            y = 0
            x = cur_round_pos / 10000
        elif cur_round_pos <= a * 2:
            x = a / 10000
            y = (cur_round_pos - a) / 10000
        elif cur_round_pos <= a * 3:
            y = a / 10000
            x = (a * 3 - cur_round_pos) / 10000
        elif cur_round_pos < a * 4:
            x = 0
            y = (a * 4 - cur_round_pos) / 10000
        ans.append('{} {}'.format(x, y))
    print('\n'.join(ans))
if __name__ == '__main__':
    sys.exit(main())

Solution (Python):
import sys

def main():
    (a, d) = map(lambda x: int(float(x) * 10000 + 1e-06), input().split(' '))
    ans = []
    for i in range(1, int(input()) + 1):
        cur_round_pos = d * i % (a * 4)
        if cur_round_pos <= a:
            y = 0
            x = cur_round_pos / 10000
        elif cur_round_pos <= a * 2:
            x = a / 10000
            y = (cur_round_pos - a) / 10000
        elif cur_round_pos <= a * 3:
            y = a / 10000
            x = (a * 3 - cur_round_pos) / 10000
        elif cur_round_pos < a * 4:
            x = 0
            y = (a * 4 - cur_round_pos) / 10000
        ans.append('{} {}'.format(x, y))
    print('\n'.join(ans))
if __name__ == '__main__':
    sys.exit(main())

Solution (Python):
from math import floor
(a, d) = map(float, input().split())
n = int(input())
res = []
for i in range(n):
    rec = i * d + d
    tra = floor(rec / a) % 4
    seg = rec - floor(rec / a) * a
    if tra == 0:
        res.append('%.8f %.8f' % (seg, 0.0))
    elif tra == 1:
        res.append('%.8f %.8f' % (a, seg))
    elif tra == 2:
        res.append('%.8f %.8f' % (a - seg, a))
    elif tra == 3:
        res.append('%.8f %.8f' % (0.0, a - seg))
print('\n'.join(res))