A team sport game has m players in a team and a tournament can have n competing teams. Team T1 ranks higher than team T2 if there is a way such that every member of T1 ranks higher than a corresponding member of T2 (note that the ranking is based on individual team members). (1) Design an efficient algorithm (pseudo code) to determine whether or not two teams T1 and T2 can be ranked. (2) Given n teams {T1, T2, ... , Tn}, abstract the team ranking problem as a graph. (3) Design an efficient algorithm (pseudo code) to find the longest sequence of teams such that Tij ranks higher than Tij + 1 for j = 1,2,..., k − 1. (4) Analyze the time complexity of your algorithm in terms of m and n.

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Types of trees

A tree data structure is a non–linear structure that stores data hierarchically. It can be defined as a group of objects, called nodes. The nodes are linked with edges. Trees begin with a root node which leads to children nodes. The last children nodes (endpoints) are called leaf nodes, and they do not have children nodes.