2 votes 2 votes number of distinct binary tree,that can be created by 5 nodes(distinct) Graph Theory data-structures binary-tree + – Aboveallplayer asked Dec 10, 2016 Aboveallplayer 668 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes $5$ distinct nodes means you can uniquely identify each node based on some parameter say a key value, Then the solution to this problem is given by bell's number. Number of binary trees possible $= \binom {2n}{n}*n!$ thor answered Dec 10, 2016 thor comment Share Follow See all 3 Comments See all 3 3 Comments reply jaggumulge commented Dec 12, 2016 reply Follow Share Could you please elaborate this solution numerically? 0 votes 0 votes Sushant Gokhale commented Dec 23, 2016 reply Follow Share I think its not correct. #unlabelled binary trees possible = nth catalan number Now, being labelled , they cn be permuted in n! ways. So, answer = $\frac{\binom{2n}{n}}{n+1} * n!$ Correct me if wrong. 3 votes 3 votes Sushant Gokhale commented Dec 23, 2016 reply Follow Share Bell no. gives partitions. It doesnt consider permutations. 0 votes 0 votes Please log in or register to add a comment.