Kangaroo:
There are two kangaroos on an x-axis ready to jump in the positive direction (i.e, toward positive infinity). The first kangaroo starts at location \(x_1\) and moves at a rate of \(v_1\) meters per jump. The second kangaroo starts at location \(x_2\) and moves at a rate of \(v_2\) meters per jump. Given the starting locations and movement rates for each kangaroo, can you determine if they’ll ever land at the same location at the same time?
Input Format
A single line of four space-separated integers denoting the respective values of \(x_1\),\(v_1\),\(x_2\) and \(v_2\).
Constraints:
- 0<=\(x_1\)<\(x_2\)<=10000
- 1<=\(v_1\)<= 10000
- 1<=\(v_2\)<= 10000
Output Format
Print YES if they can land on the same location at the same time; otherwise, print NO.
Sample Input 0
0 3 4 2
Sample Output 0
YES
Explanation 0
The two kangaroos jump through the following sequence of locations:
- 0—>3—>6—>9—>12
- 4—>6—>8—>10—>12
Thus, the kangaroos meet after 4 jumps and we print YES.
Sample Input 1
0 2 5 3
Sample Output 1
NO
Explanation 1
The second kangaroo has a starting location that is ahead (further to the right) of the first kangaroo’s starting location (i.e.,\(x_2\) > \(x_1\) ) Because the second kangaroo moves at a faster rate (meaning \(v_2\) > \(v_1\) ) and is already ahead of the first kangaroo, the first kangaroo will never be able to catch up. Thus, we print NO.
Solution
import sys
#!/usr/bin/py
x1,v1,x2,v2 = raw_input().strip().split(' ')
x1,v1,x2,v2 = [int(x1),int(v1),int(x2),int(v2)]
if v2 < v1 and (x1 - x2)%(v2 - v1) == 0:
print('YES')
else:
print("NO")