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rm (short for remove) is a basic command on Unix and Unix-like operating systems used to remove objects such as computer files, directories and symbolic links from file systems and also special files such as device nodes, pipes and sockets, similar to the del command in MS-DOS, OS/2, and Microsoft Windows. The command is also available in the ...
The procedure begins by examining the key; null denotes the arrival of a terminal node or end of a string key. If the node is terminal it has no children, it is removed from the trie (line 14). However, an end of string key without the node being terminal indicates that the key does not exist, thus the procedure does not modify the trie.
For this purpose, m - 1 keys from the current node, the new key inserted, one key from the parent node and j keys from the sibling node are seen as an ordered array of m + j + 1 keys. The array becomes split by half, so that ⌊ ( m + j + 1)/2 ⌋ lowest keys stay in the current node, the next (middle) key is inserted in the parent and the rest ...
The decrease key operation replaces the value of a node with a given value with a lower value, and the increase key operation does the same but with a higher value. This involves finding the node with the given value, changing the value, and then down-heapifying or up-heapifying to restore the heap property. Decrease key can be done as follows:
In a doubly linked list, one can insert or delete a node in a constant number of operations given only that node's address. To do the same in a singly linked list, one must have the address of the pointer to that node, which is either the handle for the whole list (in case of the first node) or the link field in the previous node. Some ...
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
An internal node (also known as an inner node, inode for short, or branch node) is any node of a tree that has child nodes. Similarly, an external node (also known as an outer node, leaf node, or terminal node) is any node that does not have child nodes. The height of a node is the length of the longest downward path to a leaf from that node ...
Every path from a given node to any of its descendant NIL nodes goes through the same number of black nodes. (Conclusion) If a node N has exactly one child, the child must be red, because if it were black, its NIL descendants would sit at a different black depth than N's NIL child, violating requirement 4.