minor
This commit is contained in:
Benjamin Qi
parent
d41d12cbb9
commit
d3ad9e208e
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@ -13,6 +13,9 @@ export const metadata = {
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permSam: [
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new Problem("CSES", "Creating Strings I", "1622", "Intro|Easy", false, [], "all perms of string"),
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],
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ex: [
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new Problem("Bronze", "Photoshoot", "988", "Normal", false, [], ""),
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],
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perm: [
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new Problem("CSES", "Chessboard and Queens", "1624", "Normal", false, [], "Recursively backtrack. See CSES book for more details."),
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new Problem("Bronze", "Livestock Lineup", "965", "Hard", false, ["permutations"], ""), // 91.95
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@ -30,7 +33,11 @@ A **permutation** is a reordering of a list of elements. Some problems will ask
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<resource source="GFG" url="write-a-c-program-to-print-all-permutations-of-a-given-string" title="Printing all Permutations of Given String"> </resource>
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</resources>
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## What's Lexicographical Order?
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## Lexicographical Order
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This term is mentioned quite frequently:
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<problems-list problems={metadata.problems.ex} />
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Think about how are words ordered in a dictionary. (In fact, this is where the term "lexicographical" comes from.)
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@ -56,6 +63,10 @@ What's going to be in the `check` function depends on the problem, but it should
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<CPPSection>
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($O(N\cdot N!)$ code)
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<IncompleteSection />
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We can just use the `next_permutation()` function. This function takes in a range and modifies it to the next greater permutation. If there is no greater permutation, it returns false. To iterate through all permutations, place it inside a `do-while` loop. We are using a `do-while` loop here instead of a typical `while` loop because a `while` loop would modify the smallest permutation before we got a chance to process it.
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```cpp
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@ -64,7 +75,7 @@ do {
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} while(next_permutation(v.begin(), v.end()));
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```
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This makes $O(N!)$ swaps.
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This makes $O(N!)$ swaps. (why?)
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</CPPSection>
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@ -88,7 +99,6 @@ public class Test {
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used[i] = false; cur.remove(cur.size()-1);
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}
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}
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static void genPerm(int _n) {
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n = _n; used = new boolean[n];
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gen();
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@ -40,9 +40,11 @@ Both Java and C++ contain two versions of sets and maps; one in which the keys a
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## HashSets
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### C++
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<LanguageSection>
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The operations on an unordered set are `insert`, which adds an element to the set if not already present, `erase`, which deletes an element if it exists, and `count`, which returns `1` if the set contains the element and `0` if it doesn't.
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<CPPSection>
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The operations on an [`unordered_set`](http://www.cplusplus.com/reference/unordered_set/unordered_set/) are `insert`, which adds an element to the set if not already present, `erase`, which deletes an element if it exists, and `count`, which returns `1` if the set contains the element and `0` if it doesn't.
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```cpp
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unordered_set<int> s;
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@ -64,7 +66,9 @@ cout << endl;
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// You can iterate through an unordered set, but it will do so in arbitrary order
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```
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### Java
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</CPPSection>
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<JavaSection>
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The operations on an unordered set are `add`, which adds an element to the set if not already present, `remove`, which deletes an element if it exists, and `contains`, which checks whether the set contains that element.
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@ -87,13 +91,19 @@ for(int element : set){
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// You can iterate through an unordered set, but it will do so in arbitrary order
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```
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</JavaSection>
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</LanguageSection>
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## HashMaps
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<problems-list problems={metadata.problems.ex} />
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### C++
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<LanguageSection>
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In an unordered map `m`, the `m[key] = value` operator assigns a value to a key and places the key and value pair into the map. The operator `m[key]` returns the value associated with the key. If the key is not present in the map, then `m[key]` is set to 0. The `count(key)` method returns the number of times the key is in the map (which is either one or zero), and therefore checks whether a key exists in the map. Lastly, `erase(key)` and `erase(it)` removes the map entry associated with the specified key or iterator. All of these operations are $O(1)$, but again, due to the hashing, this has a high constant factor.
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<CPPSection>
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In an [`unordered_map`](http://www.cplusplus.com/reference/unordered_map/unordered_map/) `m`, the `m[key] = value` operator assigns a value to a key and places the key and value pair into the map. The operator `m[key]` returns the value associated with the key. If the key is not present in the map, then `m[key]` is set to 0. The `count(key)` method returns the number of times the key is in the map (which is either one or zero), and therefore checks whether a key exists in the map. Lastly, `erase(key)` and `erase(it)` removes the map entry associated with the specified key or iterator. All of these operations are $O(1)$, but again, due to the hashing, this has a high constant factor.
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```cpp
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unordered_map<int, int> m;
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@ -106,6 +116,11 @@ cout << m.count(7) << '\n' ; // 0
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cout << m.count(1) << '\n' ; // 1
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```
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</CPPSection>
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<JavaSection>
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### Java
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In the unordered map, the `put(key, value)` method assigns a value to a key and places the key and value pair into the map. The `get(key)` method returns the value associated with the key. The `containsKey(key)` method checks whether a key exists in the map. Lastly, `remove(key)` removes the map entry associated with the specified key. All of these operations are $O(1)$, but again, due to the hashing, this has a high constant factor.
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@ -121,13 +136,21 @@ System.out.println(map.containsKey(7)); // false
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System.out.println(map.containsKey(1)); // true
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```
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</JavaSection>
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</LanguageSection>
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## Hacking
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In USACO contests, unordered sets and maps generally fine, but the built-in hashing algorithm for C++ is vulnerable to pathological data sets causing abnormally slow runtimes. Apparently [Java](https://codeforces.com/blog/entry/62393?#comment-464875) is not vulnerable to this, however.
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<LanguageSection>
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<CPPSection>
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<resources>
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<resource source="Mark Nelson" title="Hash Functions for C++ Unordered Containers" url="https://marknelson.us/posts/2011/09/03/hash-functions-for-c-unordered-containers.html" starred>How to create user-defined hash function for `unordered_map`.</resource>
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<resource title="Blowing up Unordered Map" source="CF" url="blog/entry/62393" starred>Explanation of this problem and how to fix it.</resource>
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<resource source="Mark Nelson" title="Hash Functions for C++ Unordered Containers" url="https://marknelson.us/posts/2011/09/03/hash-functions-for-c-unordered-containers.html" starred>How to create user-defined hash function for `unordered_map`.</resource>
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<resource title="Blowing up Unordered Map" source="CF" url="blog/entry/62393" starred>Explanation of this problem and how to fix it.</resource>
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</resources>
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### Implementation
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@ -148,6 +171,17 @@ unordered_map<int,int,chash> U;
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(explain assumptions that are required for this to work)
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</CPPSection>
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<JavaSection>
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</JavaSection>
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</LanguageSection>
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## Problems
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<problems-list problems={metadata.problems.standard} />
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@ -2,7 +2,7 @@
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id: binary-search-sorted
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title: "Binary Search on a Sorted Array"
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author: Siyong Huang, Michael Cao, Nathan Chen
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description: Introduces sorting and binary searching on a sorted array.
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description: "?"
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prerequisites:
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- Bronze - Introduction to Data Structures
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frequency: 4
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@ -34,15 +34,27 @@ Suppose that we want to find an element in a sorted array of size $N$ in $O(\log
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## Library Functions
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### C++
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<LanguageSection>
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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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<CPPSection>
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### Java
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<resources>
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<resource source="CPP" url="http://www.cplusplus.com/reference/algorithm/lower_bound/" title="lower_bound"> </resource>
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<resource source="CPP" url="http://www.cplusplus.com/reference/algorithm/upper_bound/" title="upper_bound"> </resource>
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</resources>
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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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</CPPSection>
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<JavaSection>
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<resources>
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<resource source="JAVA" url="https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#binarySearch(int[],%20int)" title="Arrays.binarySearch"> </resource>
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<resource source="JAVA" url="https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html#binarySearch(java.util.List,%20T)" title="Collections.binarySearch"> </resource>
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</resources>
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</JavaSection>
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</LanguageSection>
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## Coordinate Compression
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@ -58,6 +58,8 @@ Usually, when using a greedy algorithm, there is a **heuristic** or **value func
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(what's a heuristic or value function?)
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<IncompleteSection />
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## Example: Studying Algorithms
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### Statement
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Reference in a new issue