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Hello, Problem Setter for this question here,
Editorial will be out soon but anyway I'll share the basic idea. I think you already know you have to somehow manage the segments. Well the answer was simply modular arithmetic and recursion.

Think of it this way :

Each round and its next round can be seen as a transition between three parameters.
1) Round No : $$$i$$$ , to track some edge cases for the most part, becomes $$$i+1$$$
2) No of chairs in current round $$$m$$$ , becomes $$$\lfloor m/2 \rfloor$$$
3) No of people in current round $$$n$$$ , becomes $$$m$$$

Let's say we recursively get to know that a subproblem for the next round will grant $$$X$$$ as the winner. We pickup the fact that the next round was formulated after rotation by $$$T_i$$$ positions. So the winner $$$X$$$ here was someone who was at a position $$$X$$$ from the perspective of person $$$0$$$/$$$1$$$(index ambiguity, basically the person with the first chair) after circling in this round. So , the real identity of $$$X$$$ has been revolving around in the round and we basically will have to undo that . Thus, for this round , in the recursion unpacking phase, we can return our winner by going back $$$T_i$$$ positions.

We did it using intervals ... Maintain vector of plausible intervals and keep on elimnating in every step ... Probably use 1 vector for odd turns and 1 for even and keep on switching could be one way

My approach was :

I gave position one to winner after last round, then I found where he was in the previous round using basic maths and updated the position. Did this until first round and that position was the answer.

ll pos=1;
ll length=1;
for(ll i=ii-1;i>=0;i--){
    length=vv[i];
    ll left=t[i];
    left%=ww[i];
    ll temp=pos;
    if(left>=pos){
        pos=ww[i];
        left-=temp;
    }
    pos-=left;
}
cout<<pos<<"\n";

So I understand that bridges are weak roads which needs to be removed. But how to calculate "For each weak city, find out the distance to nearest strong city".

How do you do multi source shortest path in weighted graph?

Link for the editorial to this problem.