OpenSoure_Repos/TheAlgorithms-C-Plus-Plus
1
0
Fork 0
mirror of https://hub.njuu.cf/TheAlgorithms/C-Plus-Plus.git synced 2023-10-11 13:05:55 +08:00
Code Issues Packages Projects Releases Wiki Activity

clang-format and clang-tidy fixes for a01765a6

Browse Source
This commit is contained in:
github-actions 2021-10-07 04:02:11 +00:00
parent a01765a6bb
commit 0f2606ffdb
1 changed files with 50 additions and 40 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

86
probability/windowed_median.cpp
View File

@ -4,8 +4,8 @@
* data stream
*
* @details
* Given a stream of integers, the algorithm calculates the median of a fixed size
* window at the back of the stream. The leading time complexity of this
* Given a stream of integers, the algorithm calculates the median of a fixed
* size window at the back of the stream. The leading time complexity of this
* algorithm is O(log(N), and it is inspired by the known algorithm to [find
* median from (infinite) data
* stream](https://www.tutorialcup.com/interview/algorithm/find-median-from-data-stream.htm),
@ -17,13 +17,13 @@
* pushing and popping. Each new value is pushed to the window back, while a
* value from the front of the window is popped. In addition, the algorithm
* manages a multi-value binary search tree (BST), implemented by std::multiset.
* For each new value that is inserted into the window, it is also inserted to the
* BST. When a value is popped from the window, it is also erased from the BST.
* Both insertion and erasion to/from the BST are O(logN) in time, with N the
* size of the window. Finally, the algorithm keeps a pointer to the root of the
* BST, and updates its position whenever values are inserted or erased to/from
* BST. The root of the tree is the median! Hence, median retrieval is always
* O(1)
* For each new value that is inserted into the window, it is also inserted to
* the BST. When a value is popped from the window, it is also erased from the
* BST. Both insertion and erasion to/from the BST are O(logN) in time, with N
* the size of the window. Finally, the algorithm keeps a pointer to the root of
* the BST, and updates its position whenever values are inserted or erased
* to/from BST. The root of the tree is the median! Hence, median retrieval is
* always O(1)
*
* Time complexity: O(logN). Space complexity: O(N). N - size of window
* @author [Yaniv Hollander](https://github.com/YanivHollander)
@ -32,8 +32,8 @@
#include <cstdlib> /// for std::rand - needed in testing
#include <ctime> /// for std::time - needed in testing
#include <list> /// for std::list - used to manage sliding window
#include <set> /// for std::multiset - used to manage multi-value sorted sliding window values
#include <vector> /// for std::vector - needed in testing
#include <set> /// for std::multiset - used to manage multi-value sorted sliding window values
#include <vector> /// for std::vector - needed in testing
/**
* @namespace probability
@ -55,7 +55,7 @@ using size_type = Window::size_type;
*/
class WindowedMedian {
const size_type _windowSize; ///< sliding window size
Window _window; ///< a sliding window of values along the stream
Window _window; ///< a sliding window of values along the stream
std::multiset<int> _sortedValues; ///< a DS to represent a balanced
/// multi-value binary search tree (BST)
std::multiset<int>::const_iterator
@ -103,13 +103,14 @@ class WindowedMedian {
}
/// However, if the erased value is on the right branch or the median
/// itself, and the number of elements is odd, the new median will be the
/// left child of the current one
/// itself, and the number of elements is odd, the new median will be
/// the left child of the current one
else if (value >= *_itMedian && sz % 2 != 0) {
--_itMedian; // O(1) - traversing one step to the left child
}
/// Find the (first) position of the value we want to erase, and erase it
/// Find the (first) position of the value we want to erase, and erase
/// it
const auto it = _sortedValues.find(value); // O(logN)
_sortedValues.erase(it); // O(logN)
}
@ -126,16 +127,16 @@ class WindowedMedian {
* @param value New value to insert
*/
void insert(int value) {
/// Push new value to the back of the sliding window - O(1)
_window.push_back(value);
insertToSorted(value); // Insert value to the multi-value BST - O(logN)
if (_window.size() > _windowSize) { /// If exceeding size of window, pop
/// from its left side
eraseFromSorted(_window.front()); /// Erase from the multi-value BST
/// the window left side value
_window
.pop_front(); /// Pop the left side value from the window - O(1)
if (_window.size() > _windowSize) { /// If exceeding size of window,
/// pop from its left side
eraseFromSorted(
_window.front()); /// Erase from the multi-value BST
/// the window left side value
_window.pop_front(); /// Pop the left side value from the window -
/// O(1)
}
}
@ -170,8 +171,8 @@ class WindowedMedian {
0.5f * *next(window.begin(), window.size() / 2 - 1); /// O(N)
}
};
} /// namespace windowed_median
} /// namespace probability
} // namespace windowed_median
} // namespace probability
/**
* @brief Self-test implementations
@ -195,32 +196,41 @@ static void test(const std::vector<int> &vals, int windowSize) {
* @returns 0 on exit
*/
int main(int argc, const char *argv[]) {
/// A few fixed test cases
test({1, 2, 3, 4, 5, 6, 7, 8, 9}, 3); /// Array of sorted values; odd window size
test({9, 8, 7, 6, 5, 4, 3, 2, 1}, 3); /// Array of sorted values - decreasing; odd window size
test({9, 8, 7, 6, 5, 4, 5, 6}, 4); /// Even window size
test({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3); /// Array with repeating values
test({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3); /// Array with same values except one
test({4, 3, 3, -5, -5, 1, 3, 4, 5}, 5); /// Array that includes repeating values including negatives
test({1, 2, 3, 4, 5, 6, 7, 8, 9},
3); /// Array of sorted values; odd window size
test({9, 8, 7, 6, 5, 4, 3, 2, 1},
3); /// Array of sorted values - decreasing; odd window size
test({9, 8, 7, 6, 5, 4, 5, 6}, 4); /// Even window size
test({3, 3, 3, 3, 3, 3, 3, 3, 3}, 3); /// Array with repeating values
test({3, 3, 3, 3, 7, 3, 3, 3, 3}, 3); /// Array with same values except one
test({4, 3, 3, -5, -5, 1, 3, 4, 5},
5); /// Array that includes repeating values including negatives
/// Array with large values - sum of few pairs exceeds MAX_INT. Window size is even - testing calculation of
/// average median between two middle values
/// Array with large values - sum of few pairs exceeds MAX_INT. Window size
/// is even - testing calculation of average median between two middle
/// values
test({470211272, 101027544, 1457850878, 1458777923, 2007237709, 823564440,
1115438165, 1784484492, 74243042, 114807987}, 6);
1115438165, 1784484492, 74243042, 114807987},
6);
/// Random test cases
std::srand(static_cast<unsigned int>(std::time(nullptr)));
std::vector<int> vals;
for (int i = 8; i < 100; i++) {
const auto n = 1 + std::rand() / ((RAND_MAX + 5u) / 20); /// Array size in the range [5, 20]
auto windowSize = 1 + std::rand() / ((RAND_MAX + 3u) / 10); /// Window size in the range [3, 10]
const auto n =
1 + std::rand() /
((RAND_MAX + 5u) / 20); /// Array size in the range [5, 20]
auto windowSize =
1 + std::rand() / ((RAND_MAX + 3u) /
10); /// Window size in the range [3, 10]
vals.clear();
vals.reserve(n);
for (int i = 0; i < n; i++) {
vals.push_back(rand() - RAND_MAX); /// Random array values (positive/negative)
vals.push_back(
rand() - RAND_MAX); /// Random array values (positive/negative)
}
test(vals, windowSize); /// Testing randomized test
test(vals, windowSize); /// Testing randomized test
}
return 0;
}