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Benjamin Qi 2020-06-02 23:56:59 -04:00
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13
Gold_1DRQ.md
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@ -33,7 +33,8 @@ My implementation can be found [here](https://github.com/bqi343/USACO/blob/maste
### Indexed Set
In the special case where all elements of the array are either zero or one (which is the case for several gold problems), users of C++ will find [indexed set](https://github.com/bqi343/USACO/blob/master/Implementations/content/data-structures/STL%20(5)/IndexedSet.h) useful. Using this, we can solve "Inversion Counting" in just a few lines (with template).
In the special case where all elements of the array are either zero or one (which is the case for several gold problems), users of C++ will find [indexed set](https://github.com/bqi343/USACO/blob/master/Implementations/content/data-structures/STL%20(5)/IndexedSet.h) useful. Using this, we can solve "Inversion Counting" in just a few lines (with template). `Tree<int>` behaves mostly the same way as `set<int>` with the additional function `order_of_key(x)`, which
counts the number of elements in the indexed set that are strictly less than `x`. See the link for more examples of usage.
```cpp
#include <ext/pb_ds/tree_policy.hpp>
@ -51,8 +52,8 @@ int main() {
int n; re(n);
Tree<int> T; ll numInv = 0;
F0R(j,n) {
int x; re(x); // T.ook(x+1) gives number of previous elements < (x+1)
numInv += j-T.ook(x+1); // so this gives # previous elements > x
int x; re(x);
numInv += j-T.ook(x); // gives # elements before it > x
T.insert(x);
}
ps(numInv);
@ -60,6 +61,8 @@ int main() {
}
```
Note that if it were not the case that all elements of the input array were distinct, then this code would be incorrect since `Tree<int>` would remove duplicates. Instead, we would use an indexed set of pairs (`Tree<pair<int,int>>`), where the first element of each pair would denote the value while the second would denote the array position.
### Practice Problems
* USACO Gold
@ -83,7 +86,7 @@ The following topics have not been required for gold (so far).
### Static Range Queries
* Range Minimum Query
* Range Minimum Query??
* Tutorial
* [Wikipedia](https://en.wikipedia.org/wiki/Range_minimum_query)
* (add)
@ -105,4 +108,4 @@ This data structure allows you to do point update and range query in $O(\log N)$
* can use segment tree with min query in place of the map mentioned in analysis
* [POI Cards](https://szkopul.edu.pl/problemset/problem/qpsk3ygf8MU7D_1Es0oc_xd8/site/?key=statement) [](81)
* [Counting Haybales (USACO Plat)](http://www.usaco.org/index.php?page=viewproblem2&cpid=578)
* lazy updates
* Lazy Updates