Contents
Is the range minimum query equivalent to the lowest common ancestor?
The range minimum query [l, r] is equivalent to the lowest common ancestor query [l’, r’], where l’ is the node corresponding to the element A [l] and r’ the node corresponding to the element A [r] . Indeed the node corresponding to the smallest element in the range has to be an ancestor of all nodes in the range, therefor also from l’ and r’ .
How to find LCA of two nodes in a range?
Query is to find LCA of two nodes that is minimum element in a range. When we use Euler’s Tour method to find LCA then we traverse the whole tree starting from the root using the Euler Tour method. In this method, we use DFS traversal with preorder traversal characteristics. A segment tree is also known as a statistic tree.
How to solve RMQ ( range minimum query )?
The array A will be partitioned into 3 parts: the prefix of the array up to the minimum, the minimum, and the remaining suffix. The root of the tree will be a node corresponding to the minimum element of the array A, the left subtree will be the Cartesian tree of the prefix, and the right subtree will be a Cartesian tree of the suffix.
Which is the smallest node in the range?
Indeed the node corresponding to the smallest element in the range has to be an ancestor of all nodes in the range, therefor also from l’ and r’ . This automatically follows from the min-heap property.
How is the range minimum query used in Topcoder?
By finding the LCA of some nodes in this tree we can actually find the common parent of two species, and we can determine that the similar characteristics they share are inherited from that parent. Range Minimum Query (RMQ) is used on arrays to find the position of an element with the minimum value between two specified indices.
When to use range minimum query ( RMQ )?
Range Minimum Query (RMQ) is used on arrays to find the position of an element with the minimum value between two specified indices. We will see later that the LCA problem can be reduced to a restricted version of an RMQ problem, in which consecutive array elements differ by exactly 1.