I am writing the below linear interpolation function, which is meant to be generic, but current result is not.
The function finds desired quantity of equally distant points linear in between two given boundary points. Both desired quantity and boundaries are given as parameters. As return, a vector of linear interpolated values is returned.
The issue I have concerns to return type, which always appear to be integer, even when it should have some mantissa, for example:
vec = interpolatePoints(5, 1, 4);
for (auto val : vec) std::cout << val << std::endl; // prints 4, 3, 2, 1
But it should have printed: 4.2, 3.4, 2.6, 1.8
What should I do to make it generic and have correct return values?
code:
template <class T>
std::vector<T> interpolatePoints(T lower_limit, T high_limit, const unsigned int quantity) {
auto step = ((high_limit - lower_limit)/(double)(quantity+1));
std::vector<T> interpolated_points;
for(unsigned int i = 1; i <= quantity; i++) {
interpolated_points.push_back((std::min(lower_limit, high_limit) + (step*i)));
}
return interpolated_points;
}
After some simplifications the function might look like:
template<typename T, typename N, typename R = std::common_type_t<double, T>>
std::vector<R> interpolate(T lo_limit, T hi_limit, N n) {
const auto lo = static_cast<R>(lo_limit);
const auto hi = static_cast<R>(hi_limit);
const auto step = (hi - lo) / (n + 1);
std::vector<R> pts(n);
const auto gen = [=, i = N{0}]() mutable { return lo + step * ++i; };
std::generate(pts.begin(), pts.end(), gen);
return pts;
}
The type of elements in the returned std::vector is std::common_type_t<double, T>. For int, it is double, for long double, it is long double. double looks like a reasonable default type.
You just have to pass correct type:
auto vec = interpolatePoints(5., 1., 4); // T deduced as double
Demo
And in C++20, you might use std::lerp, to have:
template <class T>
std::vector<T> interpolatePoints(T lower_limit, T high_limit, const unsigned int quantity) {
auto step = 1 / (quantity + 1.);
std::vector<T> interpolated_points;
for(unsigned int i = 1; i <= quantity; i++) {
interpolated_points.push_back(std::lerp(lower_limit, high_limit, step * i));
}
return interpolated_points;
}
Demo
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.
say I have a std::vector with N elements. I would like to copy every n-th element of it to a new vector, or average up to that element then copy it (downsample the original vector). So I want to do this
std::vector<double> vec(N);
long n = 4;
std::vector<double> ds(N/n);
for(long i = 0; i < ds.size(); i+=n)
{
ds[i] = vec[i*n];
}
or
for(long i = 0; i < ds.size(); i+=n)
{
double tmp = 0;
for(long j = 0; j < n; j++)
{
tmp += vec[i*n+j];
}
ds[i] = tmp/static_cast<double>(n);
}
Is there a way to do this using the standard algorithms of C++? Like using std::copy with binary functions? I have billions of elements that I want to treat this way, and I want this to be as fast as possible.
PS: I would prefer not to use external libraries such as boost.
For readability, the loop would be a good idea, as pointed out by Vlad in the comments. But if you really want to do someting like this, you could try:
int cnt=0,n=3;
vector<int> u(v.size()/3);
copy_if (v.begin(), v.end(), u.begin(),
[&cnt,&n] (int i)->bool {return ++cnt %n ==0; } );
If you want to average, it's getting worse as you'd have to similar tricks combining transform() with copy_if().
Edit:
If you're looking for performance, you'd better stick to the loop, as stressed in the comments by davidhigh: it will avoid the overhead of the call to the lambda function for each element.
If you're looking for an algorithm because you're doing this very often, you'd better write your own generic one.
You could write your own generic algorithms inspired from the design principles used in <algorithm>.
For the copy of every n elements:
template<class in_it, class out_it>
out_it copy_every_n( in_it b, in_it e, out_it r, size_t n) {
for (size_t i=distance(b,e)/n; i--; advance (b,n))
*r++ = *b;
return r;
}
Example of use:
vector<int> v {1,2,3,4,5,6,7,8,9,10};
vector<int> z(v.size()/3);
copy_every_n(v.begin(), v.end(), z.begin(), 3);
For averaging the elements n by n, you can use:
template<class in_it, class out_it>
out_it average_every_n( in_it b, in_it e, out_it r, size_t n) {
typename out_it::value_type tmp=0;
for (size_t cnt=0; b!=e; b++) {
tmp+=*b;
if (++cnt==n) {
cnt=0;
*r++=tmp/n;
tmp=0;
}
}
return r;
}
Example of use:
vector<int> w(v.size()/3);
average_every_n(v.begin(), v.end(), w.begin(), 3);
The advantage over your inital loops, is that this will work not only on vectors, but on any container providing the begin() and end() iterator. And it avoids overheads that I pointed out in my other answer.
If to use only standard library features and algorithms and if it is not allowed to use loops then the code can look the following way. Take into account that the code is based on the C++ 2014. If you need a code that will be compiled by a compiler that supports only C++ 2011 then you have to make some minor changes.
#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>
#include <iterator>
int main()
{
const size_t N = 4;
std::vector<double> src = { 1.1, 2.2, 3.3, 4.4, 5.5, 6.6, 7.7, 8.8, 9.9 };
size_t n = src.size() / N;
std::vector<double> dst( n );
std::copy_if( src.begin(), std::next( src.begin(), n * N ), dst.begin(),
[i = 0] ( auto ) mutable { return ( i = ( i + 1 ) % N ) == 0; } );
for ( double x : dst ) std::cout << x << ' ';
std::cout << std::endl;
dst.assign( n, 0.0 );
std::accumulate( src.begin(), std::next( src.begin(), n * N ), dst.begin(),
[i = 0] ( auto acc, auto x ) mutable
{
*acc += x;
if ( ( i = ( i + 1 ) % N ) == 0 ) *acc++ /= N;
return acc;
} );
for ( double x : dst ) std::cout << x << ' ';
std::cout << std::endl;
}
The program output is
4.4 8.8
2.75 7.15
This compound expression in the if condition
if ( ( i = ( i + 1 ) % N ) == 0 ) *acc++ /= N;
you can replace with more simpler one
if ( ++i % N == 0 ) *acc++ /= N;
You may have explicitly stated that you prefer not to use Boost, but any non-Boost solution would really be implementing exactly this sort of thing anyway, so I'll show you how I would do it in Boost. Ultimately, I think you're better off writing a simple loop.
Downsampling uses strided
boost::copy(
input | strided(2),
std::back_inserter(output));
Downsampling average additionally uses transformed, though this solution is non-generic and specifically relies upon vector being contiguous:
boost::copy(
input | strided(2) | transformed([](auto& x){
return std::accumulate(&x, &x + 2, 0) / 2.;
}),
std::back_inserter(output));
Of course that has issues if the input isn't an exact multiple of the stride length, so it'd probably be better to do something like:
auto downsample_avg = [](auto& input, int n){
return input | strided(n) | transformed([&,n](auto& x){
auto begin = &x;
auto end = begin + std::min<size_t>(n, &input.back() - begin + 1);
return std::accumulate(begin, end, 0.0) / (end - begin);
});
};
boost::copy(
downsample_avg(input, 2),
std::back_inserter(output));
how about this implemention?
#include <iterator>
template<typename InputIt, typename OutputIt>
OutputIt DownSample(InputIt first, InputIt last, OutputIt d_first,
typename std::iterator_traits<InputIt>::difference_type n) {
while (first < last) {
*(d_first++) = *first;
std::advance(first, n);
}
return d_first;
}
I want to fill a vector<float> with values, starting from a, increasing by inc, up to and including b. So basically what e.g. vec = 2:0.5:4 in Matlab would do - vec should now be { 2.0, 2.5, 3.0, 3.5, 4.0 }.
The best I could come up with is
vector<float> vec(10);
float increment = 0.5f;
std::generate(begin(vec), end(vec), [&increment]() {static float start = 2.0f; return start += increment ; });
But obviously it is incorrect as it starts at 2.5f, not 2.0f. And I would like to specify the parameters a bit easier or more concise.
I could imagine doing it in a dedicated class, but that would require quite some code.
Also I've looked at std::iota, but it can only increase by +1.
Any ideas on the best, concise approach? Using C++11 (and some parts of 14) welcome.
Edit: Of course I've also used a for-loop like:
for (float i = -1.0f; i <= 1.0f; i += 0.05f) {
vec.emplace_back(i);
}
but it has the problem that it sometimes doesn't go up to the end value, as in this example, because of float impreciseness (or rather representation). Fixing that requires some code and I think there should be a more concise way?
You could write your own variant of std::iota that also accepts a stride argument.
template<typename ForwardIterator, typename T>
void strided_iota(ForwardIterator first, ForwardIterator last, T value, T stride)
{
while(first != last) {
*first++ = value;
value += stride;
}
}
In your example, you'd use it as
std::vector<float> vec(10);
strided_iota(std::begin(vec), std::next(std::begin(vec), 5), 2.0f, 0.5f);
Live demo
I don't think you really need any fancy features for this.
void fill_vec(vector<float>& vec, float a, float inc, float b)
{
for(float n = a; n <= b; n += inc)
vec.push_back(n);
}
If you're worried about floating point precision missing the upper range, then you can add a small amount (often denoted by epsilon for this sort of thing):
float eps = 0.0000001f;
for(float n = a; n <= b + eps; n += inc)
If you include <cfloat>, you can use FLT_EPSILON which may vary between platforms to suit the implementation.
If the issue is that you want to include all the float values, then loop on integers and do the necessary calculations to go back to the float value within the loop.
for (int i = 20; i <= 40; i += 5) {
vec.emplace_back(i/10.0);
}
Here is an approach:
#include <iostream>
#include <vector>
#include <algorithm>
// functor
class generator_float
{
float _start, _inc;
public:
generator_float(float start, float inc): _start(start), _inc(inc) {};
float operator()() {
float tmp = _start;
_start += _inc;
return tmp;
}
};
int main()
{
std::vector<float> vec(10);
std::generate(std::begin(vec), std::end(vec), generator_float(2,0.5));
for(auto&& elem: vec)
std::cout << elem << " ";
std::cout << std::endl;
}
You can use a functor that works for both for iota and generate. Overload the function call and increment operator appropriately:
template <typename T>
class ArithmeticProgression
{
T val;
T inc;
public:
ArithmeticProg(T val, T inc) : val(val), inc(inc) {}
ArithmeticProg& operator++() noexcept(noexcept(val += inc))
{
val += inc;
return *this;
}
T operator()() noexcept(noexcept(val += inc))
{
auto tmp = val;
val += inc;
return tmp;
}
operator T() const noexcept {return val;}
};
template <typename T, typename U>
ArProg<typename std::common_type<T, U>::type> makeArithmeticProg( T val, U inc )
{
return {val, inc};
}
Usage:
int main()
{
std::vector<float> vec;
std::generate_n(std::back_inserter(vec), 5, makeArithmeticProg(2.0f, 0.5f) );
for (auto f : vec)
std::cout << f << ", ";
std::cout << '\n';
std::iota( std::begin(vec), std::end(vec), makeArithmeticProg(2.5f, 0.3f) );
for (auto f : vec)
std::cout << f << ", ";
}
Demo.
I want to sort a large array of integers (say 1 millon elements) lexicographically.
Example:
input [] = { 100, 21 , 22 , 99 , 1 , 927 }
sorted[] = { 1 , 100, 21 , 22 , 927, 99 }
I have done it using the simplest possible method:
convert all numbers to strings (very costly because it will take huge memory)
use std:sort with strcmp as comparison function
convert back the strings to integers
Is there a better method than this?
Use std::sort() with a suitable comparison function. This cuts down on the memory requirements.
The comparison function can use n % 10, n / 10 % 10, n / 100 % 10 etc. to access the individual digits (for positive integers; negative integers work a bit differently).
To provide any custom sort ordering, you can provide a comparator to std::sort. In this case, it's going to be somewhat complex, using logarithms to inspect individual digits of your number in base 10.
Here's an example — comments inline describe what's going on.
#include <iostream>
#include <algorithm>
#include <cmath>
#include <cassert>
int main() {
int input[] { 100, 21, 22, 99, 1, 927, -50, -24, -160 };
/**
* Sorts the array lexicographically.
*
* The trick is that we have to compare digits left-to-right
* (considering typical Latin decimal notation) and that each of
* two numbers to compare may have a different number of digits.
*
* This is very efficient in storage space, but inefficient in
* execution time; an approach that pre-visits each element and
* stores a translated representation will at least double your
* storage requirements (possibly a problem with large inputs)
* but require only a single translation of each element.
*/
std::sort(
std::begin(input),
std::end(input),
[](int lhs, int rhs) -> bool {
// Returns true if lhs < rhs
// Returns false otherwise
const auto BASE = 10;
const bool LHS_FIRST = true;
const bool RHS_FIRST = false;
const bool EQUAL = false;
// There's no point in doing anything at all
// if both inputs are the same; strict-weak
// ordering requires that we return `false`
// in this case.
if (lhs == rhs) {
return EQUAL;
}
// Compensate for sign
if (lhs < 0 && rhs < 0) {
// When both are negative, sign on its own yields
// no clear ordering between the two arguments.
//
// Remove the sign and continue as for positive
// numbers.
lhs *= -1;
rhs *= -1;
}
else if (lhs < 0) {
// When the LHS is negative but the RHS is not,
// consider the LHS "first" always as we wish to
// prioritise the leading '-'.
return LHS_FIRST;
}
else if (rhs < 0) {
// When the RHS is negative but the LHS is not,
// consider the RHS "first" always as we wish to
// prioritise the leading '-'.
return RHS_FIRST;
}
// Counting the number of digits in both the LHS and RHS
// arguments is *almost* trivial.
const auto lhs_digits = (
lhs == 0
? 1
: std::ceil(std::log(lhs+1)/std::log(BASE))
);
const auto rhs_digits = (
rhs == 0
? 1
: std::ceil(std::log(rhs+1)/std::log(BASE))
);
// Now we loop through the positions, left-to-right,
// calculating the digit at these positions for each
// input, and comparing them numerically. The
// lexicographic nature of the sorting comes from the
// fact that we are doing this per-digit comparison
// rather than considering the input value as a whole.
const auto max_pos = std::max(lhs_digits, rhs_digits);
for (auto pos = 0; pos < max_pos; pos++) {
if (lhs_digits - pos == 0) {
// Ran out of digits on the LHS;
// prioritise the shorter input
return LHS_FIRST;
}
else if (rhs_digits - pos == 0) {
// Ran out of digits on the RHS;
// prioritise the shorter input
return RHS_FIRST;
}
else {
const auto lhs_x = (lhs / static_cast<decltype(BASE)>(std::pow(BASE, lhs_digits - 1 - pos))) % BASE;
const auto rhs_x = (rhs / static_cast<decltype(BASE)>(std::pow(BASE, rhs_digits - 1 - pos))) % BASE;
if (lhs_x < rhs_x)
return LHS_FIRST;
else if (rhs_x < lhs_x)
return RHS_FIRST;
}
}
// If we reached the end and everything still
// matches up, then something probably went wrong
// as I'd have expected to catch this in the tests
// for equality.
assert("Unknown case encountered");
}
);
std::cout << '{';
for (auto x : input)
std::cout << x << ", ";
std::cout << '}';
// Output: {-160, -24, -50, 1, 100, 21, 22, 927, 99, }
}
Demo
There are quicker ways to calculate the number of digits in a number, but the above will get you started.
Here's another algorithm which does some of the computation before sorting. It seems to be quite fast, despite the additional copying (see comparisons).
Note:
it only supports positive integers
in only supports integers <= std::numeric_limits<int>::max()/10
N.B. you can optimize count_digits and my_pow10; for example, see Three Optimization Tips for C++ from Andrei Alexandrescu and Any way faster than pow() to compute an integer power of 10 in C++?
Helpers:
#include <random>
#include <vector>
#include <utility>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <limits>
#include <iterator>
// non-optimized version
int count_digits(int p) // returns `0` for `p == 0`
{
int res = 0;
for(; p != 0; ++res)
{
p /= 10;
}
return res;
}
// non-optimized version
int my_pow10(unsigned exp)
{
int res = 1;
for(; exp != 0; --exp)
{
res *= 10;
}
return res;
}
Algorithm (note - not in-place):
// helper to provide integers with the same number of digits
template<class T, class U>
std::pair<T, T> lexicographic_pair_helper(T const p, U const maxDigits)
{
auto const digits = count_digits(p);
// append zeros so that `l` has `maxDigits` digits
auto const l = static_cast<T>( p * my_pow10(maxDigits-digits) );
return {l, p};
}
template<class RaIt>
using pair_vec
= std::vector<std::pair<typename std::iterator_traits<RaIt>::value_type,
typename std::iterator_traits<RaIt>::value_type>>;
template<class RaIt>
pair_vec<RaIt> lexicographic_sort(RaIt p_beg, RaIt p_end)
{
if(p_beg == p_end) return {};
auto max = *std::max_element(p_beg, p_end);
auto maxDigits = count_digits(max);
pair_vec<RaIt> result;
result.reserve( std::distance(p_beg, p_end) );
for(auto i = p_beg; i != p_end; ++i)
result.push_back( lexicographic_pair_helper(*i, maxDigits) );
using value_type = typename pair_vec<RaIt>::value_type;
std::sort(begin(result), end(result),
[](value_type const& l, value_type const& r)
{
if(l.first < r.first) return true;
if(l.first > r.first) return false;
return l.second < r.second; }
);
return result;
}
Usage example:
int main()
{
std::vector<int> input = { 100, 21 , 22 , 99 , 1 , 927 };
// generate some numbers
/*{
constexpr int number_of_elements = 1E6;
std::random_device rd;
std::mt19937 gen( rd() );
std::uniform_int_distribution<>
dist(0, std::numeric_limits<int>::max()/10);
for(int i = 0; i < number_of_elements; ++i)
input.push_back( dist(gen) );
}*/
std::cout << "unsorted: ";
for(auto const& e : input) std::cout << e << ", ";
std::cout << "\n\n";
auto sorted = lexicographic_sort(begin(input), end(input));
std::cout << "sorted: ";
for(auto const& e : sorted) std::cout << e.second << ", ";
std::cout << "\n\n";
}
Here's a community wiki to compare the solutions. I took nim's code and made it easily extensible. Feel free to add your solutions and outputs.
Sample runs an old slow computer (3 GB RAM, Core2Duo U9400) with g++4.9 # -O3 -march=native:
number of elements: 1e+03
size of integer type: 4
reference solution: Lightness Races in Orbit
solution "dyp":
duration: 0 ms and 301 microseconds
comparison to reference solution: exact match
solution "Nim":
duration: 2 ms and 160 microseconds
comparison to reference solution: exact match
solution "nyarlathotep":
duration: 8 ms and 126 microseconds
comparison to reference solution: exact match
solution "notbad":
duration: 1 ms and 102 microseconds
comparison to reference solution: exact match
solution "Eric Postpischil":
duration: 2 ms and 550 microseconds
comparison to reference solution: exact match
solution "Lightness Races in Orbit":
duration: 17 ms and 469 microseconds
comparison to reference solution: exact match
solution "pts":
duration: 1 ms and 92 microseconds
comparison to reference solution: exact match
==========================================================
number of elements: 1e+04
size of integer type: 4
reference solution: Lightness Races in Orbit
solution "nyarlathotep":
duration: 109 ms and 712 microseconds
comparison to reference solution: exact match
solution "Lightness Races in Orbit":
duration: 272 ms and 819 microseconds
comparison to reference solution: exact match
solution "dyp":
duration: 1 ms and 748 microseconds
comparison to reference solution: exact match
solution "notbad":
duration: 16 ms and 115 microseconds
comparison to reference solution: exact match
solution "pts":
duration: 15 ms and 10 microseconds
comparison to reference solution: exact match
solution "Eric Postpischil":
duration: 33 ms and 301 microseconds
comparison to reference solution: exact match
solution "Nim":
duration: 17 ms and 83 microseconds
comparison to reference solution: exact match
==========================================================
number of elements: 1e+05
size of integer type: 4
reference solution: Lightness Races in Orbit
solution "Nim":
duration: 217 ms and 4 microseconds
comparison to reference solution: exact match
solution "pts":
duration: 199 ms and 505 microseconds
comparison to reference solution: exact match
solution "dyp":
duration: 20 ms and 330 microseconds
comparison to reference solution: exact match
solution "Eric Postpischil":
duration: 415 ms and 477 microseconds
comparison to reference solution: exact match
solution "Lightness Races in Orbit":
duration: 3955 ms and 58 microseconds
comparison to reference solution: exact match
solution "notbad":
duration: 215 ms and 259 microseconds
comparison to reference solution: exact match
solution "nyarlathotep":
duration: 1341 ms and 46 microseconds
comparison to reference solution: mismatch found
==========================================================
number of elements: 1e+06
size of integer type: 4
reference solution: Lightness Races in Orbit
solution "Lightness Races in Orbit":
duration: 52861 ms and 314 microseconds
comparison to reference solution: exact match
solution "Eric Postpischil":
duration: 4757 ms and 608 microseconds
comparison to reference solution: exact match
solution "nyarlathotep":
duration: 15654 ms and 195 microseconds
comparison to reference solution: mismatch found
solution "dyp":
duration: 233 ms and 779 microseconds
comparison to reference solution: exact match
solution "pts":
duration: 2181 ms and 634 microseconds
comparison to reference solution: exact match
solution "Nim":
duration: 2539 ms and 9 microseconds
comparison to reference solution: exact match
solution "notbad":
duration: 2675 ms and 362 microseconds
comparison to reference solution: exact match
==========================================================
number of elements: 1e+07
size of integer type: 4
reference solution: Lightness Races in Orbit
solution "notbad":
duration: 33425 ms and 423 microseconds
comparison to reference solution: exact match
solution "pts":
duration: 26000 ms and 398 microseconds
comparison to reference solution: exact match
solution "Eric Postpischil":
duration: 56206 ms and 359 microseconds
comparison to reference solution: exact match
solution "Lightness Races in Orbit":
duration: 658540 ms and 342 microseconds
comparison to reference solution: exact match
solution "nyarlathotep":
duration: 187064 ms and 518 microseconds
comparison to reference solution: mismatch found
solution "Nim":
duration: 30519 ms and 227 microseconds
comparison to reference solution: exact match
solution "dyp":
duration: 2624 ms and 644 microseconds
comparison to reference solution: exact match
The algorithms have to be structs with function-call operator templates that support the interface:
template<class RaIt> operator()(RaIt begin, RaIt end);
A copy of the input data is provided as a parameter, the algorithm is expected to provide the result in the same range (e.g. in-place sort).
#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>
#include <random>
#include <vector>
#include <utility>
#include <cmath>
#include <cassert>
#include <chrono>
#include <cstring>
#include <climits>
#include <functional>
#include <cstdlib>
#include <iomanip>
using duration_t = decltype( std::chrono::high_resolution_clock::now()
- std::chrono::high_resolution_clock::now());
template<class T>
struct result_t
{
std::vector<T> numbers;
duration_t duration;
char const* name;
};
template<class RaIt, class F>
result_t<typename std::iterator_traits<RaIt>::value_type>
apply_algorithm(RaIt p_beg, RaIt p_end, F f, char const* name)
{
using value_type = typename std::iterator_traits<RaIt>::value_type;
std::vector<value_type> inplace(p_beg, p_end);
auto start = std::chrono::high_resolution_clock::now();
f(begin(inplace), end(inplace));
auto end = std::chrono::high_resolution_clock::now();
auto duration = end - start;
return {std::move(inplace), duration, name};
}
// non-optimized version
int count_digits(int p) // returns `0` for `p == 0`
{
int res = 0;
for(; p != 0; ++res)
{
p /= 10;
}
return res;
}
// non-optimized version
int my_pow10(unsigned exp)
{
int res = 1;
for(; exp != 0; --exp)
{
res *= 10;
}
return res;
}
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// paste algorithms here
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
int main(int argc, char** argv)
{
using integer_t = int;
constexpr integer_t dist_min = 0;
constexpr integer_t dist_max = std::numeric_limits<integer_t>::max()/10;
constexpr std::size_t default_number_of_elements = 1E6;
const std::size_t number_of_elements = argc>1 ? std::atoll(argv[1]) :
default_number_of_elements;
std::cout << "number of elements: ";
std::cout << std::scientific << std::setprecision(0);
std::cout << (double)number_of_elements << "\n";
std::cout << /*std::defaultfloat <<*/ std::setprecision(6);
std::cout.unsetf(std::ios_base::floatfield);
std::cout << "size of integer type: " << sizeof(integer_t) << "\n\n";
std::vector<integer_t> input;
{
input.reserve(number_of_elements);
std::random_device rd;
std::mt19937 gen( rd() );
std::uniform_int_distribution<> dist(dist_min, dist_max);
for(std::size_t i = 0; i < number_of_elements; ++i)
input.push_back( dist(gen) );
}
auto b = begin(input);
auto e = end(input);
using res_t = result_t<integer_t>;
std::vector< std::function<res_t()> > algorithms;
#define MAKE_BINDER(B, E, ALGO, NAME) \
std::bind( &apply_algorithm<decltype(B),decltype(ALGO)>, \
B,E,ALGO,NAME )
constexpr auto lightness_name = "Lightness Races in Orbit";
algorithms.push_back( MAKE_BINDER(b, e, lightness(), lightness_name) );
algorithms.push_back( MAKE_BINDER(b, e, dyp(), "dyp") );
algorithms.push_back( MAKE_BINDER(b, e, nim(), "Nim") );
algorithms.push_back( MAKE_BINDER(b, e, pts(), "pts") );
algorithms.push_back( MAKE_BINDER(b, e, epost(), "Eric Postpischil") );
algorithms.push_back( MAKE_BINDER(b, e, nyar(), "nyarlathotep") );
algorithms.push_back( MAKE_BINDER(b, e, notbad(), "notbad") );
{
std::srand( std::random_device()() );
std::random_shuffle(begin(algorithms), end(algorithms));
}
std::vector< result_t<integer_t> > res;
for(auto& algo : algorithms)
res.push_back( algo() );
auto reference_solution
= *std::find_if(begin(res), end(res),
[](result_t<integer_t> const& p)
{ return 0 == std::strcmp(lightness_name, p.name); });
std::cout << "reference solution: "<<reference_solution.name<<"\n\n";
for(auto const& e : res)
{
std::cout << "solution \""<<e.name<<"\":\n";
auto ms =
std::chrono::duration_cast<std::chrono::microseconds>(e.duration);
std::cout << "\tduration: "<<ms.count()/1000<<" ms and "
<<ms.count()%1000<<" microseconds\n";
std::cout << "\tcomparison to reference solution: ";
if(e.numbers.size() != reference_solution.numbers.size())
{
std::cout << "ouput count mismatch\n";
break;
}
auto mismatch = std::mismatch(begin(e.numbers), end(e.numbers),
begin(reference_solution.numbers)).first;
if(end(e.numbers) == mismatch)
{
std::cout << "exact match\n";
}else
{
std::cout << "mismatch found\n";
}
}
}
Current algorithms; note I replaced the digit counters and pow-of-10 with the global function, so we all benefit if someone optimizes.
struct lightness
{
template<class RaIt> void operator()(RaIt b, RaIt e)
{
using T = typename std::iterator_traits<RaIt>::value_type;
/**
* Sorts the array lexicographically.
*
* The trick is that we have to compare digits left-to-right
* (considering typical Latin decimal notation) and that each of
* two numbers to compare may have a different number of digits.
*
* This is very efficient in storage space, but inefficient in
* execution time; an approach that pre-visits each element and
* stores a translated representation will at least double your
* storage requirements (possibly a problem with large inputs)
* but require only a single translation of each element.
*/
std::sort(
b,
e,
[](T lhs, T rhs) -> bool {
// Returns true if lhs < rhs
// Returns false otherwise
const auto BASE = 10;
const bool LHS_FIRST = true;
const bool RHS_FIRST = false;
const bool EQUAL = false;
// There's no point in doing anything at all
// if both inputs are the same; strict-weak
// ordering requires that we return `false`
// in this case.
if (lhs == rhs) {
return EQUAL;
}
// Compensate for sign
if (lhs < 0 && rhs < 0) {
// When both are negative, sign on its own yields
// no clear ordering between the two arguments.
//
// Remove the sign and continue as for positive
// numbers.
lhs *= -1;
rhs *= -1;
}
else if (lhs < 0) {
// When the LHS is negative but the RHS is not,
// consider the LHS "first" always as we wish to
// prioritise the leading '-'.
return LHS_FIRST;
}
else if (rhs < 0) {
// When the RHS is negative but the LHS is not,
// consider the RHS "first" always as we wish to
// prioritise the leading '-'.
return RHS_FIRST;
}
// Counting the number of digits in both the LHS and RHS
// arguments is *almost* trivial.
const auto lhs_digits = (
lhs == 0
? 1
: std::ceil(std::log(lhs+1)/std::log(BASE))
);
const auto rhs_digits = (
rhs == 0
? 1
: std::ceil(std::log(rhs+1)/std::log(BASE))
);
// Now we loop through the positions, left-to-right,
// calculating the digit at these positions for each
// input, and comparing them numerically. The
// lexicographic nature of the sorting comes from the
// fact that we are doing this per-digit comparison
// rather than considering the input value as a whole.
const auto max_pos = std::max(lhs_digits, rhs_digits);
for (auto pos = 0; pos < max_pos; pos++) {
if (lhs_digits - pos == 0) {
// Ran out of digits on the LHS;
// prioritise the shorter input
return LHS_FIRST;
}
else if (rhs_digits - pos == 0) {
// Ran out of digits on the RHS;
// prioritise the shorter input
return RHS_FIRST;
}
else {
const auto lhs_x = (lhs / static_cast<decltype(BASE)>(std::pow(BASE, lhs_digits - 1 - pos))) % BASE;
const auto rhs_x = (rhs / static_cast<decltype(BASE)>(std::pow(BASE, rhs_digits - 1 - pos))) % BASE;
if (lhs_x < rhs_x)
return LHS_FIRST;
else if (rhs_x < lhs_x)
return RHS_FIRST;
}
}
// If we reached the end and everything still
// matches up, then something probably went wrong
// as I'd have expected to catch this in the tests
// for equality.
assert("Unknown case encountered");
// dyp: suppress warning and throw
throw "up";
}
);
}
};
namespace ndyp
{
// helper to provide integers with the same number of digits
template<class T, class U>
std::pair<T, T> lexicographic_pair_helper(T const p, U const maxDigits)
{
auto const digits = count_digits(p);
// append zeros so that `l` has `maxDigits` digits
auto const l = static_cast<T>( p * my_pow10(maxDigits-digits) );
return {l, p};
}
template<class RaIt>
using pair_vec
= std::vector<std::pair<typename std::iterator_traits<RaIt>::value_type,
typename std::iterator_traits<RaIt>::value_type>>;
template<class RaIt>
pair_vec<RaIt> lexicographic_sort(RaIt p_beg, RaIt p_end)
{
if(p_beg == p_end) return pair_vec<RaIt>{};
auto max = *std::max_element(p_beg, p_end);
auto maxDigits = count_digits(max);
pair_vec<RaIt> result;
result.reserve( std::distance(p_beg, p_end) );
for(auto i = p_beg; i != p_end; ++i)
result.push_back( lexicographic_pair_helper(*i, maxDigits) );
using value_type = typename pair_vec<RaIt>::value_type;
std::sort(begin(result), end(result),
[](value_type const& l, value_type const& r)
{
if(l.first < r.first) return true;
if(l.first > r.first) return false;
return l.second < r.second; }
);
return result;
}
}
struct dyp
{
template<class RaIt> void operator()(RaIt b, RaIt e)
{
auto pairvec = ndyp::lexicographic_sort(b, e);
std::transform(begin(pairvec), end(pairvec), b,
[](typename decltype(pairvec)::value_type const& e) { return e.second; });
}
};
namespace nnim
{
bool comp(int l, int r)
{
int lv[10] = {}; // probably possible to get this from numeric_limits
int rv[10] = {};
int lc = 10; // ditto
int rc = 10;
while (l || r)
{
if (l)
{
auto t = l / 10;
lv[--lc] = l - (t * 10);
l = t;
}
if (r)
{
auto t = r / 10;
rv[--rc] = r - (t * 10);
r = t;
}
}
while (lc < 10 && rc < 10)
{
if (lv[lc] == rv[rc])
{
lc++;
rc++;
}
else
return lv[lc] < rv[rc];
}
return lc > rc;
}
}
struct nim
{
template<class RaIt> void operator()(RaIt b, RaIt e)
{
std::sort(b, e, nnim::comp);
}
};
struct pts
{
template<class T> static bool lex_less(T a, T b) {
unsigned la = 1, lb = 1;
for (T t = a; t > 9; t /= 10) ++la;
for (T t = b; t > 9; t /= 10) ++lb;
const bool ll = la < lb;
while (la > lb) { b *= 10; ++lb; }
while (lb > la) { a *= 10; ++la; }
return a == b ? ll : a < b;
}
template<class RaIt> void operator()(RaIt b, RaIt e)
{
std::sort(b, e, lex_less<typename std::iterator_traits<RaIt>::value_type>);
}
};
struct epost
{
static bool compare(int x, int y)
{
static const double limit = .5 * (log(INT_MAX) - log(INT_MAX-1));
double lx = log10(x);
double ly = log10(y);
double fx = lx - floor(lx); // Get the mantissa of lx.
double fy = ly - floor(ly); // Get the mantissa of ly.
return fabs(fx - fy) < limit ? lx < ly : fx < fy;
}
template<class RaIt> void operator()(RaIt b, RaIt e)
{
std::sort(b, e, compare);
}
};
struct nyar
{
static bool lexiSmaller(int i1, int i2)
{
int digits1 = count_digits(i1);
int digits2 = count_digits(i2);
double val1 = i1/pow(10.0, digits1-1);
double val2 = i2/pow(10.0, digits2-1);
while (digits1 > 0 && digits2 > 0 && (int)val1 == (int)val2)
{
digits1--;
digits2--;
val1 = (val1 - (int)val1)*10;
val2 = (val2 - (int)val2)*10;
}
if (digits1 > 0 && digits2 > 0)
{
return (int)val1 < (int)val2;
}
return (digits2 > 0);
}
template<class RaIt> void operator()(RaIt b, RaIt e)
{
std::sort(b, e, lexiSmaller);
}
};
struct notbad
{
static int up_10pow(int n) {
int ans = 1;
while (ans < n) ans *= 10;
return ans;
}
static bool compare(int v1, int v2) {
int ceil1 = up_10pow(v1), ceil2 = up_10pow(v2);
while ( ceil1 != 0 && ceil2 != 0) {
if (v1 / ceil1 < v2 / ceil2) return true;
else if (v1 / ceil1 > v2 / ceil2) return false;
ceil1 /= 10;
ceil2 /= 10;
}
if (v1 < v2) return true;
return false;
}
template<class RaIt> void operator()(RaIt b, RaIt e)
{
std::sort(b, e, compare);
}
};
I believe the following works as a sort comparison function for positive integers provided the integer type used is substantially narrower than the double type (e.g., 32-bit int and 64-bit double) and the log10 routine used returns exactly correct results for exact powers of 10 (which a good implementation does):
static const double limit = .5 * (log(INT_MAX) - log(INT_MAX-1));
double lx = log10(x);
double ly = log10(y);
double fx = lx - floor(lx); // Get the mantissa of lx.
double fy = ly - floor(ly); // Get the mantissa of ly.
return fabs(fx - fy) < limit ? lx < ly : fx < fy;
It works by comparing the mantissas of the logarithms. The mantissas are the fractional parts of the logarithm, and they indicate the value of the significant digits of a number without the magnitude (e.g., the logarithms of 31, 3.1, and 310 have exactly the same mantissa).
The purpose of fabs(fx - fy) < limit is to allow for errors in taking the logarithm, which occur both because implementations of log10 are imperfect and because the floating-point format forces some error. (The integer portions of the logarithms of 31 and 310 use different numbers of bits, so there are different numbers of bits left for the significand, so they end up being rounded to slightly different values.) As long as the integer type is substantially narrower than the double type, the calculated limit will be much larger than the error in log10. Thus, the test fabs(fx - fy) < limit essentially tells us whether two calculated mantissas would be equal if calculated exactly.
If the mantissas differ, they indicate the lexicographic order, so we return fx < fy. If they are equal, then the integer portion of the logarithm tells us the order, so we return lx < ly.
It is simple to test whether log10 returns correct results for every power of ten, since there are so few of them. If it does not, adjustments can be made easily: Insert if (1-fx < limit) fx = 0; if (1-fu < limit) fy = 0;. This allows for when log10 returns something like 4.99999… when it should have returned 5.
This method has the advantage of not using loops or division (which is time-consuming on many processors).
The task sounds like a natural fit for an MSD variant of Radix Sort with padding ( http://en.wikipedia.org/wiki/Radix_sort ).
Depends on how much code you want to throw at it. The simple code as the others show is O(log n) complexity, while a fully optimized radix sort would be O(kn).
A compact solution if all your numbers are nonnegative and they are small enough so that multiplying them by 10 doesn't cause an overflow:
template<class T> bool lex_less(T a, T b) {
unsigned la = 1, lb = 1;
for (T t = a; t > 9; t /= 10) ++la;
for (T t = b; t > 9; t /= 10) ++lb;
const bool ll = la < lb;
while (la > lb) { b *= 10; ++lb; }
while (lb > la) { a *= 10; ++la; }
return a == b ? ll : a < b;
}
Run it like this:
#include <iostream>
#include <algorithm>
int main(int, char **) {
unsigned short input[] = { 100, 21 , 22 , 99 , 1 , 927 };
unsigned input_size = sizeof(input) / sizeof(input[0]);
std::sort(input, input + input_size, lex_less<unsigned short>);
for (unsigned i = 0; i < input_size; ++i) {
std::cout << ' ' << input[i];
}
std::cout << std::endl;
return 0;
}
You could try using the % operator to give you access to each individual digit eg 121 % 100 will give you the first digit and check that way but you'll have to find a way to get around the fact they have different sizes.
So find the maximum value in array. I don't know if theres a function for this in built you could try.
int Max (int* pdata,int size)
{
int temp_max =0 ;
for (int i =0 ; i < size ; i++)
{
if (*(pdata+i) > temp_max)
{
temp_max = *(pdata+i);
}
}
return temp_max;
}
This function will return the number of digits in the number
int Digit_checker(int n)
{
int num_digits = 1;
while (true)
{
if ((n % 10) == n)
return num_digits;
num_digits++;
n = n/10;
}
return num_digits;
}
Let number of digits in max equal n.
Once you have this open a for loop in the format of
for (int i = 1; i < n ; i++)
then you can go through your and use "data[i] % (10^(n-i))" to get access to the first digit then
sort that and then on the next iteration you'll get access to the second digit. I Don't know how you'll sort them though.
It wont work for negative numbers and you'll have to get around data[i] % (10^(n-i)) returning itself for numbers with less digits than max
Overload the < operator to compare two integers lexicographically. For each integer, find the smallest 10^k, which is not less than the given integer. Than compare the digits one by one.
class CmpIntLex {
int up_10pow(int n) {
int ans = 1;
while (ans < n) ans *= 10;
return ans;
}
public:
bool operator ()(int v1, int v2) {
int ceil1 = up_10pow(v1), ceil2 = up_10pow(v2);
while ( ceil1 != 0 && ceil2 != 0) {
if (v1 / ceil1 < v2 / ceil2) return true;
else if (v1 / ceil1 > v2 / ceil2) return false;
ceil1 /= 10;
ceil2 /= 10;
}
if (v1 < v2) return true;
return false;
}
int main() {
vector<int> vi = {12,45,12134,85};
sort(vi.begin(), vi.end(), CmpIntLex());
}
While some other answers here (Lightness's, notbad's) are already showing quite good code, I believe I can add one solution which might be more performant (since it requires neither division nor power in each loop; but it requires floating point arithmetic, which again might make it slow, and possibly inaccurate for large numbers):
#include <algorithm>
#include <iostream>
#include <assert.h>
// method taken from http://stackoverflow.com/a/1489873/671366
template <class T>
int numDigits(T number)
{
int digits = 0;
if (number < 0) digits = 1; // remove this line if '-' counts as a digit
while (number) {
number /= 10;
digits++;
}
return digits;
}
bool lexiSmaller(int i1, int i2)
{
int digits1 = numDigits(i1);
int digits2 = numDigits(i2);
double val1 = i1/pow(10.0, digits1-1);
double val2 = i2/pow(10.0, digits2-1);
while (digits1 > 0 && digits2 > 0 && (int)val1 == (int)val2)
{
digits1--;
digits2--;
val1 = (val1 - (int)val1)*10;
val2 = (val2 - (int)val2)*10;
}
if (digits1 > 0 && digits2 > 0)
{
return (int)val1 < (int)val2;
}
return (digits2 > 0);
}
int main(int argc, char* argv[])
{
// just testing whether the comparison function works as expected:
assert (lexiSmaller(1, 100));
assert (!lexiSmaller(100, 1));
assert (lexiSmaller(100, 22));
assert (!lexiSmaller(22, 100));
assert (lexiSmaller(927, 99));
assert (!lexiSmaller(99, 927));
assert (lexiSmaller(1, 927));
assert (!lexiSmaller(927, 1));
assert (lexiSmaller(21, 22));
assert (!lexiSmaller(22, 21));
assert (lexiSmaller(22, 99));
assert (!lexiSmaller(99, 22));
// use the comparison function for the actual sorting:
int input[] = { 100 , 21 , 22 , 99 , 1 ,927 };
std::sort(&input[0], &input[5], lexiSmaller);
std::cout << "sorted: ";
for (int i=0; i<6; ++i)
{
std::cout << input[i];
if (i<5)
{
std::cout << ", ";
}
}
std::cout << std::endl;
return 0;
}
Though I have to admit I haven't tested the performance yet.
Here is the dumb solution that doesn't use any floating point tricks. It's pretty much the same as the string comparison, but doesn't use a string per say, doesn't also handle negative numbers, to do that add a section at the top...
bool comp(int l, int r)
{
int lv[10] = {}; // probably possible to get this from numeric_limits
int rv[10] = {};
int lc = 10; // ditto
int rc = 10;
while (l || r)
{
if (l)
{
auto t = l / 10;
lv[--lc] = l - (t * 10);
l = t;
}
if (r)
{
auto t = r / 10;
rv[--rc] = r - (t * 10);
r = t;
}
}
while (lc < 10 && rc < 10)
{
if (lv[lc] == rv[rc])
{
lc++;
rc++;
}
else
return lv[lc] < rv[rc];
}
return lc > rc;
}
It's fast, and I'm sure it's possible to make it faster still, but it works and it's dumb enough to understand...
EDIT: I ate to dump lots of code, but here is a comparison of all the solutions so far..
#include <iostream>
#include <vector>
#include <algorithm>
#include <iterator>
#include <random>
#include <vector>
#include <utility>
#include <cmath>
#include <cassert>
#include <chrono>
std::pair<int, int> lexicographic_pair_helper(int p, int maxDigits)
{
int digits = std::log10(p);
int l = p*std::pow(10, maxDigits-digits);
return {l, p};
}
bool l_comp(int l, int r)
{
int lv[10] = {}; // probably possible to get this from numeric_limits
int rv[10] = {};
int lc = 10; // ditto
int rc = 10;
while (l || r)
{
if (l)
{
auto t = l / 10;
lv[--lc] = l - (t * 10);
l = t;
}
if (r)
{
auto t = r / 10;
rv[--rc] = r - (t * 10);
r = t;
}
}
while (lc < 10 && rc < 10)
{
if (lv[lc] == rv[rc])
{
lc++;
rc++;
}
else
return lv[lc] < rv[rc];
}
return lc > rc;
}
int up_10pow(int n) {
int ans = 1;
while (ans < n) ans *= 10;
return ans;
}
bool l_comp2(int v1, int v2) {
int n1 = up_10pow(v1), n2 = up_10pow(v2);
while ( v1 != 0 && v2 != 0) {
if (v1 / n1 < v2 / n2) return true;
else if (v1 / n1 > v2 / n2) return false;
v1 /= 10;
v2 /= 10;
n1 /= 10;
n2 /= 10;
}
if (v1 == 0 && v2 != 0) return true;
return false;
}
int main()
{
std::vector<int> numbers;
{
constexpr int number_of_elements = 1E6;
std::random_device rd;
std::mt19937 gen( rd() );
std::uniform_int_distribution<> dist;
for(int i = 0; i < number_of_elements; ++i) numbers.push_back( dist(gen) );
}
std::vector<int> lo(numbers);
std::vector<int> dyp(numbers);
std::vector<int> nim(numbers);
std::vector<int> nb(numbers);
std::cout << "starting..." << std::endl;
{
auto start = std::chrono::high_resolution_clock::now();
/**
* Sorts the array lexicographically.
*
* The trick is that we have to compare digits left-to-right
* (considering typical Latin decimal notation) and that each of
* two numbers to compare may have a different number of digits.
*
* This probably isn't very efficient, so I wouldn't do it on
* "millions" of numbers. But, it works...
*/
std::sort(
std::begin(lo),
std::end(lo),
[](int lhs, int rhs) -> bool {
// Returns true if lhs < rhs
// Returns false otherwise
const auto BASE = 10;
const bool LHS_FIRST = true;
const bool RHS_FIRST = false;
const bool EQUAL = false;
// There's no point in doing anything at all
// if both inputs are the same; strict-weak
// ordering requires that we return `false`
// in this case.
if (lhs == rhs) {
return EQUAL;
}
// Compensate for sign
if (lhs < 0 && rhs < 0) {
// When both are negative, sign on its own yields
// no clear ordering between the two arguments.
//
// Remove the sign and continue as for positive
// numbers.
lhs *= -1;
rhs *= -1;
}
else if (lhs < 0) {
// When the LHS is negative but the RHS is not,
// consider the LHS "first" always as we wish to
// prioritise the leading '-'.
return LHS_FIRST;
}
else if (rhs < 0) {
// When the RHS is negative but the LHS is not,
// consider the RHS "first" always as we wish to
// prioritise the leading '-'.
return RHS_FIRST;
}
// Counting the number of digits in both the LHS and RHS
// arguments is *almost* trivial.
const auto lhs_digits = (
lhs == 0
? 1
: std::ceil(std::log(lhs+1)/std::log(BASE))
);
const auto rhs_digits = (
rhs == 0
? 1
: std::ceil(std::log(rhs+1)/std::log(BASE))
);
// Now we loop through the positions, left-to-right,
// calculating the digit at these positions for each
// input, and comparing them numerically. The
// lexicographic nature of the sorting comes from the
// fact that we are doing this per-digit comparison
// rather than considering the input value as a whole.
const auto max_pos = std::max(lhs_digits, rhs_digits);
for (auto pos = 0; pos < max_pos; pos++) {
if (lhs_digits - pos == 0) {
// Ran out of digits on the LHS;
// prioritise the shorter input
return LHS_FIRST;
}
else if (rhs_digits - pos == 0) {
// Ran out of digits on the RHS;
// prioritise the shorter input
return RHS_FIRST;
}
else {
const auto lhs_x = (lhs / static_cast<decltype(BASE)>(std::pow(BASE, lhs_digits - 1 - pos))) % BASE;
const auto rhs_x = (rhs / static_cast<decltype(BASE)>(std::pow(BASE, rhs_digits - 1 - pos))) % BASE;
if (lhs_x < rhs_x)
return LHS_FIRST;
else if (rhs_x < lhs_x)
return RHS_FIRST;
}
}
// If we reached the end and everything still
// matches up, then something probably went wrong
// as I'd have expected to catch this in the tests
// for equality.
assert("Unknown case encountered");
}
);
auto end = std::chrono::high_resolution_clock::now();
auto elapsed = end - start;
std::cout << "Lightness: " << elapsed.count() << '\n';
}
{
auto start = std::chrono::high_resolution_clock::now();
auto max = *std::max_element(begin(dyp), end(dyp));
int maxDigits = std::log10(max);
std::vector<std::pair<int,int>> temp;
temp.reserve(dyp.size());
for(auto const& e : dyp) temp.push_back( lexicographic_pair_helper(e, maxDigits) );
std::sort(begin(temp), end(temp), [](std::pair<int, int> const& l, std::pair<int, int> const& r)
{ if(l.first < r.first) return true; if(l.first > r.first) return false; return l.second < r.second; });
auto end = std::chrono::high_resolution_clock::now();
auto elapsed = end - start;
std::cout << "Dyp: " << elapsed.count() << '\n';
}
{
auto start = std::chrono::high_resolution_clock::now();
std::sort (nim.begin(), nim.end(), l_comp);
auto end = std::chrono::high_resolution_clock::now();
auto elapsed = end - start;
std::cout << "Nim: " << elapsed.count() << '\n';
}
// {
// auto start = std::chrono::high_resolution_clock::now();
// std::sort (nb.begin(), nb.end(), l_comp2);
// auto end = std::chrono::high_resolution_clock::now();
// auto elapsed = end - start;
// std::cout << "notbad: " << elapsed.count() << '\n';
// }
std::cout << (nim == lo) << std::endl;
std::cout << (nim == dyp) << std::endl;
std::cout << (lo == dyp) << std::endl;
// std::cout << (lo == nb) << std::endl;
}
Based on #Oswald's answer, below is some code that does the same.
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
bool compare(string a, string b){
// Check each digit
int i = 0, j = 0;
while(i < a.size() && j < b.size()){
// If different digits
if(a[i] - '0' != b[j] - '0')
return (a[i] - '0' < b[j] - '0');
i++, j++;
}
// Different sizes
return (a.size() < b.size());
}
int main(){
vector<string> array = {"1","2","3","4","5","6","7","8","9","10","11","12"};
sort(array.begin(), array.end(), compare);
for(auto value : array)
cout << value << " ";
return 0;
}
Input: 1 2 3 4 5 6 7 8 9 10 11 12
Output: 1 10 11 12 2 3 4 5 6 7 8 9