long to see that the successor of is there' just no other number that is greater than and also smaller than howeverthe computer can' do things "at glance"it needs an algorithm here it isfirstthe program goes to the original node' right childwhich must have key larger than the node then it goes to this right child' left child (if it has one)and to this left child' left childand so onfollowing down the path of left children the last left child in this path is the successor of the original nodeas shown in figure to find successor of this node go to right child go to left child go to left child successor no left child figure finding the successor why does this algorithm workwhat we're really looking for is the smallest of the set of nodes that are larger than the original node when you go to the original node' right childall the nodes in the resulting subtree are greater than the original node because this is how binary search tree is defined now we want the smallest value in this subtree as we learnedyou can find the minimum value in subtree by following the path down all the left children thusthis algorithm finds the minimum value that is greater than the original nodethis is what we mean by its successor if the right child of the original node has no left childrenthis right child is itself the successoras shown in figure