Problem Statement
In a binary tree, every node has an optional left, and optional right child node. A BST (binary search tree) is a binary tree that satsifies the following properties:
1) Every node has a unique value
2) The value at a given node must be greater than the value at every node in its left subtree
3) The value at a given node must be less than the value at every node in its right subtree
The depth of a node in a BST is defined as such:
1) The top node (root) has depth 0
2) Every node has depth 1 higher than its parent
Usually, when given a list of distinct values, it is best to build a balanced binary search tree - a tree where the size of the left subtree is approximately the same as the size of the right subtree at each node. A balanced tree isn't always the best solution though. Given a int[] values of distinct values and a int[] probs containing the percentage chance of each element being accessed, your method will return the best (lowest) access score achievable by a BST containing the given values. The access score of any BST is computed by adding together the access scores for all of its nodes. The access score for a particular node is calculated by the formula p*(d+1) where p is the probability of that node being accessed, and d is the depth of that node in the tree.
1) Every node has a unique value
2) The value at a given node must be greater than the value at every node in its left subtree
3) The value at a given node must be less than the value at every node in its right subtree
The depth of a node in a BST is defined as such:
1) The top node (root) has depth 0
2) Every node has depth 1 higher than its parent
Usually, when given a list of distinct values, it is best to build a balanced binary search tree - a tree where the size of the left subtree is approximately the same as the size of the right subtree at each node. A balanced tree isn't always the best solution though. Given a int[] values of distinct values and a int[] probs containing the percentage chance of each element being accessed, your method will return the best (lowest) access score achievable by a BST containing the given values. The access score of any BST is computed by adding together the access scores for all of its nodes. The access score for a particular node is calculated by the formula p*(d+1) where p is the probability of that node being accessed, and d is the depth of that node in the tree.
Definition
- Class:
- SkewTree
- Method:
- bestScore
- Parameters:
- int[], int[]
- Returns:
- int
- Method signature:
- int bestScore(int[] values, int[] probs)
- (be sure your method is public)
Constraints
- values and probs will both contain between 1 and 50 elements, inclusive.
- Each element of values and probs will be between 1 and 1000, inclusive.
- Each element of values will be unique.
- values and probs will contain the same number of elements.
Examples
{1,2}{1,2}Returns: 4
The best tree looks like: 2 \ 1{1,2,4,3,5,6}{1,2,3,4,5,6}Returns: 44
Here the best tree is: 5 / \ / \ 3 6 / \ 2 4 / 1 The score is 5*1 + 4*2 + 6*2 + 2*3 + 3*3 + 1*4 = 44{6,5,3,7,51,36}{65,13,49,62,34,16}Returns: 492
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