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feat: Treap Data Structure (#2458)
* feat: Treap Data Structure * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: suggested changes * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * fix: add more self-tests * fix: suggested changes Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * fix: add namespace prefixs * suggested changes Co-authored-by: David Leal <halfpacho@gmail.com> * fix: use containers * fix: add initialization * fix: suggested changes * fix: a few `clang-tidy` warnings * fix: segmentation fault --------- Co-authored-by: realstealthninja <68815218+realstealthninja@users.noreply.github.com> Co-authored-by: David Leal <halfpacho@gmail.com>
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KAIRAO ZHENG
GitHub
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259
data_structures/treap.cpp
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259
data_structures/treap.cpp
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/**
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* @file
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* @brief A balanced binary search tree (BST) on the basis of binary search tree
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* and heap: the [Treap](https://en.wikipedia.org/wiki/Treap) algorithm
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* implementation
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*
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* @details
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* Implementation of the treap data structre
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*
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* Support operations including insert, erase, and query (the rank of specified
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* element or the element ranked x) as the same as BST
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*
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* But these operations take O(log N) time, since treap keeps property of heap
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* using rotate operation, and the desired depth of the tree is O(log N).
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* There's very little chance that it will degenerate into a chain like BST
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*
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* @author [Kairao ZHENG](https://github.com/fgmn)
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*/
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#include <array> /// For array
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#include <cassert> /// For assert
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#include <iostream> /// For IO operations
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/**
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* @namespace
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* @brief Data Structures
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*/
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namespace data_structures {
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/**
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* @namespace
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* @brief Functions for the [Treap](https://en.wikipedia.org/wiki/Treap)
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* algorithm implementation
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*/
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namespace treap {
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const int maxNode = 1e5 + 5; ///< maximum number of nodes
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/**
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* @brief Struct representation of the treap
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*/
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struct Treap {
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int root = 0; ///< root of the treap
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int treapCnt = 0; ///< Total number of current nodes in the treap
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std::array<int, maxNode> key = {}; ///< Node identifier
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std::array<int, maxNode> priority = {}; ///< Random priority
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std::array<std::array<int, 2>, maxNode> childs = {
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{}}; ///< [i][0] represents the
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///< left child of node i, and
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///[i][1] represents the right
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std::array<int, maxNode> cnt =
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{}; ///< Maintains the subtree size for ranking query
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std::array<int, maxNode> size = {}; ///< The number of copies per node
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/**
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* @brief Initialization
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*/
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Treap() : treapCnt(1) {
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priority[0] = INT32_MAX;
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size[0] = 0;
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}
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/**
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* @brief Update the subtree size of the node
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* @param x The node to update
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*/
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void update(int x) {
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size[x] = size[childs[x][0]] + cnt[x] + size[childs[x][1]];
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}
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/**
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* @brief Rotate without breaking the property of BST
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* @param x The node to rotate
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* @param t 0 represent left hand, while 1 right hand
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*/
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void rotate(int &x, int t) {
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int y = childs[x][t];
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childs[x][t] = childs[y][1 - t];
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childs[y][1 - t] = x;
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// The rotation will only change itself and its son nodes
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update(x);
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update(y);
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x = y;
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}
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/**
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* @brief Insert a value into the specified subtree (internal method)
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* @param x Insert into the subtree of node x (Usually x=root)
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* @param k Key to insert
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*/
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void _insert(int &x, int k) {
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if (x) {
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if (key[x] == k) {
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cnt[x]++;
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} // If the node already exists, the number of copies is ++
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else {
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int t = (key[x] < k); // Insert according to BST properties
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_insert(childs[x][t], k);
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// After insertion, the heap properties are retained by rotation
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if (priority[childs[x][t]] < priority[x]) {
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rotate(x, t);
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}
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}
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} else { // Create a new node
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x = treapCnt++;
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key[x] = k;
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cnt[x] = 1;
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priority[x] = rand(); // Random priority
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childs[x][0] = childs[x][1] = 0;
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}
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update(x);
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}
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/**
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* @brief Erase a value from the specified subtree (internal method)
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* @param x Erase from the subtree of node x (Usually x=root)
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* @param k Key to erase
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*/
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void _erase(int &x, int k) {
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if (key[x] == k) {
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if (cnt[x] > 1) {
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cnt[x]--;
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} // If the node has more than one copy, the number of copies --
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else {
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if (childs[x][0] == 0 && childs[x][1] == 0) {
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x = 0;
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return;
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} // If there are no children, delete and return
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// Otherwise, we need to rotate the sons and delete them
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// recursively
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int t = (priority[childs[x][0]] > priority[childs[x][1]]);
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rotate(x, t);
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_erase(x, k);
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}
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} else { // Find the target value based on BST properties
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_erase(childs[x][key[x] < k], k);
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}
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update(x);
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}
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/**
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* @brief Find the KTH largest value (internal method)
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* @param x Query the subtree of node x (Usually x=root)
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* @param k The queried rank
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* @return The element ranked number k
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*/
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int _get_k_th(int &x, int k) {
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if (k <= size[childs[x][0]]) {
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return _get_k_th(childs[x][0], k);
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}
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k -= size[childs[x][0]] + cnt[x];
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if (k <= 0) {
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return key[x];
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}
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return _get_k_th(childs[x][1], k);
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}
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/**
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* @brief Query the rank of specified element (internal method)
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* @param x Query the subtree of node x (Usually x=root)
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* @param k The queried element
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* @return The rank of element k
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*/
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int _get_rank(int x, int k) {
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if (!x) {
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return 0;
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}
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if (k == key[x]) {
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return size[childs[x][0]] + 1;
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}
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else if (k < key[x]) {
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return _get_rank(childs[x][0], k);
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}
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else {
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return size[childs[x][0]] + cnt[x] + _get_rank(childs[x][1], k);
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}
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}
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/**
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* @brief Get the predecessor node of element k
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* @param k The queried element
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* @return The predecessor
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*/
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int get_predecessor(int k) {
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int x = root, pre = -1;
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while (x) {
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if (key[x] < k) {
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pre = key[x], x = childs[x][1];
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} else {
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x = childs[x][0];
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}
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}
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return pre;
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}
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/**
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* @brief Get the successor node of element k
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* @param k The queried element
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* @return The successor
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*/
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int get_next(int k) {
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int x = root, next = -1;
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while (x) {
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if (key[x] > k) {
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next = key[x], x = childs[x][0];
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} else {
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x = childs[x][1];
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}
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}
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return next;
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}
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/**
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* @brief Insert element (External method)
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* @param k Key to insert
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*/
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void insert(int k) { _insert(root, k); }
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/**
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* @brief Erase element (External method)
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* @param k Key to erase
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*/
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void erase(int k) { _erase(root, k); }
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/**
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* @brief Get the KTH largest value (External method)
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* @param k The queried rank
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* @return The element ranked number x
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*/
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int get_k_th(int k) { return _get_k_th(root, k); }
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/**
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* @brief Get the rank of specified element (External method)
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* @param k The queried element
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* @return The rank of element k
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*/
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int get_rank(int k) { return _get_rank(root, k); }
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};
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} // namespace treap
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} // namespace data_structures
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/**
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* @brief Self-test implementations
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* @returns void
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*/
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static void test() {
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data_structures::treap::Treap mTreap; ///< Treap object instance
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mTreap.insert(1);
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mTreap.insert(2);
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mTreap.insert(3);
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assert(mTreap.get_k_th(2) == 2);
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mTreap.insert(4);
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mTreap.insert(5);
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mTreap.insert(6);
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assert(mTreap.get_next(4) == 5);
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mTreap.insert(7);
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assert(mTreap.get_predecessor(7) == 6);
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mTreap.erase(4);
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assert(mTreap.get_k_th(4) == 5);
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assert(mTreap.get_rank(5) == 4);
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mTreap.insert(10);
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assert(mTreap.get_rank(10) == 7);
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assert(mTreap.get_predecessor(10) == 7);
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std::cout << "All tests have successfully passed!\n";
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}
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/**
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* @brief Main function
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* @returns 0 on exit
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*/
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int main() {
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test(); // run self-test implementations
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return 0;
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}
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