"Leetcode" 96. Unique binary Search trees-the number of the only two-pronged sort tree

First, Description:

Second, the idea:

BST (binary sort tree): The result of the middle sequence traversal is a non-descending sequence, and the results of the middle sequence traversal of the different binary trees with the same node (number and value) are the same;

When the number of nodes of Zuozi is determined, the number of right subtree is also determined;

When the number of nodes is 0 or 1 o'clock, there are only 1 binary trees, expressed as f (0) =1,f (1) =f (0) *f (0);

When the number of nodes is 2 o'clock, the total number of Species = left subtree is empty f (0) * Right subtree is not empty f (1) + left subtree is not empty f (1) * Right subtree is empty f (0), i.e. f (0) *f (1) +f (1) *f (0) = 2 species;

When the number of nodes is 3 o'clock, there is a left dial hand tree is empty f (0) * Right subtree is not empty f (2) + left subtree is not empty f (2) * Right subtree is empty f (0) + left subtree is not empty f (1) *f (1), i.e. f (0) *f (2) +f (2) *f (0) +f (1) *f (1) =1*2+2*1+1 *1=5 species;

......

When the number of nodes is n, the result is f (0) *f (n-1) +f (1) *f (n-2) +......+f (n-2) *f (1) +f (n-1) *f (0);

From the above law can be obtained, when the number of nodes n is greater than 0 o'clock, n corresponding to the different binary tree species is always dependent on n equals 0-(n-1) when the corresponding value is obtained, it can be 0-(n-1) value corresponding to the number of the two-fork tree is saved to a hashmap<k,v> collection, Recursive invocation only need to get the corresponding value from the collection;

Have you ever felt like the Fibonacci sequence, the same principle.

Third, the code:

 Public classSolution { Public intNumtrees (intN) {if(N==0 | | n==1){            return1; } Map<integer, integer> map =NewHashmap<integer, integer>(); Map.put (0, 1); Map.put (1, 1);  for(inti=2;i<=n;i++){            intCount = 0;  for(intj=0;j<i;j++) {Count+ = Map.get (j) *map.get (i-j-1);//minus 1 is in addition to the root node.} map.put (I, count); }        returnMap.get (n);//n the number of trees corresponding to    }}

"Leetcode" 96. Unique binary Search trees-the number of the only two-pronged sort tree