Instantiate an internal node.
Instantiate an internal node.
The ordering that is applied to key values
The ordering that is applied to key values
Obtain the node stored at a given key if it exists, None otherwise
Obtain the node stored at a given key if it exists, None otherwise
Aggregator that defines semantics of prefix sum
create a new Black node from a key, value, left subtree and right subtree
create a new Black node from a key, value, left subtree and right subtree
Obtain the prefix (cumulative) sum of values <= a given key 'k'.
Obtain the prefix (cumulative) sum of values <= a given key 'k'. If 'open' is true, sums the open interval for keys strictly < k. If 'k' is not present in the map, then the sum for keys < k is returned.
create a new Red node from a key, value, left subtree and right subtree
create a new Red node from a key, value, left subtree and right subtree
Base trait for R/B nodes supporting prefix-sum query