I have a std::vector<PLY> that holds a number of structs:
struct PLY {
int x;
int y;
int greyscale;
}
Some of the PLY's could be duplicates in terms of their position x and y but not necessarily in terms of their greyscale value. What is the best way to find those (position-) duplicates and replace them with a single PLY instace which has a greyscale value that represents the average greyscale of all duplicates?
E.g: PLY a{1,1,188} is a duplicate of PLY b{1,1,255}. Same (x,y) position possibly different greyscale.
Based on your description of Ply you need these operators:
auto operator==(const Ply& a, const Ply& b)
{
return a.x == b.x && a.y == b.y;
}
auto operator<(const Ply& a, const Ply& b)
{
// whenever you can be lazy!
return std::make_pair(a.x, a.y) < std::make_pair(b.x, b.y);
}
Very important: if the definition "Two Ply are identical if their x and y are identical" is not general valid, then defining comparator operators that ignore greyscale is a bad ideea. In that case you should define separate function objects or non-operator functions and pass them around to function.
There is a nice rule of thumb that a function should not have more than a loop. So instead of a nested 2 for loops, we define this helper function which computes the average of consecutive duplicates and also returns the end of the consecutive duplicates range:
// prereq: [begin, end) has at least one element
// i.e. begin != end
template <class It>
auto compute_average_duplicates(It begin, It end) -> std::pair<int, It>
// (sadly not C++17) concepts:
//requires requires(It i) { {*i} -> Ply; }
{
auto it = begin + 1;
int sum = begin->greyscale;
for (; it != end && *begin == *it; ++it) {
sum += it->greyscale;
}
// you might need rounding instead of truncation:
return std::make_pair(sum / std::distance(begin, it), it);
}
With this we can have our algorithm:
auto foo()
{
std::vector<Ply> v = {{1, 5, 10}, {2, 4, 6}, {1, 5, 2}};
std::sort(std::begin(v), std::end(v));
for (auto i = std::begin(v); i != std::end(v); ++i) {
decltype(i) j;
int average;
std::tie(average, j) = compute_average_duplicates(i, std::end(v));
// C++17 (coming soon in a compiler near you):
// auto [average, j] = compute_average_duplicates(i, std::end(v));
if (i + 1 == j)
continue;
i->greyscale = average;
v.erase(i + 1, j);
// std::vector::erase Invalidates iterators and references
// at or after the point of the erase
// which means i remains valid, and `++i` (from the for) is correct
}
}
You can apply lexicographical sorting first. During sorting you should take care of overflowing greyscale. With current approach you will have some roundoff error, but it will be small as i first sum and only then average.
In the second part you need to remove duplicates from the array. I used additional array of indices to copy every element not more than once. If you have some forbidden value for x, y or greyscale you can use it and thus get along without additional array.
struct PLY {
int x;
int y;
int greyscale;
};
int main()
{
struct comp
{
bool operator()(const PLY &a, const PLY &b) { return a.x != b.x ? a.x < b.x : a.y < b.y; }
};
vector<PLY> v{ {1,1,1}, {1,2,2}, {1,1,2}, {1,3,5}, {1,2,7} };
sort(begin(v), end(v), comp());
vector<bool> ind(v.size(), true);
int s = 0;
for (int i = 1; i < v.size(); ++i)
{
if (v[i].x == v[i - 1].x &&v[i].y == v[i - 1].y)
{
v[s].greyscale += v[i].greyscale;
ind[i] = false;
}
else
{
int d = i - s;
if (d != 1)
{
v[s].greyscale /= d;
}
s = i;
}
}
s = 0;
for (int i = 0; i < v.size(); ++i)
{
if (ind[i])
{
if (s != i)
{
v[s] = v[i];
}
++s;
}
}
v.resize(s);
}
So you need to check, is PLY a1 { 1,1,1 }; duplicates PLY a2 {2,2,1};
So simple method is to override operator == to check a1.x == a2.x and a1.y == a2.y. After you can write own function removeDuplicates(std::vector<PLU>& mPLY); which will use iterators of this vector, compare and remove. But better to use std::list if you want to remove from middle of array too frequently.
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This the C++ code for the sweeping line algorithm that I am using. I am using HeapSort to sort the points. But I am getting the below 2 errors:
Line 214: Char 5: error: no matching function for call to 'heapSort'
heapSort(arr, n);
Line 134: Char 6: note: candidate function not viable: no known conversion from 'Segment [2]' to 'int *' for 1st argument
void heapSort(int arr[], int n)
1 error generated.
I am not exactly why it is throwing the 2 errors.
// Implementation of Sweep Line Algorithm
#include <bits/stdc++.h>
using namespace std;
// A point in 2D plane
struct Point
{
int x, y;
};
// A line segment with left as Point
// with smaller x value and right with
// larger x value.
struct Segment
{
Point left, right;
};
// An event for sweep line algorithm
// An event has a point, the position
// of point (whether left or right) and
// index of point in the original input
// array of segments.
struct Event {
int x, y;
bool isLeft;
int index;
Event(int x, int y, bool l, int i) : x(x), y(y), isLeft(l), index(i) {}
// This is for maintaining the order in set.
bool operator<(const Event& e) const {
return y < e.y;
}
};
// Given three colinear points p, q, r, the function checks if
// point q lies on line segment 'pr'
bool onSegment(Point p, Point q, Point r)
{
if (q.x <= max(p.x, r.x) && q.x >= min(p.x, r.x) &&
q.y <= max(p.y, r.y) && q.y >= min(p.y, r.y))
return true;
return false;
}
// To find orientation of ordered triplet (p, q, r).
// The function returns following values
// 0 --> p, q and r are colinear
// 1 --> Clockwise
// 2 --> Counterclockwise
int orientation(Point p, Point q, Point r)
{
// See https://www.geeksforgeeks.org/orientation-3-ordered-points/
// for details of below formula.
int val = (q.y - p.y) * (r.x - q.x) -
(q.x - p.x) * (r.y - q.y);
if (val == 0) return 0; // colinear
return (val > 0)? 1: 2; // clock or counterclock wise
}
// The main function that returns true if line segment 'p1q1'
// and 'p2q2' intersect.
bool doIntersect(Segment s1, Segment s2)
{
Point p1 = s1.left, q1 = s1.right, p2 = s2.left, q2 = s2.right;
// Find the four orientations needed for general and
// special cases
int o1 = orientation(p1, q1, p2);
int o2 = orientation(p1, q1, q2);
int o3 = orientation(p2, q2, p1);
int o4 = orientation(p2, q2, q1);
// General case
if (o1 != o2 && o3 != o4)
return true;
// Special Cases
// p1, q1 and p2 are colinear and p2 lies on segment p1q1
if (o1 == 0 && onSegment(p1, p2, q1)) return true;
// p1, q1 and q2 are colinear and q2 lies on segment p1q1
if (o2 == 0 && onSegment(p1, q2, q1)) return true;
// p2, q2 and p1 are colinear and p1 lies on segment p2q2
if (o3 == 0 && onSegment(p2, p1, q2)) return true;
// p2, q2 and q1 are colinear and q1 lies on segment p2q2
if (o4 == 0 && onSegment(p2, q1, q2)) return true;
return false; // Doesn't fall in any of the above cases
}
// Find predecessor of iterator in s.
auto pred(set<Event> &s, set<Event>::iterator it) {
return it == s.begin() ? s.end() : --it;
}
// Find successor of iterator in s.
auto succ(set<Event> &s, set<Event>::iterator it) {
return ++it;
}
void heapify(int arr[], int n, int i)
{
int largest = i; // Initialize largest as root
int l = 2 * i + 1; // left = 2*i + 1
int r = 2 * i + 2; // right = 2*i + 2
// If left child is larger than root
if (l < n && arr[l] > arr[largest])
largest = l;
// If right child is larger than largest so far
if (r < n && arr[r] > arr[largest])
largest = r;
// If largest is not root
if (largest != i) {
swap(arr[i], arr[largest]);
// Recursively heapify the affected sub-tree
heapify(arr, n, largest);
}
}
// main function to do heap sort
void heapSort(int arr[], int n)
{
// Build heap (rearrange array)
for (int i = n / 2 - 1; i >= 0; i--)
heapify(arr, n, i);
// One by one extract an element from heap
for (int i = n - 1; i > 0; i--) {
// Move current root to end
swap(arr[0], arr[i]);
// call max heapify on the reduced heap
heapify(arr, i, 0);
}
}
// Returns true if any two lines intersect.
bool isIntersect(Segment arr[], int n)
{
// Pushing all points to a vector of events
vector<Event> e;
for (int i = 0; i < n; ++i) {
e.push_back(Event(arr[i].left.x, arr[i].left.y, true, i));
e.push_back(Event(arr[i].right.x, arr[i].right.y, false, i));
}
// Sorting all events according to x coordinate.
sort(e.begin(), e.end(), [](Event &e1, Event &e2) {return e1.x < e2.x;});
// For storing active segments.
set<Event> s;
// Traversing through sorted points
for (int i=0; i<2*n; i++)
{
Event curr = e[i];
int index = curr.index;
// If current point is left of its segment
if (curr.isLeft)
{
// Get above and below points
auto next = s.lower_bound(curr);
auto prev = pred(s, next);
// Check if current point intersects with
// any of its adjacent
if (next != s.end() && doIntersect(arr[next->index], arr[index]))
return true;
if (prev != s.end() && doIntersect(arr[prev->index], arr[index]))
return true;
// Insert current point (or event)
s.insert(curr);
}
// If current point is right of its segment
else
{
// Find the iterator
auto it = s.find(curr);
// Find above and below points
auto next = succ(s, it);
auto prev = pred(s, it);
// If above and below point intersect
if (next != s.end() && prev != s.end())
if (doIntersect(arr[prev->index], arr[next->index]))
return true;
// Return current point
s.erase(curr);
}
}
return false;
}
// Driver code
int main() {
Segment arr[] = { {{0, 0}, {0, 4}}, {{1, 0}, {5, 0}}};
int n = sizeof(arr)/sizeof(arr[0]);
heapSort(arr, n);
cout << isIntersect(arr, n);
return 0;
}
The function heapSort is declared like
void heapSort(int arr[], int n);
that is its first parameter has the type int arr[] that is adjusted by the compiler to the type int *.
But you are calling the function passing an array of the type Segment[2] as the first argument
Segment arr[] = { {{0, 0}, {0, 4}}, {{1, 0}, {5, 0}}};
int n = sizeof(arr)/sizeof(arr[0]);
heapSort(arr, n);
And there is no implicit conversion from the type Segment[2] (the type of the array arr used as a function argument) to the type int * (the type of the first parameter of the function) after adjusting the type of the first parameter int[] to the type int * implicitly by the compiler.
One of solutions is to rewrite the function heapSort as a template function for example like
template <typename T>
void heapSort( T arr[], int n);
In this case you will need to rewrite other functions that are used by the function heapSort also as template functions,
Like the title says I am trying to use a binary search method to search a sorted vector for the closest given value and return its index. I have attempted to use lower/upper_bound() but the returned value is either the first or last vector value, or "0". Below is the txt file which i have read the temp and voltage into vectors.
1.4 1.644290 -12.5
1.5 1.642990 -13.6
1.6 1.641570 -14.8
1.7 1.640030 -16.0
1.8 1.638370 -17.1
This is my current linear search that works
double Convert::convertmVtoK(double value) const
{
assert(!mV.empty());
auto it = std::min_element(mV.begin(), mV.end(), [value] (double a, double b) {
return std::abs(value - a) < std::abs(value - b);
});
assert(it != mV.end());
int index = std::distance(mV.begin(), it);
std::cout<<kelvin[index];
return kelvin[index];
}
This is the algorithm I am currently trying to get working to improve performance.
double Convert::convertmVtoK(double value)
{
auto it = lower_bound(mV.begin(), mV.end(), value);
if (it == mV.begin())
{
it = mV.begin();
}
else
{
--it;
}
auto jt = upper_bound(mV.begin(), mV.end(), value), out = it;
if (it == mV.end() || jt != mV.end() && value - *it > *jt - value)
{
out = jt;
}
cout<<"This is conversion mV to K"<<" "<< *out;
Any suggestions would be much appreciated. I believe the issue may lie with the vector being sorted in descending order but i need the order to remain the same in order to compare the values.
SOLVED thanks to #John. For anyone who needs this in the future here is what works.
double Convert::convertmVtoK(double value) const
{
auto it = lower_bound(mV.begin(), mV.end(), value, [](double a, double b){ return a > b; });
int index = std::distance(mV.begin(), it);
std::cout<<kelvin[index];
}
Since you have a non-increasing range (sorted in descending order), you can use std::lower_bound with a greater than operator, as mentioned in comments. However, this only gets you the first result past or equal to your number. It doesn't mean it's the "closest", which is what you asked for.
Instead, I would use std::upper_bound, so you don't have to check for equality (on double just to make it worse) and then drop back one to get the other bounding data point, and compute which one is actually closer. Along with some boundary checks:
#include <vector>
#include <algorithm>
#include <iostream>
#include <functional>
#include <iterator>
// for nonincreasing range of double, find closest to value, return its index
int index_closest(std::vector<double>::iterator begin, std::vector<double>::iterator end, double value) {
if (begin == end){
// we're boned
throw std::exception("index_closest has no valid index to return");
}
auto it = std::upper_bound(begin, end, value, std::greater<double>());
// first member is closest
if (begin == it)
return 0;
// last member is closest. end is one past that.
if (end == it)
return std::distance(begin, end) - 1;
// between two, need to see which is closer
double diff1 = abs(value - *it);
double diff2 = abs(value - *(it-1));
if (diff2 < diff1)
--it;
return std::distance(begin, it);
}
int main()
{
std::vector<double> data{ -12.5, -13.6, -14.8, -16.0, -17.1 };
for (double value = -12.0; value > -18.99; value = value - 1.0) {
int index = index_closest(data.begin(), data.end(), value);
std::cout << value << " is closest to " << data[index] << " at index " << index << std::endl;
}
}
output
-12 is closest to -12.5 at index 0
-13 is closest to -12.5 at index 0
-14 is closest to -13.6 at index 1
-15 is closest to -14.8 at index 2
-16 is closest to -16 at index 3
-17 is closest to -17.1 at index 4
-18 is closest to -17.1 at index 4
Note that, e.g. -14 is closer to -13.6 than -14.8, as a specific counterexample to your current working point. Also note the importance of inputs at both end points.
From there you are welcome to take kelvin[i]. I wasn't happy with using an external data array for the function's return value when you don't need to do that, so I just returned the index.
You might use the following to get the iterator with closest value:
auto FindClosest(const std::vector<double>& v, double value)
{
// assert(std::is_sorted(v.begin(), v.end(), std::greater<>{}));
auto it = std::lower_bound(v.begin(), v.end(), value, std::greater<>{});
if (it == v.begin()) {
return it;
} else if (it == v.end()) {
return it - 1;
} else {
return std::abs(value - *it) < std::abs(value - *(it - 1)) ?
it : it - 1;
}
}
This method works but am not 100% sure it always gives closest value. Incorporated part of #KennyOstrom 's method.
double Convert::convertmVtoK(double value) const
{
auto it = lower_bound(mV.begin(), mV.end(), value, [](double a, double b){ return a > b; });
int index = std::distance(mV.begin(), it);
if(value>mV[0] || value < mV.back())
{
std::cout<<"Warning: Voltage Out of Range"<<"\n";
}
else if(value==mV[0] || value==mV.back()
||fabs(value - mV[index]) <= 0.0001 * fabs(value))
{
std::cout<<kelvin[index];
return kelvin[index];
}
else
{
double diff1 = std::abs(value - mV[index]);
double diff2 = std::abs(value - mV[index-1]);
if (diff2 < diff1)
{
std::cout<<kelvin[index-1];
return kelvin[index-1];
}
else
{
std::cout<<kelvin[index];
return kelvin[index];
}
}
}
I've got an array (actually std::vector) size ~ 7k elements.
If you draw this data, there will be a diagram of the combustion of the fuel. But I want to minimize this vector from 7k elements to 721 (every 0.5 degree) elements or ~ 1200 (every 0.3 degree). Of course I want save diagram the same. How can I do it?
Now I am getting every 9 element from big vector to new and cutting other evenly from front and back of vector to get 721 size.
QVector <double> newVMTVector;
for(QVector <double>::iterator itv = oldVmtDataVector.begin(); itv < oldVmtDataVector.end() - 9; itv+=9){
newVMTVector.push_back(*itv);
}
auto useless = newVMTVector.size() - 721;
if(useless%2 == 0){
newVMTVector.erase(newVMTVector.begin(), newVMTVector.begin() + useless/2);
newVMTVector.erase(newVMTVector.end() - useless/2, newVMTVector.end());
}
else{
newVMTVector.erase(newVMTVector.begin(), newVMTVector.begin() + useless/2+1);
newVMTVector.erase(newVMTVector.end() - useless/2, newVMTVector.end());
}
newVMTVector.squeeze();
oldVmtDataVector.clear();
oldVmtDataVector = newVMTVector;
I can swear there is an algorithm that averages and reduces the array.
The way I understand it you want to pick the elements [0, k, 2k, 3k ... ] where n is 10 or n is 6.
Here's a simple take:
template <typename It>
It strided_inplace_reduce(It it, It const last, size_t stride) {
It out = it;
if (stride < 1) return last;
while (it < last)
{
*out++ = *it;
std::advance(it, stride);
}
return out;
}
Generalizing a bit for non-random-access iterators:
Live On Coliru
#include <iterator>
namespace detail {
// version for random access iterators
template <typename It>
It strided_inplace_reduce(It it, It const last, size_t stride, std::random_access_iterator_tag) {
It out = it;
if (stride < 1) return last;
while (it < last)
{
*out++ = *it;
std::advance(it, stride);
}
return out;
}
// other iterator categories
template <typename It>
It strided_inplace_reduce(It it, It const last, size_t stride, ...) {
It out = it;
if (stride < 1) return last;
while (it != last) {
*out++ = *it;
for (size_t n = stride; n && it != last; --n)
{
it = std::next(it);
}
}
return out;
}
}
template <typename Range>
auto strided_inplace_reduce(Range& range, size_t stride) {
using std::begin;
using std::end;
using It = decltype(begin(range));
It it = begin(range), last = end(range);
return detail::strided_inplace_reduce(it, last, stride, typename std::iterator_traits<It>::iterator_category{});
}
#include <vector>
#include <list>
#include <iostream>
int main() {
{
std::vector<int> v { 1,2,3,4,5,6,7,8,9 };
v.erase(strided_inplace_reduce(v, 2), v.end());
std::copy(v.begin(), v.end(), std::ostream_iterator<int>(std::cout << "\nv: ", " "));
}
{
std::list<int> l { 1,2,3,4,5,6,7,8,9 };
l.erase(strided_inplace_reduce(l, 4), l.end());
std::copy(l.begin(), l.end(), std::ostream_iterator<int>(std::cout << "\nl: ", " "));
}
}
Prints
v: 1 3 5 7 9
l: 1 5 9
What you need is an interpolation. There are many libraries providing many types of interpolation. This one is very lightweight and easy to setup and run:
http://kluge.in-chemnitz.de/opensource/spline/
All you need to do is create the second vector that contains the X values, pass both vectors to generate spline, and generate interpolated results every 0.5 degrees or whatever:
std::vector<double> Y; // Y is your current vector of fuel combustion values with ~7k elements
std::vector<double> X;
X.reserve(Y.size());
double step_x = 360 / (double)Y.size();
for (int i = 0; i < X.size(); ++i)
X[i] = i*step_x;
tk::spline s;
s.set_points(X, Y);
double interpolation_step = 0.5;
std::vector<double> interpolated_results;
interpolated_results.reserve(std::ceil(360/interpolation_step) + 1);
for (double i = 0.0, int j = 0; i <= 360; i += interpolation_step, ++j) // <= in order to obtain range <0;360>
interpolated_results[j] = s(i);
if (fmod(360, interpolation_step) != 0.0) // for steps that don't divide 360 evenly, e.g. 0.7 deg, we need to close the range
interpolated_results.back() = s(360);
// now interpolated_results contain values every 0.5 degrees
This should give you and idea how to use this kind of libraries. If you need some other interpolation type, just find the one that suits your needs. The usage should be similar.
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I want to add two bolean vectors
vector<bool> v1= {0,0,1}
vector<bool> v2= {1,0,1}
vector<bool> resultedVector = v1+v2
The answer should be:
resultedVector = {1,1,0};
Does anyone know, how to do in c++/c++11 ?
I want to increment every time given boolean vector by 1. And just want to use binary operations. Or could create bolean truth table of given number of variable.
To perform binary addition in C++, you can use the function described here:
Adding binary numbers in C++
I implemented the function from that link to fit your specifications like this:
std::vector<bool> add(const std::vector<bool>& a, const std::vector<bool>& b)
{
bool c;
std::vector<bool> result;
for(int i = 0; i < a.size() ; i++){
result.push_back(false);
result[i] = ((a[i] ^ b[i]) ^ c); // c is carry
c = ((a[i] & b[i]) | (a[i] & c)) | (b[i] & c);
}
return result;
}
This function takes two vectors of bools (and assumes they are the same size) and returns their result vector. Obviously this function doesn't handle overflow or numbers of different sizes. You can modify it yourself if you need those capabilities. Also, you seem to be talking about an overloaded operator for a bool vector, and you can do that by checking out operator overloading, but this logic will allow you to add two boolean numbers stored in vectors.
I'm not sure that I understand your question. Since this looks like homework and the point of the question seems to be operators overloading, here's an idea, not the complete answer:
#include <vector>
std::vector< bool > operator+( const std::vector<bool>& a, const std::vector<bool>& b )
{
std::vector< bool > r;
// your code goes here
return r;
}
int main()
{
std::vector< bool > a, b, c;
c = a + b;
return 0;
}
EDIT - one day later
Here's a solution to your increment problem (demo):
#include <iostream>
#include <vector>
// preinc - no grow on overflow
std::vector< bool >& operator++( std::vector<bool>& v )
{
for ( auto e : v )
if ( e = !e )
break;
return v;
}
// postinc - no grow on overflow
std::vector< bool > operator++( std::vector<bool>& v, int )
{
auto t { v };
operator++( v );
return t;
}
// insert
std::ostream& operator<<( std::ostream& os, const std::vector< bool > v )
{
for ( std::vector< bool >::const_reverse_iterator ci = v.rbegin(); ci != v.rend(); ++ci )
os << *ci ? '1' : '0';
return os;
}
int main()
{
std::vector< bool > b {0,0,0,0};
for ( int i = 0; i < 16; ++i )
{
std::cout << b << std::endl;
++b;
}
return 0;
}
Here's how you can use a stateful functor:
struct BitAdder {
bool carry_ = 0x0; // Range is [0, 1].
// Only accepts single bit values for a and b.
bool operator()(bool a, bool b) {
assert(a == (a & 0x1) && b == (b & 0x1));
char sum = a + b + carry_;
carry_ = (sum & 0x2) >> 1; // Keep in range.
return sum & 0x1;
}
};
// Code is more straightforward when bits are stored in reverse.
std::vector<bool> v = {0, 1, 1, 1, 0}; // To be interpreted as: 1110 (14).
std::vector<bool> w = {1, 0, 1, 1, 0}; // To be interpreted as: 1101 (13).
std::vector<bool> result = {0, 0, 0, 0, 0}; // Will become: 11011 (27).
assert(v.size() <= w.size()); // v and w can be iterated over together.
assert(v.size() <= result.size()); // There is enough space to store the bits.
assert(v[v.size() - 1] + w[v.size() - 1] < 2); // No overflow can happen.
std::transform(v.cbegin(), v.cend(), w.cbegin(), result.begin(), BitAdder());
std::cout << "want: 11011, got: ";
std::copy(result.crbegin(), result.crend(), std::ostream_iterator<bool>(std::cout));
std::cout << '\n';
Live Demo
How would you solve the problem of finding the points of a (integer) grid within a circle centered on the origin of the axis, with the results ordered by norm, as in distance from the centre, in C++?
I wrote an implementation that works (yeah, I know, it is extremely inefficient, but for my problem anything more would be overkill). I'm extremely new to C++, so my biggest problem was finding a data structure capable of
being sort-able;
being able to save an array in one of its elements,
rather than the implementation of the algorithm. My code is as follows. Thanks in advance, everyone!
typedef std::pair<int, int[2]> norm_vec2d;
bool norm_vec2d_cmp (norm_vec2d a, norm_vec2d b)
{
bool bo;
bo = (a.first < b.first ? true: false);
return bo;
}
int energy_to_momenta_2D (int energy, std::list<norm_vec2d> *momenta)
{
int i, j, norm, n=0;
int energy_root = (int) std::sqrt(energy);
norm_vec2d temp;
for (i=-energy_root; i<=energy_root; i++)
{
for (j =-energy_root; j<=energy_root; j++)
{
norm = i*i + j*j;
if (norm <= energy)
{
temp.first = norm;
temp.second[0] = i;
temp.second[1] = j;
(*momenta).push_back (temp);
n++;
}
}
}
(*momenta).sort(norm_vec2d_cmp);
return n;
}
How would you solve the problem of finding the points of a (integer) grid within a circle centered on the origin of the axis, with the results ordered by norm, as in distance from the centre, in C++?
I wouldn't use a std::pair to hold the points. I'd create my own more descriptive type.
struct Point {
int x;
int y;
int square() const { return x*x + y*y; }
Point(int x = 0, int y = 0)
: x(x), y(y) {}
bool operator<(const Point& pt) const {
if( square() < pt.square() )
return true;
if( pt.square() < square() )
return false;
if( x < pt.x )
return true;
if( pt.x < x)
return false;
return y < pt.y;
}
friend std::ostream& operator<<(std::ostream& os, const Point& pt) {
return os << "(" << pt.x << "," << pt.y << ")";
}
};
This data structure is (probably) exactly the same size as two ints, it is less-than comparable, it is assignable, and it is easily printable.
The algorithm walks through all of the valid points that satisfy x=[0,radius] && y=[0,x] && (x,y) inside circle:
std::set<Point>
GetListOfPointsInsideCircle(double radius = 1) {
std::set<Point> result;
// Only examine bottom half of quadrant 1, then
// apply symmetry 8 ways
for(Point pt(0,0); pt.x <= radius; pt.x++, pt.y = 0) {
for(; pt.y <= pt.x && pt.square()<=radius*radius; pt.y++) {
result.insert(pt);
result.insert(Point(-pt.x, pt.y));
result.insert(Point(pt.x, -pt.y));
result.insert(Point(-pt.x, -pt.y));
result.insert(Point(pt.y, pt.x));
result.insert(Point(-pt.y, pt.x));
result.insert(Point(pt.y, -pt.x));
result.insert(Point(-pt.y, -pt.x));
}
}
return result;
}
I chose a std::set to hold the data for two reasons:
It is stored is sorted order, so I don't have to std::sort it, and
It rejects duplicates, so I don't have to worry about points whose reflection are identical
Finally, using this algorithm is dead simple:
int main () {
std::set<Point> vp = GetListOfPointsInsideCircle(2);
std::copy(vp.begin(), vp.end(),
std::ostream_iterator<Point>(std::cout, "\n"));
}
It's always worth it to add a point class for such geometric problem, since usually you have more than one to solve. But I don't think it's a good idea to overload the 'less' operator to satisfy the first need encountered. Because:
Specifying the comparator where you sort will make it clear what order you want there.
Specifying the comparator will allow to easily change it without affecting your generic point class.
Distance to origin is not a bad order, but for a grid but it's probably better to use row and columns (sort by x first then y).
Such comparator is slower and will thus slow any other set of points where you don't even care about norm.
Anyway, here is a simple solution using a specific comparator and trying to optimize a bit:
struct v2i{
int x,y;
v2i(int px, int py) : x(px), y(py) {}
int norm() const {return x*x+y*y;}
};
bool r_comp(const v2i& a, const v2i& b)
{ return a.norm() < b.norm(); }
std::vector<v2i> result;
for(int x = -r; x <= r; ++x) {
int my = r*r - x*x;
for(int y = 0; y*y <= my; ++y) {
result.push_back(v2i(x,y));
if(y > 0)
result.push_back(v2i(x,-y));
}
}
std::sort(result.begin(), result.end(), r_comp);