This is my rather unconventional solution using sorted contest array(by start time or end time) and wormhole array. The solution yields O(NlogN) since it sorts the contest array twice by its start-time order and end-time order.
Now I get it, I was misinterpreting question all this time. Actually after finish of each round, lead is not the difference between points of that round. But the lead is difference between the points achieved through all rounds including current round - Lakpa Tashi Bhutia
Problem in short: You are given a tree with N nodes, where each node i has a value v[i] associated with it. Find nodes i and j, such that i is an ancestor of j and (v[i] - v[j]) is maximized. N <= 10^5.
Indian National Olympiad in Informatics (INOI) is round 2 out of 3 (i.e. intermediate) for selection into Indian IOI team.