competitive-programming/2023_10_05/frogs-and-mosquitos

The algorithm is designed to solve a problem involving frogs and mosquitoes. The frogs are located at certain positions and have a certain tongue length. Mosquitoes land at certain positions. If a mosquito lands within the reach of a frog's tongue, the frog will eat the mosquito and its tongue length will increase by the size of the mosquito. If a mosquito lands outside the reach of any frog, it will not be eaten.

The algorithm uses a data structure called a segment tree to efficiently manage the positions and tongue lengths of the frogs. A segment tree is a binary tree used for storing information about segments or intervals, and is especially useful for range query problems.

The algorithm starts by initializing a segment tree with the positions and tongue lengths of the frogs. Each node in the segment tree represents a range of positions, and stores the maximum tongue length of any frog within that range.

When a mosquito lands, the algorithm searches the segment tree to find a frog that can reach the mosquito. This is done by checking if the mosquito's position is within the range of a node and if the maximum tongue length in that node is sufficient to reach the mosquito. If such a node is found, the frog's tongue length is updated and the node's maximum value is also updated.

If no such node is found, the mosquito is added to a set of uneaten mosquitoes.

The algorithm also includes a function to insert a new segment into the segment tree. This function is used to update the tree when a frog's tongue length increases. The function ensures that the tree remains balanced and that the maximum values in each node are correct.

Finally, the algorithm includes a function to check if there is a position within a given range that contains exactly a certain number of segments. This function is not used in the main part of the algorithm, but could be useful for additional queries about the positions and tongue lengths of the frogs.