Two people start races from two different points p1 and p2. They cover s1 and s2 meters in a jump. Find if they will ever meet at a point after the same number of jumps.
Input : p1 = 6, s1 = 3, p2 = 8, s2 = 2 Output : Yes Explanation: 6->9->12 8->10->12 They meet after two jumps. Input : p1 = 4, s1 = 4, p2 = 8, s2 = 2 Output : Yes Explanation: 4->8->12 8->10->12 Input : p1 = 0, s1 = 2, p2 = 5, s2 = 3 Output : No Input : p1 = 42, s1 = 3, p2 = 94, s2 = 2 Output : Yes
A simple solution is to make them jump one by one. After every jump, see if they are same point or not.
An efficient solution is based on below facts:
Since starting points are always different, they will meet if following conditions are met.
(1) Speeds are not same
(2) Difference between speeds divide the total distance between initial points.
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