Question

Uses of trees in multi dimensions. 10 points.

don't say I don't know if you know say please and don't write unnecessary word

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Answer 1

Answer:

Food, paper, furniture ,oxygen and etc.....

Answer 2

Answer:

The multidimensional binary search tree (abbreviated k-d tree) is defined as a data structure for storing multikey records. 

Explanation:

The multidimensional binary search tree (abbreviated k-d tree) is defined as a data structure for storing multikey records. This structure has been implemented to solve a number of "geometric" problems in statistics and data analysis.A k-d tree (short for k-dimensional tree) is defined as a space-partitioning data structure for organizing points in a k-dimensional space. Data structure k-d trees are implemented for several applications, for example, searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches). k-d trees are treated as a special case of binary space partitioning trees.

The k-d tree is a binary tree in which every leaf node is treated as a k-dimensional point. Every non-leaf node can be imagined as implicitly generating a splitting hyperplane (used as median) that divides the space into two parts, called as half-spaces. Points to the left of this hyperplane are treated by the left subtree of that node and points to the right of the hyperplane are treated by the right subtree. We can select the hyperplane direction in the following way: every node in the tree is associated with one of the k dimensions, along with the hyperplane perpendicular to that dimension's axis. So, for example, if for a particular split the "x" axis is selected, all points in the subtree with a less "x" value than the node will appear in the left subtree and all points with higher "x" value will be in the right subtree. In such a case, the hyperplane would be set by the x-value of the point, and its normal indicates the unit x-axis. A popular practice is to sort a fixed number of randomly selected points, and implement the median of those points to serve as the splitting plane.

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