Cops and the Thief Devu issue


I have been trying to solve question Cops and the Thief Devu. At first I realized that I understand what the question need to tell but when I went through the sample example and its explanation, it makes me confused and puzzled.
Here I’d like to highlight key points of the question

  1. Cops run at a maximum speed of x houses per minute in a straight line.

  2. Cops will search for a maximum of y minutes

This way if the input will be

4 7 8

12 52 56 8

Then cops can cover the house from 12 to 68 (12 +(7x8)) not from 1 to 68 because the cop is at 12 house and if he start moving in a straight line then he can inspect only 56 (7*8) houses from its current house i.e. 12 (correct me if my calculation is wrong or I’m missing something)

Lets take another example

2 10 2

21 75

Like stated above, cops can cover the house from 21 to 41 (21 +(10x2)) not from 1 to 41

Any idea what I missed?

~Thanks in advance

In second example [2,10,2] and [21,75]. Here first cop can cover from 1 to 41 as thief should not hide in house 1 to 41 as first cop can reach these houses in worst case. You should not consider just houses from 21 to 41. Similar way for second cop.