I have used Floyd Cycle Detection Algorithm to find out the size of the cycle.
Now the answer for all the nodes which are a part of the cycle is the size of cycle.
And for the other nodes, ans is = size_of_cycle + minimum_distance_of_a_node_which_is_a_part_of_cycle.

This approach passed all the test cases except 4 (in which it is showing TLE). Here is the link to the code Code I think the time complexity of my solution is $$$O(N)$$$.