/**
 * @file
 * @brief [Persistent segment tree with range updates (lazy
 * propagation)](https://en.wikipedia.org/wiki/Persistent_data_structure)
 *
 * @details
 * A normal segment tree facilitates making point updates and range queries in
 * logarithmic time. Lazy propagation preserves the logarithmic time with range
 * updates. So, a segment tree with lazy propagation enables doing range updates
 * and range queries in logarithmic time, but it doesn't save any information
 * about itself before the last update. A persistent data structure always
 * preserves the previous version of itself when it is modified. That is, a new
 * version of the segment tree is generated after every update. It saves all
 * previous versions of itself (before every update) to facilitate doing range
 * queries in any version. More memory is used ,but the logarithmic time is
 * preserved because the new version points to the same nodes, that the previous
 * version points to, that are not affected by the update. That is, only the
 * nodes that are affected by the update and their ancestors are copied. The
 * rest is copied using lazy propagation in the next queries. Thus preserving
 * the logarithmic time because the number of nodes copied after any update is
 * logarithmic.
 *
 * @author [Magdy Sedra](https://github.com/MSedra)
 */
#include <iostream>  /// for IO operations
#include <memory>    /// to manage dynamic memory
#include <vector>    /// for std::vector

/**
 * @namespace range_queries
 * @brief Range queries algorithms
 */
namespace range_queries {

/**
 * @brief Range query here is range sum, but the code can be modified to make
 * different queries like range max or min.
 */
class perSegTree {
 private:
    class Node {
     public:
        std::shared_ptr<Node> left = nullptr;   /// pointer to the left node
        std::shared_ptr<Node> right = nullptr;  /// pointer to the right node
        int64_t val = 0,
                prop = 0;  /// val is the value of the node (here equals to the
                           /// sum of the leaf nodes children of that node),
                           /// prop is the value to be propagated/added to all
                           /// the leaf nodes children of that node
    };

    uint32_t n = 0;  /// number of elements/leaf nodes in the segment tree
    std::vector<std::shared_ptr<Node>>
        ptrs{};  /// ptrs[i] holds a root pointer to the segment tree after the
                 /// ith update. ptrs[0] holds a root pointer to the segment
                 /// tree before any updates
    std::vector<int64_t> vec{};  /// values of the leaf nodes that the segment
                                 /// tree will be constructed with

    /**
     * @brief Creating a new node with the same values of curr node
     * @param curr node that would be copied
     * @returns the new node
     */
    std::shared_ptr<Node> newKid(std::shared_ptr<Node> const &curr) {
        auto newNode = std::make_shared<Node>(Node());
        newNode->left = curr->left;
        newNode->right = curr->right;
        newNode->prop = curr->prop;
        newNode->val = curr->val;
        return newNode;
    }

    /**
     * @brief If there is some value to be propagated to the passed node, value
     * is added to the node and the children of the node, if exist, are copied
     * and the propagated value is also added to them
     * @param i the left index of the range that the passed node holds its sum
     * @param j the right index of the range that the passed node holds its sum
     * @param curr pointer to the node to be propagated
     * @returns void
     */
    void lazy(const uint32_t &i, const uint32_t &j,
              std::shared_ptr<Node> const &curr) {
        if (!curr->prop) {
            return;
        }
        curr->val += (j - i + 1) * curr->prop;
        if (i != j) {
            curr->left = newKid(curr->left);
            curr->right = newKid(curr->right);
            curr->left->prop += curr->prop;
            curr->right->prop += curr->prop;
        }
        curr->prop = 0;
    }

    /**
     * @brief Constructing the segment tree with the early passed vector. Every
     * call creates a node to hold the sum of the given range, set its pointers
     * to the children, and set its value to the sum of the children's values
     * @param i the left index of the range that the created node holds its sum
     * @param j the right index of the range that the created node holds its sum
     * @returns pointer to the newly created node
     */
    std::shared_ptr<Node> construct(const uint32_t &i, const uint32_t &j) {
        auto newNode = std::make_shared<Node>(Node());
        if (i == j) {
            newNode->val = vec[i];
        } else {
            uint32_t mid = i + (j - i) / 2;
            auto leftt = construct(i, mid);
            auto right = construct(mid + 1, j);
            newNode->val = leftt->val + right->val;
            newNode->left = leftt;
            newNode->right = right;
        }
        return newNode;
    }

    /**
     * @brief Doing range update, checking at every node if it has some value to
     * be propagated. All nodes affected by the update are copied and
     * propagation value is added to the leaf of them
     * @param i the left index of the range that the passed node holds its sum
     * @param j the right index of the range that the passed node holds its sum
     * @param l the left index of the range to be updated
     * @param r the right index of the range to be updated
     * @param value the value to be added to every element whose index x
     * satisfies l<=x<=r
     * @param curr pointer to the current node, which has value = the sum of
     * elements whose index x satisfies i<=x<=j
     * @returns pointer to the current newly created node
     */
    std::shared_ptr<Node> update(const uint32_t &i, const uint32_t &j,
                                 const uint32_t &l, const uint32_t &r,
                                 const int64_t &value,
                                 std::shared_ptr<Node> const &curr) {
        lazy(i, j, curr);
        if (i >= l && j <= r) {
            std::shared_ptr<Node> newNode = newKid(curr);
            newNode->prop += value;
            lazy(i, j, newNode);
            return newNode;
        }
        if (i > r || j < l) {
            return curr;
        }
        auto newNode = std::make_shared<Node>(Node());
        uint32_t mid = i + (j - i) / 2;
        newNode->left = update(i, mid, l, r, value, curr->left);
        newNode->right = update(mid + 1, j, l, r, value, curr->right);
        newNode->val = newNode->left->val + newNode->right->val;
        return newNode;
    }

    /**
     * @brief Querying the range from index l to index r, checking at every node
     * if it has some value to be propagated. Current node's value is returned
     * if its range is completely inside the wanted range, else 0 is returned
     * @param i the left index of the range that the passed node holds its sum
     * @param j the right index of the range that the passed node holds its sum
     * @param l the left index of the range whose sum should be returned as a
     * result
     * @param r the right index of the range whose sum should be returned as a
     * result
     * @param curr pointer to the current node, which has value = the sum of
     * elements whose index x satisfies i<=x<=j
     * @returns sum of elements whose index x satisfies l<=x<=r
     */
    int64_t query(const uint32_t &i, const uint32_t &j, const uint32_t &l,
                  const uint32_t &r, std::shared_ptr<Node> const &curr) {
        lazy(i, j, curr);
        if (j < l || r < i) {
            return 0;
        }
        if (i >= l && j <= r) {
            return curr->val;
        }
        uint32_t mid = i + (j - i) / 2;
        return query(i, mid, l, r, curr->left) +
               query(mid + 1, j, l, r, curr->right);
    }

    /**
     * public methods that can be used directly from outside the class. They
     * call the private functions that do all the work
     */
 public:
    /**
     * @brief Constructing the segment tree with the values in the passed
     * vector. Returned root pointer is pushed in the pointers vector to have
     * access to the original version if the segment tree is updated
     * @param vec vector whose values will be used to build the segment tree
     * @returns void
     */
    void construct(const std::vector<int64_t>
                       &vec)  // the segment tree will be built from the values
                              // in "vec", "vec" is 0 indexed
    {
        if (vec.empty()) {
            return;
        }
        n = vec.size();
        this->vec = vec;
        auto root = construct(0, n - 1);
        ptrs.push_back(root);
    }

    /**
     * @brief Doing range update by passing the left and right indexes of the
     * range as well as the value to be added.
     * @param l the left index of the range to be updated
     * @param r the right index of the range to be updated
     * @param value the value to be added to every element whose index x
     * satisfies l<=x<=r
     * @returns void
     */
    void update(const uint32_t &l, const uint32_t &r,
                const int64_t
                    &value)  // all elements from index "l" to index "r" would
                             // by updated by "value", "l" and "r" are 0 indexed
    {
        ptrs.push_back(update(
            0, n - 1, l, r, value,
            ptrs[ptrs.size() -
                 1]));  // saving the root pointer to the new segment tree
    }

    /**
     * @brief Querying the range from index l to index r, getting the sum of the
     * elements whose index x satisfies l<=x<=r
     * @param l the left index of the range whose sum should be returned as a
     * result
     * @param r the right index of the range whose sum should be returned as a
     * result
     * @param version the version to query on. If equals to 0, the original
     * segment tree will be queried
     * @returns sum of elements whose index x satisfies l<=x<=r
     */
    int64_t query(
        const uint32_t &l, const uint32_t &r,
        const uint32_t
            &version)  // querying the range from "l" to "r" in a segment tree
                       // after "version" updates, "l" and "r" are 0 indexed
    {
        return query(0, n - 1, l, r, ptrs[version]);
    }

    /**
     * @brief Getting the number of versions after updates so far which is equal
     * to the size of the pointers vector
     * @returns the number of versions
     */
    uint32_t size()  // returns the number of segment trees (versions) , the
                     // number of updates done so far = returned value - 1
                     // ,because one of the trees is the original segment tree
    {
        return ptrs.size();
    }
};
}  // namespace range_queries

/**
 * @brief Test implementations
 * @returns void
 */
static void test() {
    std::vector<int64_t> arr = {-5, 2, 3, 11, -2, 7, 0, 1};
    range_queries::perSegTree tree;
    std::cout << "Elements before any updates are {";
    for (uint32_t i = 0; i < arr.size(); ++i) {
        std::cout << arr[i];
        if (i != arr.size() - 1) {
            std::cout << ",";
        }
    }
    std::cout << "}\n";
    tree.construct(
        arr);  // constructing the original segment tree (version = 0)
    std::cout << "Querying range sum on version 0 from index 2 to 4 = 3+11-2 = "
              << tree.query(2, 4, 0) << '\n';
    std::cout
        << "Subtract 7 from all elements from index 1 to index 5 inclusive\n";
    tree.update(1, 5, -7);  // subtracting 7 from index 1 to index 5
    std::cout << "Elements of the segment tree whose version = 1 (after 1 "
                 "update) are {";
    for (uint32_t i = 0; i < arr.size(); ++i) {
        std::cout << tree.query(i, i, 1);
        if (i != arr.size() - 1) {
            std::cout << ",";
        }
    }
    std::cout << "}\n";
    std::cout << "Add 10 to all elements from index 0 to index 7 inclusive\n";
    tree.update(0, 7, 10);  // adding 10 to all elements
    std::cout << "Elements of the segment tree whose version = 2 (after 2 "
                 "updates) are {";
    for (uint32_t i = 0; i < arr.size(); ++i) {
        std::cout << tree.query(i, i, 2);
        if (i != arr.size() - 1) {
            std::cout << ",";
        }
    }
    std::cout << "}\n";
    std::cout << "Number of segment trees (versions) now = " << tree.size()
              << '\n';
    std::cout << "Querying range sum on version 0 from index 3 to 5 = 11-2+7 = "
              << tree.query(3, 5, 0) << '\n';
    std::cout << "Querying range sum on version 1 from index 3 to 5 = 4-9+0 = "
              << tree.query(3, 5, 1) << '\n';
}

/**
 * @brief Main function
 * @returns 0 on exit
 */
int main() {
    test();  // run self-test implementations
    return 0;
}