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MSedra 2021-01-27 19:14:08 +02:00
parent 37d2a06719
commit 558b74f1dd
1 changed files with 64 additions and 68 deletions
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130
range_queries/persistent_segment_tree_with_lazy_propagation.cpp
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@ -1,7 +1,6 @@
#include<iostream> #include<iostream>
#include<vector> #include<vector>
using namespace std;
// query -> range sum // query -> range sum
class perSegTree { class perSegTree {
@ -10,17 +9,17 @@ private:
public: public:
Node *left; Node *left;
Node *right; Node *right;
long long val, prop; int64_t val, prop;
int version; int version;
Node() { Node() {
left = right = NULL; left = right = nullptr;
val = prop = version = 0; val = prop = version = 0;
} }
}; };
int n; // number of elements in the segment tree int n; // number of elements in the segment tree
vector<Node *> ptrs; // ptrs[i] holds a root pointer to the segment tree after the ith update std::vector<Node *> ptrs; // ptrs[i] holds a root pointer to the segment tree after the ith update
Node *newKid(Node *curr) { Node *newKid(Node *curr) {
Node *newNode = new Node(); Node *newNode = new Node();
*newNode = *curr; *newNode = *curr;
@ -28,8 +27,9 @@ private:
} }
void lazy(int i, int j, Node *curr) { void lazy(int i, int j, Node *curr) {
if (!curr->prop) if (!curr->prop) {
return; return;
}
curr->val += (j - i + 1) * curr->prop; curr->val += (j - i + 1) * curr->prop;
if (i != j) { if (i != j) {
curr->left = newKid(curr->left); curr->left = newKid(curr->left);
@ -41,11 +41,11 @@ private:
curr->prop = 0; curr->prop = 0;
} }
void construct(int i, int j, vector<int> &vec, Node *&curr) { void construct(int i, int j, std::vector<int> &vec, Node *&curr) {
curr = new Node(); curr = new Node();
if (i == j) if (i == j) {
curr->val = vec[i]; curr->val = vec[i];
else { } else {
int mid = i + (j - i) / 2; int mid = i + (j - i) / 2;
construct(i, mid, vec, curr->left); construct(i, mid, vec, curr->left);
construct(mid + 1, j, vec, curr->right); construct(mid + 1, j, vec, curr->right);
@ -62,8 +62,9 @@ private:
lazy(i, j, newNode); lazy(i, j, newNode);
return newNode; return newNode;
} }
if (i > r || j < l) if (i > r || j < l) {
return curr; return curr;
}
Node *newNode = new Node(); Node *newNode = new Node();
int mid = i + (j - i) / 2; int mid = i + (j - i) / 2;
newNode->left = update(i, mid, l, r, value, curr->left); newNode->left = update(i, mid, l, r, value, curr->left);
@ -73,76 +74,68 @@ private:
return newNode; return newNode;
} }
long long query(int i, int j, int l, int r, Node *curr) { int64_t query(int i, int j, int l, int r, Node *curr) {
lazy(i, j, curr); lazy(i, j, curr);
if (j < l || r < i) if (j < l || r < i) {
return 0; return 0;
if (i >= l && j <= r) }
if (i >= l && j <= r) {
return curr->val; return curr->val;
}
int mid = i + (j - i) / 2; int mid = i + (j - i) / 2;
return query(i, mid, l, r, curr->left) + query(mid + 1, j, l, r, curr->right); return query(i, mid, l, r, curr->left) + query(mid + 1, j, l, r, curr->right);
} }
void clear(Node *&curr, int version) { void clear(Node *&curr, int version) {
if (!curr || curr->version != version) if (!curr || curr->version != version) {
return; return;
}
clear(curr->left, version); clear(curr->left, version);
clear(curr->right, version); clear(curr->right, version);
delete curr; delete curr;
} }
bool isValidRange(int l, int r) { public:
return l <= r && l >= 0 && l < n && r >= 0 && r < n; perSegTree() {
n = 0;
} }
public: void construct(std::vector<int> &vec) // the segment tree will be built from the values in "vec", "vec" is 0 indexed
void construct(vector<int> &vec) // the segment tree will be built from the values in "vec", "vec" is 0 indexed
{ {
if (vec.empty()) if (vec.empty()) {
return; return;
}
n = vec.size(); n = vec.size();
Node *root; Node *root = nullptr;
construct(0, n - 1, vec, root); construct(0, n - 1, vec, root);
ptrs.push_back(root); ptrs.push_back(root);
} }
void update(int l, int r, int value) // all elements from index "l" to index "r" would by updated by "value", "l" and "r" are 0 indexed void update(int l, int r,
int value) // all elements from index "l" to index "r" would by updated by "value", "l" and "r" are 0 indexed
{ {
try { ptrs.push_back(update(0, n - 1, l, r, value,
if (!ptrs.size()) // if function "construct" is not called yet ptrs[ptrs.size() - 1])); // saving the root pointer to the new segment tree
throw "Original segment tree does'nt exist";
if (!isValidRange(l, r)) // checking if the range is valid
throw "Invalid range";
ptrs.push_back(update(0, n - 1, l, r, value,ptrs[ptrs.size() - 1])); // saving the root pointer to the new segment tree
}
catch (const char *error) {
cout << error << '\n';
}
} }
long long query(int l, int r, int version) // querying the range from "l" to "r" in a segment tree after "version" updates, "l" and "r" are 0 indexed int64_t query(int l, int r,
int version) // querying the range from "l" to "r" in a segment tree after "version" updates, "l" and "r" are 0 indexed
{ {
try {
if (!isValidRange(l, r)) // checking if the range is valid
throw "Invalid range";
if (!(version >= 0 && version < ptrs.size())) // checking if "version" is not a valid version of any segment tree after updates so far
throw "Invalid version";
return query(0, n - 1, l, r, ptrs[version]); return query(0, n - 1, l, r, ptrs[version]);
} }
catch (const char *error) {
cout << error << '\n';
return 0;
}
}
void clear() { void clear() {
for (int i = ptrs.size() - 1; i >= 0; --i) for (int i = (int) ptrs.size() - 1; i >= 0; --i) {
clear(ptrs[i],i); // every segment tree clears its nodes (nodes that were created when this segment tree was created) clear(ptrs[i],
while (!ptrs.empty()) i); // every segment tree clears its nodes (nodes that were created when this segment tree was created)
}
while (!ptrs.empty()) {
ptrs.pop_back(); ptrs.pop_back();
} }
}
int 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 int
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(); return ptrs.size();
} }
@ -150,37 +143,40 @@ public:
int main() { int main() {
vector<int> arr = {-5, 2, 3, 11, -2, 7, 0, 1}; std::vector<int> arr = {-5, 2, 3, 11, -2, 7, 0, 1};
perSegTree tree; perSegTree tree;
cout << "Elements before any updates are {"; std::cout << "Elements before any updates are {";
for (int i = 0; i < arr.size(); ++i) { for (int i = 0; i < arr.size(); ++i) {
cout << arr[i]; std::cout << arr[i];
if (i != arr.size() - 1) if (i != arr.size() - 1) {
cout << ","; std::cout << ",";
} }
cout << "}\n"; }
std::cout << "}\n";
tree.construct(arr); // constructing the original segment tree (version = 0) tree.construct(arr); // constructing the original segment tree (version = 0)
cout << "Querying range sum on version 0 from index 2 to 4 = 3+11-2 = " << tree.query(2, 4, 0) << '\n'; std::cout << "Querying range sum on version 0 from index 2 to 4 = 3+11-2 = " << tree.query(2, 4, 0) << '\n';
cout << "Subtract 7 from all elements from index 1 to index 5 inclusive\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 tree.update(1, 5, -7); // subtracting 7 from index 1 to index 5
cout << "Elements of the segment tree whose version = 1 (after 1 update) are {"; std::cout << "Elements of the segment tree whose version = 1 (after 1 update) are {";
for (int i = 0; i < arr.size(); ++i) { for (int i = 0; i < arr.size(); ++i) {
cout << tree.query(i, i, 1); std::cout << tree.query(i, i, 1);
if (i != arr.size() - 1) if (i != arr.size() - 1) {
cout << ","; std::cout << ",";
} }
cout << "}\n"; }
cout << "Add 10 to all elements from index 0 to index 7 inclusive\n"; 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 tree.update(0, 7, 10); // adding 10 to all elements
cout << "Elements of the segment tree whose version = 2 (after 2 updates) are {"; std::cout << "Elements of the segment tree whose version = 2 (after 2 updates) are {";
for (int i = 0; i < arr.size(); ++i) { for (int i = 0; i < arr.size(); ++i) {
cout << tree.query(i, i, 2); std::cout << tree.query(i, i, 2);
if (i != arr.size() - 1) if (i != arr.size() - 1) {
cout << ","; std::cout << ",";
} }
cout << "}\n"; }
cout << "Number of segment trees (versions) now = " << tree.size() << '\n'; std::cout << "}\n";
cout << "Querying range sum on version 0 from index 3 to 5 = 11-2+7 = " << tree.query(3, 5, 0) << '\n'; std::cout << "Number of segment trees (versions) now = " << tree.size() << '\n';
cout << "Querying range sum on version 1 from index 3 to 5 = 4-9+0 = " << tree.query(3, 5, 1) << '\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';
tree.clear(); tree.clear();
} }