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@ -14,6 +14,9 @@ export const metadata = {
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new Problem("HR", "Bubble Sort", "https://www.hackerrank.com/challenges/ctci-bubble-sort/problem", "Easy", false, [], "O(N^2)"),
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new Problem("HR", "Bubble Sort", "https://www.hackerrank.com/challenges/ctci-bubble-sort/problem", "Easy", false, [], "O(N^2)"),
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new Problem("Silver", "Out of Sorts", "834", "Very Hard", false, []),
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new Problem("Silver", "Out of Sorts", "834", "Very Hard", false, []),
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],
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],
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count: [
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new Problem("Silver", "Counting Haybales", "666", "Normal", false, []),
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],
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cses: [
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cses: [
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new Problem("CSES", "Apartments", "1084", "Normal", false, [], "Sort applicants and apartments, then greedily assign applicants"),
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new Problem("CSES", "Apartments", "1084", "Normal", false, [], "Sort applicants and apartments, then greedily assign applicants"),
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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."),
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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."),
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@ -50,17 +53,18 @@ There are many sorting algorithms, here are some sources to learn about the popu
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- [HackerEarth Mergesort](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/tutorial/)
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- [HackerEarth Mergesort](https://www.hackerearth.com/practice/algorithms/sorting/merge-sort/tutorial/)
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- $O(N\log N)$
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- $O(N\log N)$
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## Library Sorting
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## Library Functions - Sorting
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- C++
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- C++
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- [std::sort Documentation](https://en.cppreference.com/w/cpp/algorithm/sort)
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- [std::sort](https://en.cppreference.com/w/cpp/algorithm/sort)
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- [std::stable\_sort documentation](http://www.cplusplus.com/reference/algorithm/stable_sort/)
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- [std::stable\_sort](http://www.cplusplus.com/reference/algorithm/stable_sort/)
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- [Golovanov399 - C++ Tricks](https://codeforces.com/blog/entry/74684)
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- [Golovanov399 - C++ Tricks](https://codeforces.com/blog/entry/74684)
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- first two related to sorting
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- first two related to sorting
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- Java
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- Java
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- [Arrays.sort Documentation](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#sort(java.lang.Object[]))
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- [Arrays.sort](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#sort(java.lang.Object[]))
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- [Collections.sort](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html#sort(java.util.List))
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- Python
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- Python
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- [Sorted Documentation](https://docs.python.org/3/howto/sorting.html)
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- [Sorting Basics](https://docs.python.org/3/howto/sorting.html)
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<info-block title="For Users of Java">
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<info-block title="For Users of Java">
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@ -74,7 +78,6 @@ Two ways to avoid this:
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</info-block>
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</info-block>
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## Binary Search
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## Binary Search
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[Binary search](https://en.wikipedia.org/wiki/Binary_search_algorithm) can be used on monotonic (what's that?) functions for a logarithmic runtime.
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[Binary search](https://en.wikipedia.org/wiki/Binary_search_algorithm) can be used on monotonic (what's that?) functions for a logarithmic runtime.
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@ -97,27 +100,33 @@ Other variations are similar, such as the following:
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<resource source="GFG" title="Binary Search" url="binary-search"></resource>
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<resource source="GFG" title="Binary Search" url="binary-search"></resource>
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</resources>
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</resources>
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### Library Functions to do Binary Search
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### Library Functions - Binary Search
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#### Java
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- [Arrays.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html)
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- [Collections.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html)
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#### C++
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#### C++
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- [lower_bound](http://www.cplusplus.com/reference/algorithm/lower_bound/)
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- [lower_bound](http://www.cplusplus.com/reference/algorithm/lower_bound/)
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- [upper_bound](http://www.cplusplus.com/reference/algorithm/upper_bound/)
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- [upper_bound](http://www.cplusplus.com/reference/algorithm/upper_bound/)
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## Example (Coordinate Compression)
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#### Java
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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):
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- [Arrays.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html)
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- [Collections.binarySearch](https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html)
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## Coordinate Compression
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Another useful application of sorting is **coordinate compression**, which takes some points and reassigns them to remove wasted space.
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<problems-list problems={metadata.problems.count} />
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> 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.
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> 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.
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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.
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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.
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(fix this part)
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### Solution
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Let's place all of the locations of the haybales into a list and sort it.
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(fix part below so transform to range $1\ldots N$)
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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 $3, 5$.
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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 $3, 5$.
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