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+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
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+persistent_seg_tree_lazy_prop.cpp File Reference
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+
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+
+
+
+
+
+
+Persistent segment tree with range updates (lazy propagation) +More...
+#include <iostream>+
#include <memory>+
#include <vector>+
+Include dependency graph for persistent_seg_tree_lazy_prop.cpp:
+
+
+
+
++Classes | |
| class | range_queries::perSegTree |
| Range query here is range sum, but the code can be modified to make different queries like range max or min. More... | |
| class | range_queries::perSegTree::Node |
+Namespaces | |
| range_queries | |
| Algorithms and Data Structures that support range queries and updates. | |
+Functions | |
| static void | test () |
| Test implementations. More... | |
| int | main () |
| Main function. More... | |
Detailed Description
+Persistent segment tree with range updates (lazy propagation)
+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.
+ +Function Documentation
+ +◆ main()
+ +
+
+
+
+
+
+
+| int main | +( | +void | +) | ++ |
◆ test()
+ +
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+ +static | +
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+Test implementations.
+- Returns
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Range query here is range sum, but the code can be modified to make different queries like range max ...
Definition: persistent_seg_tree_lazy_prop.cpp:39
uint32_t size()
Getting the number of versions after updates so far which is equal to the size of the pointers vector...
Definition: persistent_seg_tree_lazy_prop.cpp:255
std::shared_ptr< Node > construct(const uint32_t &i, const uint32_t &j)
Constructing the segment tree with the early passed vector. Every call creates a node to hold the sum...
Definition: persistent_seg_tree_lazy_prop.cpp:106
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)
Querying the range from index l to index r, checking at every node if it has some value to be propaga...
Definition: persistent_seg_tree_lazy_prop.cpp:171
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)
Doing range update, checking at every node if it has some value to be propagated. All nodes affected ...
Definition: persistent_seg_tree_lazy_prop.cpp:135
T size(T... args)
+Here is the call graph for this function:
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diff --git a/d5/d58/persistent__seg__tree__lazy__prop_8cpp.js b/d5/d58/persistent__seg__tree__lazy__prop_8cpp.js
new file mode 100644
index 000000000..e09619b80
--- /dev/null
+++ b/d5/d58/persistent__seg__tree__lazy__prop_8cpp.js
@@ -0,0 +1,7 @@
+var persistent__seg__tree__lazy__prop_8cpp =
+[
+ [ "perSegTree", "d8/d28/classrange__queries_1_1per_seg_tree.html", "d8/d28/classrange__queries_1_1per_seg_tree" ],
+ [ "Node", "d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html", "d5/d66/classrange__queries_1_1per_seg_tree_1_1_node" ],
+ [ "main", "d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "test", "d5/d58/persistent__seg__tree__lazy__prop_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
\ No newline at end of file
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diff --git a/d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html b/d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html
new file mode 100644
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@@ -0,0 +1,137 @@
+
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- Generated by
1.9.1
+
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+|
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+range_queries::perSegTree::Node Class Reference
+
+
+
The documentation for this class was generated from the following file:
+
+Collaboration diagram for range_queries::perSegTree::Node:
+
+[legend]
+
+
++Public Attributes | |
| +std::shared_ptr< Node > | left = nullptr |
| +std::shared_ptr< Node > | right = nullptr |
| pointer to the left node | |
| +int64_t | val = 0 |
| pointer to the right node | |
| +int64_t | prop = 0 |
The documentation for this class was generated from the following file:
-
+
- range_queries/persistent_seg_tree_lazy_prop.cpp +
+
+
+
diff --git a/d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.js b/d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.js
new file mode 100644
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--- /dev/null
+++ b/d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.js
@@ -0,0 +1,7 @@
+var classrange__queries_1_1per_seg_tree_1_1_node =
+[
+ [ "left", "d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html#ab3e7bf5a91911c17907b30b250108013", null ],
+ [ "prop", "d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html#adeb7de2a7341362c3c6edf4d48476656", null ],
+ [ "right", "d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html#a9adb4639a0797e94a3e556b6b902c088", null ],
+ [ "val", "d5/d66/classrange__queries_1_1per_seg_tree_1_1_node.html#acc044f787c90b815773726d7fdfdaccf", null ]
+];
\ No newline at end of file
diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
index 81f9e90a8..862c9d227 100644
--- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html
+++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
@@ -365,6 +365,7 @@ Range Queries
-
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- Generated by 1.9.1
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+
+
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+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+range_queries::perSegTree::Node Member List
+
+
+
+This is the complete list of members for range_queries::perSegTree::Node, including all inherited members.
+| left (defined in range_queries::perSegTree::Node) | range_queries::perSegTree::Node | |
| prop (defined in range_queries::perSegTree::Node) | range_queries::perSegTree::Node | |
| right | range_queries::perSegTree::Node | |
| val | range_queries::perSegTree::Node |
+
+
+
diff --git a/d6/d47/classrange__queries_1_1per_seg_tree__coll__graph.map b/d6/d47/classrange__queries_1_1per_seg_tree__coll__graph.map
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diff --git a/d6/d47/classrange__queries_1_1per_seg_tree__coll__graph.md5 b/d6/d47/classrange__queries_1_1per_seg_tree__coll__graph.md5
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--- /dev/null
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+795dd1dc2068bb7278c65eea4a5d5a52
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diff --git a/d8/d28/classrange__queries_1_1per_seg_tree.html b/d8/d28/classrange__queries_1_1per_seg_tree.html
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+
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- Generated by 1.9.1
+
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+|
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Classes |
+Public Member Functions |
+Private Member Functions |
+Private Attributes |
+List of all members
+
+
+range_queries::perSegTree Class Reference
+
+
+
+
+
+
+
The documentation for this class was generated from the following file:
+Range query here is range sum, but the code can be modified to make different queries like range max or min. + More...
+
+Collaboration diagram for range_queries::perSegTree:
+
+[legend]
+
+
++Classes | |
| class | Node |
+Public Member Functions | |
| void | construct (const std::vector< int64_t > &vec) |
| 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. More... | |
| void | update (const uint32_t &l, const uint32_t &r, const int64_t &value) |
| Doing range update by passing the left and right indexes of the range as well as the value to be added. More... | |
| int64_t | query (const uint32_t &l, const uint32_t &r, const uint32_t &version) |
| Querying the range from index l to index r, getting the sum of the elements whose index x satisfies l<=x<=r. More... | |
| uint32_t | size () |
| Getting the number of versions after updates so far which is equal to the size of the pointers vector. More... | |
+Private Member Functions | |
| std::shared_ptr< Node > | newKid (std::shared_ptr< Node > const &curr) |
| Creating a new node with the same values of curr node. More... | |
| void | lazy (const uint32_t &i, const uint32_t &j, std::shared_ptr< Node > const &curr) |
| 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. More... | |
| std::shared_ptr< Node > | construct (const uint32_t &i, const uint32_t &j) |
| 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. More... | |
| 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) |
| 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. More... | |
| 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) |
| 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. More... | |
+Private Attributes | |
| +uint32_t | n = 0 |
| +std::vector< std::shared_ptr< Node > > | ptrs {} |
| number of elements/leaf nodes in the segment tree | |
| std::vector< int64_t > | vec {} |
Detailed Description
+Range query here is range sum, but the code can be modified to make different queries like range max or min.
+Member Function Documentation
+ +◆ construct() [1/2]
+ +
+
+
+
+
+
+
+
|
+ +inline | +
+
+
+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.
+public methods that can be used directly from outside the class. They call the private functions that do all the work
- Parameters
-
+
+
+vec vector whose values will be used to build the segment tree
+
- Returns
- void
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std::vector< std::shared_ptr< Node > > ptrs
number of elements/leaf nodes in the segment tree
Definition: persistent_seg_tree_lazy_prop.cpp:54
std::shared_ptr< Node > construct(const uint32_t &i, const uint32_t &j)
Constructing the segment tree with the early passed vector. Every call creates a node to hold the sum...
Definition: persistent_seg_tree_lazy_prop.cpp:106
std::vector< int64_t > vec
Definition: persistent_seg_tree_lazy_prop.cpp:57
T empty(T... args)
T push_back(T... args)
T size(T... args)
+Here is the call graph for this function:
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+◆ construct() [2/2]
+ +
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+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.
+- Parameters
-
+
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+i the left index of the range that the created node holds its sum j the right index of the range that the created node holds its sum
+
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- pointer to the newly created node
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+T right(T... args)
Definition: linkedlist_implentation_usingarray.cpp:14
◆ lazy()
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+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.
+- Parameters
-
+
+
+i the left index of the range that the passed node holds its sum j the right index of the range that the passed node holds its sum curr pointer to the node to be propagated
+
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- void
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std::shared_ptr< Node > newKid(std::shared_ptr< Node > const &curr)
Creating a new node with the same values of curr node.
Definition: persistent_seg_tree_lazy_prop.cpp:65
+Here is the call graph for this function:
+
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+◆ newKid()
+ +
+
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+ +inlineprivate | +
+
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+Creating a new node with the same values of curr node.
+values of the leaf nodes that the segment tree will be constructed with
- Parameters
-
+
+
+curr node that would be copied
+
- Returns
- the new node
+
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+
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+◆ query() [1/2]
+ +
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+ +inlineprivate | +
+
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+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.
+- Parameters
-
+
+
+i the left index of the range that the passed node holds its sum j the right index of the range that the passed node holds its sum l the left index of the range whose sum should be returned as a result r the right index of the range whose sum should be returned as a result 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
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void lazy(const uint32_t &i, const uint32_t &j, std::shared_ptr< Node > const &curr)
If there is some value to be propagated to the passed node, value is added to the node and the childr...
Definition: persistent_seg_tree_lazy_prop.cpp:83
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)
Querying the range from index l to index r, checking at every node if it has some value to be propaga...
Definition: persistent_seg_tree_lazy_prop.cpp:171
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+◆ query() [2/2]
+ +
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+ +inline | +
+
+
+Querying the range from index l to index r, getting the sum of the elements whose index x satisfies l<=x<=r.
+- Parameters
-
+
+
+l the left index of the range whose sum should be returned as a result r the right index of the range whose sum should be returned as a result 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
+Here is the call graph for this function:
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+
+◆ size()
+ +
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+ +inline | +
◆ update() [1/2]
+ +
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+ +inlineprivate | +
+
+
+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.
+- Parameters
-
+
+
+i the left index of the range that the passed node holds its sum j the right index of the range that the passed node holds its sum l the left index of the range to be updated r the right index of the range to be updated value the value to be added to every element whose index x satisfies l<=x<=r 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
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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)
Doing range update, checking at every node if it has some value to be propagated. All nodes affected ...
Definition: persistent_seg_tree_lazy_prop.cpp:135
+Here is the call graph for this function:
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+◆ update() [2/2]
+ +
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+
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+ +inline | +
+
+
+Doing range update by passing the left and right indexes of the range as well as the value to be added.
+- Parameters
-
+
+
+l the left index of the range to be updated r the right index of the range to be updated value the value to be added to every element whose index x satisfies l<=x<=r
+
- Returns
- void
+
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+Here is the call graph for this function:
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+Member Data Documentation
+ +◆ vec
+ +
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+
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+
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+
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+ +private | +
+
+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
+ +The documentation for this class was generated from the following file:
-
+
- range_queries/persistent_seg_tree_lazy_prop.cpp +
+
+
+
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new file mode 100644
index 000000000..2690c5d6c
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@@ -0,0 +1,16 @@
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+ [ "construct", "d8/d28/classrange__queries_1_1per_seg_tree.html#ac83bcabf5a8db8b0d8d156a4c1bcd4c3", null ],
+ [ "construct", "d8/d28/classrange__queries_1_1per_seg_tree.html#a67d8371bc998c67d53e8f64db4f52767", null ],
+ [ "lazy", "d8/d28/classrange__queries_1_1per_seg_tree.html#ace7f57935b3bb9446f11c239fd89ae79", null ],
+ [ "newKid", "d8/d28/classrange__queries_1_1per_seg_tree.html#acacb937f95a078a236a4a58f9630a045", null ],
+ [ "query", "d8/d28/classrange__queries_1_1per_seg_tree.html#ae8ae4b1835e5e8aec32f68c5059ed4d4", null ],
+ [ "query", "d8/d28/classrange__queries_1_1per_seg_tree.html#ad484002bcb701820d55f32ea5d525571", null ],
+ [ "size", "d8/d28/classrange__queries_1_1per_seg_tree.html#a0fe4e431f3e09c274ecd7d2d58dcb865", null ],
+ [ "update", "d8/d28/classrange__queries_1_1per_seg_tree.html#af16c0c87b29119f066041d6e71ab50e0", null ],
+ [ "update", "d8/d28/classrange__queries_1_1per_seg_tree.html#af87494e6cf012d28c4f5b9d1c15f9c5d", null ],
+ [ "n", "d8/d28/classrange__queries_1_1per_seg_tree.html#a6f5b36111f90807a9fdf6bbca04f535e", null ],
+ [ "ptrs", "d8/d28/classrange__queries_1_1per_seg_tree.html#a1eac9cf0613dfc8e2b0195009dd5c9d5", null ],
+ [ "vec", "d8/d28/classrange__queries_1_1per_seg_tree.html#a8ff495d2f389b4aaa54449c26c6078f3", null ]
+];
\ No newline at end of file
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@@ -294,7 +294,7 @@ Here is the call graph for this function:-
+
+
- Generated by 1.9.1
+