mirror of
https://github.com/TheAlgorithms/C-Plus-Plus.git
synced 2026-02-03 10:35:34 +08:00
0d766b0f8a
* chore: add cache and build comment to git ignore
* fix: add cmakelists to dynamic programming
* fix: add cmakelists to greedy_algorithms
* fix: add cmakelists to operations_on_datastructures
* fix: add cmakelists to range_queries
* fix: add `dynamic_programmin`, `greedy_algorithms`, `range_queries` and `operations_on_datastructures` subdirectories to cmakelists.txt
* fix: init of transform_reduce in dynamic_programming
* fix: add an include for functional in catalan_numbers
* chore: bump CXX standard to 20
* revert: bump CXX standard to 20
* chore: bump c++ version to 17 and add justification
Arm supports c++ 17
Esp32 supports c++ 23
decision was made to be 17 because it seemed to offer the best combatability
* fix: compilation error in catalan numbers
* fix: add <set> header to longest increasing subsequence nlogn
* fix: add cmath & algorithm header to mo.cpp
* fix: remove register key word from fast integer
* fix: replace using namespace std with std::cin and std::cout
* docs: typo in c++17
* fix: memory leak in bellman_ford
* fix: typo in bellman_ford
* fix: typo in word_break
* fix: dynamic array in coin_change
* fix dynamic array in egg_dropping puzzle
* chore: remove unnecessary comment
* fix: add vla to be an error
* chore: add extra warnings
* fix: use add_compile options instead of set()
* fix: compile options are not strings
* fix: vla in floyd_warshall
* fix: vla in egg_dropping_puzzel
* fix: vla in coin_change
* fix: vla in edit_distance
* fix: vla in floyd_warshall
* feat: remove kadane and replace it with kadane2
* fix: vla in longest_common_subsequence
* fix: int overflow in floyd_warshall
* fix: vla in lisnlogn
* fix: use const vector& instead of array
* fix: use dynamic array instead of vla in knapsack
* fix: use of and in msvc is unsupported by default adding permissive flag fixes it
* test: make executables the tests themselves
* Revert "test: make executables the tests themselves"
This reverts commit 7a16c31c4e.
* fix: make dist constant in print
* fix: namespace issue in unbounded_0_1
* fix: include cstdint to fix compilation
83 lines
2.4 KiB
C++
83 lines
2.4 KiB
C++
/**
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* @file
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* @brief Provides utilities to compute Catalan numbers using dynamic
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programming.
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* A Catalan numbers satisfy these recurrence relations:
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* C(0) = C(1) = 1; C(n) = sum(C(i).C(n-i-1)), for i = 0 to n-1
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* Read more about Catalan numbers here:
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https://en.wikipedia.org/wiki/Catalan_number
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https://oeis.org/A000108/
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*/
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#include <cassert> /// for assert
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#include <cstdint> /// for std::uint64_t
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#include <cstdlib> /// for std::size_t
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#include <functional> /// for std::plus & std::multiplies
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#include <numeric> /// for std::transform_reduce
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#include <vector> /// for std::vector
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/**
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* @brief computes and caches Catalan numbers
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*/
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class catalan_numbers {
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using value_type = std::uint64_t;
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std::vector<value_type> known{1, 1};
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value_type compute_next() {
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return std::transform_reduce(known.begin(), known.end(), known.rbegin(),
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static_cast<value_type>(0), std::plus<>(),
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std::multiplies<>());
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}
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void add() { known.push_back(this->compute_next()); }
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public:
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/**
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* @brief computes the n-th Catalan number and updates the cache.
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* @return the n-th Catalan number
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*/
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value_type get(std::size_t n) {
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while (known.size() <= n) {
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this->add();
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}
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return known[n];
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}
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};
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void test_catalan_numbers_up_to_20() {
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// data verified with https://oeis.org/A000108/
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catalan_numbers cn;
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assert(cn.get(0) == 1ULL);
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assert(cn.get(1) == 1ULL);
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assert(cn.get(2) == 2ULL);
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assert(cn.get(3) == 5ULL);
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assert(cn.get(4) == 14ULL);
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assert(cn.get(5) == 42ULL);
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assert(cn.get(6) == 132ULL);
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assert(cn.get(7) == 429ULL);
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assert(cn.get(8) == 1430ULL);
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assert(cn.get(9) == 4862ULL);
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assert(cn.get(10) == 16796ULL);
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assert(cn.get(11) == 58786ULL);
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assert(cn.get(12) == 208012ULL);
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assert(cn.get(13) == 742900ULL);
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assert(cn.get(14) == 2674440ULL);
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assert(cn.get(15) == 9694845ULL);
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assert(cn.get(16) == 35357670ULL);
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assert(cn.get(17) == 129644790ULL);
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assert(cn.get(18) == 477638700ULL);
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assert(cn.get(19) == 1767263190ULL);
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assert(cn.get(20) == 6564120420ULL);
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}
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void test_catalan_numbers_25() {
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// data verified with https://oeis.org/A000108/
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catalan_numbers cn;
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assert(cn.get(25) == 4861946401452ULL);
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}
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int main() {
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test_catalan_numbers_up_to_20();
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test_catalan_numbers_25();
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}
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