|
|
|
|
@ -14,6 +14,9 @@ export const metadata = {
|
|
|
|
|
new Problem("HR", "Bubble Sort", "https://www.hackerrank.com/challenges/ctci-bubble-sort/problem", "Easy", false, [], "O(N^2)"),
|
|
|
|
|
new Problem("Silver", "Out of Sorts", "834", "Very Hard", false, []),
|
|
|
|
|
],
|
|
|
|
|
count: [
|
|
|
|
|
new Problem("Silver", "Counting Haybales", "666", "Normal", false, []),
|
|
|
|
|
],
|
|
|
|
|
cses: [
|
|
|
|
|
new Problem("CSES", "Apartments", "1084", "Normal", false, [], "Sort applicants and apartments, then greedily assign applicants"),
|
|
|
|
|
new Problem("CSES", "Ferris Wheel", "1090", "Normal", false, [], "Sort children, keep a left pointer and a right pointer. Each gondola either is one child from the right pointer or two children, one left and one right."),
|
|
|
|
|
@ -50,17 +53,18 @@ There are many sorting algorithms, here are some sources to learn about the popu
|
|
|
|
|
- [HackerEarth Mergesort](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/tutorial/)
|
|
|
|
|
- $O(N\log N)$
|
|
|
|
|
|
|
|
|
|
## Library Sorting
|
|
|
|
|
## Library Functions - Sorting
|
|
|
|
|
|
|
|
|
|
- C++
|
|
|
|
|
- [std::sort Documentation](https://en.cppreference.com/w/cpp/algorithm/sort)
|
|
|
|
|
- [std::stable\_sort documentation](http://www.cplusplus.com/reference/algorithm/stable_sort/)
|
|
|
|
|
- [std::sort](https://en.cppreference.com/w/cpp/algorithm/sort)
|
|
|
|
|
- [std::stable\_sort](http://www.cplusplus.com/reference/algorithm/stable_sort/)
|
|
|
|
|
- [Golovanov399 - C++ Tricks](https://codeforces.com/blog/entry/74684)
|
|
|
|
|
- first two related to sorting
|
|
|
|
|
- Java
|
|
|
|
|
- [Arrays.sort Documentation](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#sort(java.lang.Object[]))
|
|
|
|
|
- [Arrays.sort](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#sort(java.lang.Object[]))
|
|
|
|
|
- [Collections.sort](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html#sort(java.util.List))
|
|
|
|
|
- Python
|
|
|
|
|
- [Sorted Documentation](https://docs.python.org/3/howto/sorting.html)
|
|
|
|
|
- [Sorting Basics](https://docs.python.org/3/howto/sorting.html)
|
|
|
|
|
|
|
|
|
|
<info-block title="For Users of Java">
|
|
|
|
|
|
|
|
|
|
@ -74,7 +78,6 @@ Two ways to avoid this:
|
|
|
|
|
</info-block>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
## Binary Search
|
|
|
|
|
|
|
|
|
|
[Binary search](https://en.wikipedia.org/wiki/Binary_search_algorithm) can be used on monotonic (what's that?) functions for a logarithmic runtime.
|
|
|
|
|
@ -97,27 +100,33 @@ Other variations are similar, such as the following:
|
|
|
|
|
<resource source="GFG" title="Binary Search" url="binary-search"></resource>
|
|
|
|
|
</resources>
|
|
|
|
|
|
|
|
|
|
### Library Functions to do Binary Search
|
|
|
|
|
|
|
|
|
|
#### Java
|
|
|
|
|
|
|
|
|
|
- [Arrays.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html)
|
|
|
|
|
- [Collections.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html)
|
|
|
|
|
### Library Functions - Binary Search
|
|
|
|
|
|
|
|
|
|
#### C++
|
|
|
|
|
|
|
|
|
|
- [lower_bound](http://www.cplusplus.com/reference/algorithm/lower_bound/)
|
|
|
|
|
- [upper_bound](http://www.cplusplus.com/reference/algorithm/upper_bound/)
|
|
|
|
|
|
|
|
|
|
## Example (Coordinate Compression)
|
|
|
|
|
#### Java
|
|
|
|
|
|
|
|
|
|
Another useful application of sorting is coordinate compression, which takes some points and reassigns them to remove wasted space. Let's consider the USACO Silver problem [Counting Haybales](http://www.usaco.org/index.php?page=viewproblem2&cpid=666):
|
|
|
|
|
- [Arrays.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html)
|
|
|
|
|
- [Collections.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html)
|
|
|
|
|
|
|
|
|
|
## Coordinate Compression
|
|
|
|
|
|
|
|
|
|
Another useful application of sorting is **coordinate compression**, which takes some points and reassigns them to remove wasted space.
|
|
|
|
|
|
|
|
|
|
<problems-list problems={metadata.problems.count} />
|
|
|
|
|
|
|
|
|
|
> Farmer John has just arranged his $N$ haybales $(1\le N \le 100,000)$ at various points along the one-dimensional road running across his farm. To make sure they are spaced out appropriately, please help him answer $Q$ queries ($1 \le Q \le 100,000$), each asking for the number of haybales within a specific interval along the road.
|
|
|
|
|
|
|
|
|
|
However, each of the points are in the range $0 \ldots 1,000,000,000$, meaning you can't store locations of haybales in, for instance, a boolean array. However, let's place all of the locations of the haybales into a list and sort it.
|
|
|
|
|
However, each of the points are in the range $0 \ldots 1,000,000,000$, meaning you can't store locations of haybales in, for instance, a boolean array.
|
|
|
|
|
|
|
|
|
|
(fix this part)
|
|
|
|
|
### Solution
|
|
|
|
|
|
|
|
|
|
Let's place all of the locations of the haybales into a list and sort it.
|
|
|
|
|
|
|
|
|
|
(fix part below so transform to range $1\ldots N$)
|
|
|
|
|
|
|
|
|
|
Now, we can map distinct points to smaller integers without gaps. For example, if the haybales existed at positions $[1, 4, 5, 9]$ and queries were $(1, 2)$ and $(4, 6)$, we can place the integers together and map them from $[1, 2, 4, 5, 6, 9] \rightarrow [1, 2, 3, 4, 5, 6]$. This effectively transforms the haybale positions into $[1, 3, 4, 6]$ and the queries into $1, 2$ and $3, 5$.
|
|
|
|
|
|
|
|
|
|
|
Nathan Wang