Let T be a binary tree and let x be an element in T. A connected tree T is a tree where for every pair of nodes u, v in T, u can be reached from v (and vice-versa) by following an alternating set of nodes and edges. The deletion of x from T will alter the structure of T, as a result of which, T need not be connected. Design an algorithm that will delete x from T and re-arrange T such that T is connected, provided T-{x} is disconnected. Analyse the time complexity of the algorithm.