Double connected component + constructed double connected graph

Construct a double connected graph: A connected graph with a bridge, how to turn it into a double connected graph by adding edge ?

A connected graph with a bridge, how to turn it into a double connected graph by adding edge? The method is to first find all the bridges and then delete the bridge edges, and each of the remaining connected blocks is a double-connected sub-graph. Each double-connected sub-graph is shrunk to a vertex, and then the bridge is added back, the last figure must be a tree, the edge connectivity is 1.

Statistics the number of nodes in the tree with a degree of 1, that is, the number of leaf nodes, recorded as the leaf. At least Add (leaf+1)/2 edges to the tree to make the tree reach the edge two, so at least the number of edges added is (leaf+1)/2 . The method is to first connect an edge between the two nearest common ancestor's two leaf nodes, so that the two points can be shrunk to the path of the ancestors, because a formed ring must be double connected. Then find the two nearest public ancestor the furthest two leaf nodes, so that a pair to find out, happens to be (leaf+1)/2 times, all the points are shrunk together.

Double connected component + constructed double connected graph