Frog and Points

Limits: 555h33m20s, 20 MB

There are N stones on across the diameter of a perfectly circle shaped pond at equal distance. The 1st stone is on one side of the pond and Nth stone being on the other side. A frog will cross the pond by jumping over the stones. However, his jump length will be constant. If a frog is in the a th stone, then a jump length of L will get him to (a+L)th stone. There are integer points in each stone. Points can be negative or positive. Positive points will be added to the frog’s score and negative point will be deducted from the frog’s score. What is the maximum number of points the frog can collect by crossing the Path once? He can go to a stone b from a if b>a; However due to the wave of the water at the pond, points of a particular stone can be changed. if his jump length is L the frog will land on the Lth stone in his first jump. When he will reach the Nth or jump pass the Nth stone the game ends. He will get to the other side.

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