binary trees family tree terminologyeach level corresponds to generation the binary tree in figure ( )for examplecontains two nodes at level one ( and )four nodes at level two (defand )and two nodes at level three ( and ithe root node always occupies level zero the depth of node is its distance from the rootwith distance being the number of levels that separate the two node' depth corresponds to the level it occupies consider node in the three trees of figure in tree ( ) has depth of in tree (bit has depth of and in (cits depth is the height of binary tree is the number of levels in the tree for examplethe three binary trees in figure have different heights(ahas height of (bhas height of and (chas height of the width of binary tree is the number of nodes on the level containing the most nodes in the three binary trees of figure (ahas width of (bhas width of and (chas width of finallythe size of binary tree is simply the number of nodes in the tree an empty tree has height of and width of and its size is level nodes - **** ( - figure possible slots for the placement of nodes in binary tree binary tree of size can have maximum height of nwhich results when there is one node per level this is the case with the binary tree in figure (cwhat is the minimum height of binary tree with nodesto determine thiswe need to consider the maximum number of nodes at each level since the nodes will have to be organized with each level at full capacity figure illustrates the slots for the possible placement of nodes within binary tree since each node can have at most two childreneach successive level in the tree doubles the number of nodes contained on the previous level this corresponds to given tree level having capacity for nodes if we sum the size of each levelwhen all of the levels are filled to capacityexcept possibly the last onewe find that the minimum height of binary tree of size is blog nc