вторник, 24 декабря 2013 г.

Codility. Train. Frog-Jmp ★

A small frog wants to get to the other side of the road. The frog is currently located at position X and wants to get to a position greater than or equal to Y. The small frog always jumps a fixed distance, D.
Count the minimal number of jumps that the small frog must perform to reach its target.
Write a function:
def solution(X, Y, D)
that, given three integers X, Y and D, returns the minimal number of jumps from position X to a position equal to or greater than Y.
For example, given:
  X = 10
  Y = 85
  D = 30
the function should return 3, because the frog will be positioned as follows:
  • after the first jump, at position 10 + 30 = 40
  • after the second jump, at position 10 + 30 + 30 = 70
  • after the third jump, at position 10 + 30 + 30 + 30 = 100
Assume that:
  • X, Y and D are integers within the range [1..1,000,000,000];
  • X ≤ Y.
Complexity:
  • expected worst-case time complexity is O(1);
  • expected worst-case space complexity is O(1).

Solution:
import math
def solution(X, Y, D):
    return int(math.ceil((Y-X)/float(D)))

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