I am currently working on a algorithm that needs to find all equal occurrences a an item in a matrix. I decided to use uBLAS matrices from boost. So my problem is:
I have a ublas::matrix looking like:
1 2 3 4 5
2 4 6 8 1
1 5 4 6 8
9 4 6 7 0
and I want to find all positions (x,y) of i.e. the value 6.
Is there a function for?
There is no ublas-specific function (as far as I can tell), you will have to scan the matrix the usual way -- through iterators or through indexed access:
typedef std::vector<std::pair<size_t, size_t> > posvec_t;
template <typename T>
posvec_t find_all(const ublas::matrix<T>& m, T val)
{
posvec_t ret;
for(size_t r=0; r<m.size1(); ++r)
for(size_t c=0; c<m.size2(); ++c)
if(m(r,c) == val)
ret.push_back( std::make_pair(r, c) );
return ret;
}
test: https://ideone.com/qhW9b
Related
Given a subset of nodes {1,2,...,N} is there any STL or boost function that returns unique undirected tours over all of them?
std::next_permutation() gives all N! directed tours, where 1-2-...-N is different from N-N-1-...-2-1.
However, in this case, I don't want both of them, but only one of them. Essentially, I would like to enumerate only N! / 2 of the tours.
The following code that uses std::next_permutation() and unordered_set works, but is there anything more efficient? The following code essentially generates all N! directed tours and discards half of them after checking against an unordered_set().
#include <vector>
#include <unordered_set>
#include <algorithm>
#include <boost/functional/hash.hpp>
template <typename T, typename U> bool unorderedset_val_there_already_add_if_not(std::unordered_set<T, U>& uos, T& val) {
if (uos.find(val) != uos.end())
return true;//val already there
uos.insert(val);
return false;//Value is new.
}
int main() {
std::vector<int> sequence{ 1, 2, 3};
std::unordered_set<std::vector<int>, boost::hash<std::vector<int>>> uos;
do {
printf("Considering ");
for (std::size_t i = 0; i < sequence.size(); i++)
printf("%d ", sequence[i]);
printf("\n");
std::vector<int> rev_sequence = sequence;
std::reverse(rev_sequence.begin(), rev_sequence.end());
if (unorderedset_val_there_already_add_if_not(uos, sequence) || unorderedset_val_there_already_add_if_not(uos, rev_sequence)) {
printf("Already there by itself or its reverse.\n");
}
else {
printf("Sequence and its reverse are new.\n");
}
} while (std::next_permutation(sequence.begin(), sequence.end()));
getchar();
}
That is, given {1,2,3}, I only want to enumerate (1-2-3), (1-3-2) and (2-1-3). The other three permutations (2-3-1), (3-1-2) and (3-2-1) should not be enumerated because their reverse sequence have already been enumerated.
If you want to stay with next_permutation rather than make own generator routine, the simplest way is filter out a half of permutation with some condition.
Very simple one: the last element should be larger than the first one.
#include <vector>
#include <algorithm>
#include "stdio.h"
int main() {
std::vector<int> sequence{ 1, 2, 3, 4};
do {
if (sequence[sequence.size()-1] > sequence[0]) {
for (std::size_t i = 0; i < sequence.size(); i++)
printf("%d ", sequence[i]);
printf("\n");
}
} while (std::next_permutation(sequence.begin(), sequence.end()));
getchar();
}
1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 4 1 3
3 1 2 4
3 2 1 4
Possible own implementation:
Generate all pairs (start; end) where start < end
Generate all permutations of `n-2` values without start and end
For every permutation make {start, permutation.., end}
1 ... 2 + permutations of {3, 4}
1 3 4 2
1 4 3 2
1 ... 3 + permutations of {2,4}
1 2 4 3
1 4 2 3
...
3 ... 4 + permutations of {1, 2}
3 1 2 4
3 2 1 4
...
Suppose you have a 2D vector defined as follows:
std::vector<vector<int>> v
and which represents a matrix:
1 1 0 1 3
0 4 6 0 1
5 0 0 3 0
6 3 0 2 5
I want to stable-partition (say with predicate el != 0) this matrix, but in all directions. This means that I want to be able to get:
1 1 6 1 3 0 0 0 0 0 1 1 1 3 0 0 1 1 1 3
5 4 0 3 1 1 1 0 1 3 4 6 1 0 0 0 0 4 6 1
6 3 0 2 5 5 4 0 3 1 5 3 0 0 0 0 0 0 5 3
0 0 0 0 0 6 3 6 2 5 6 3 2 5 0 0 6 3 2 5
(down) (up) (right) (left)
For two directions, this can be done very simply by iterating through the outer vector and partitioning the inner vectors (in order or in reverse). However for the other directions I do not know how to go about doing the same.
Is there a way to achieve this using std::stable_partition. Is there maybe another data structure (which supports indexing like vectors) which will allow me to do this more easily?
If I have ti implement this by scratch, is there maybe a standard or recommended way to do it?
You don't need to write your own implementation of the algorithm. Iterators are the customization point when you want to use an existing algorithm for a custom data structure. Unfortunately, writing your own iterator requires quite some boilerplate. I think boost can help, but if you want to stay with what the standard library offers, to my knowledge there is no way around writing it yourself.
The following is to be taken with a grain of salt. I assume all inner vectors are of same size. I do not take into account const_iterators, because you wont need them to use std::stable_partition. I have omitted some member functions that you will have to add yourself. The algorithm requires the iterator to adhere to two named concepts, namely LegacyBidirectionalIterator and ValueSwappable. That being said, here is how you can implement an iterator that enables you to iterate columns of the 2d vector:
#include <iostream>
#include <vector>
struct vector2d_col_iterator {
using container_t = std::vector<std::vector<int>>;
container_t& container;
size_t row;
size_t col;
vector2d_col_iterator& operator++(){
++row;
return *this;
}
bool operator==(const vector2d_col_iterator& other) const {
return col == other.col && row == other.row;
}
bool operator !=(const vector2d_col_iterator& other) const {
return !(*this == other);
}
int& operator*() { return container[row][col]; }
static vector2d_col_iterator begin(container_t& container,int col) {
return {container,0,col};
}
static vector2d_col_iterator end(container_t& container,int col) {
return {container,container.size(),col};
}
};
int main() {
std::vector<std::vector<int>> v{ {1,2,3},{4,5,6}};
auto begin = vector2d_col_iterator::begin(v,1);
auto end = vector2d_col_iterator::end(v,1);
for ( ; begin != end; ++begin) std::cout << *begin << " ";
}
Output:
2 5
Live example
Efficiency is not a really big issue, the matrices will be relatively small. I just want to find the simplest, clearest way of doing this. Preferably without having to write a stable_partition implementation from scratch.
If the matrices are really small (lets say ~20x20 elements) and efficiency is really not a concern, then the simplest is perhaps to use std::stable_partition only on the inner vectors. You can transpose the matrix, call the algorithm in a loop for all inner vectors, transpose again. Done. Thats basically ~10 lines of code. Your choice ;)
With range-v3, you might do:
const std::vector<std::vector<int>> v = /*..*/;
auto is_zero = [](int e){ return e == 0; };
auto right = v;
for (auto& row : right) {
ranges::stable_partition(row | ranges::view::reverse, is_zero);
}
print(right);
auto top = v;
for (std::size_t i = 0; i != v[0].size(); ++i) {
auto col_view = top | ranges::view::transform([i](auto& row)-> int& { return row[i]; });
ranges::stable_partition(col_view, is_zero);
}
print(top);
Demo
I have come across a problem where we want to tell the maximum size of the longest increasing sub-sequence.
an array A consisting of N integers.
M queries (Li, Ri)
for each query we wants to find the length of the longest increasing subsequence in
array A[Li], A[Li + 1], ..., A[Ri].
I implemented finding the sub-sequence using dp approach
// mind the REPN, LLD, these are macros I use for programming
// LLD = long long int
// REPN(i, a, b) = for (int i = a; i < b; ++i)
LLD a[n], dp[n];
REPN(i, 0, n)
{
scanf("%lld", &a[i]);
dp[i] = 1;
}
REPN(i, 1, n)
{
REPN(j, 0, i)
{
if(a[i] > a[j])
dp[i] = std::max(dp[j] + 1, dp[i]);
}
}
For example:
Array: 1 3 8 9 7 2 4 5 10 6
dplis: 1 2 3 4 3 1 3 4 5 5
max: 5
But if it was for range Li=2 & Ri=9
Then:
Array: 3 8 9 7 2 4 5 10
dplis: 1 2 3 2 1 2 3 4
max: 4
How can i determine the maximum longest increasing sub-sequence in a sub array?
PS: I don't want to recompute the whole dplis array, I want to use the original one because too much computation will kill the purpose of the question.
One of the approaches was to construct a complete 2D DP array that consists of sub-sequence from position i where range of i is from 0 to n, but it fails on many cases due to TLE(Time limit exceeded)
REPN(k,0,n) {
REPN(i,k+1,n) {
REPN(j,k,i) {
if(a[i]>a[j]) dp[k][i]=std::max(dp[k][j]+1, dp[k][i]);
}
}
}
REPN(i,0,q) {
read(l); read(r);
LLD max=-1;
REPN(i,0,r) {
if(max<dp[l-1][i]) max=dp[l-1][i];
}
printf("%lld\n", max);
}
If you have any new logic/implementation, I will gladly study it in-depth. Cheers.
This question already exists:
Recursion all combinations of lower triangle C++
Closed 8 years ago.
I recently posted a poor question on how to use recursion to estimate all combinations of lower triangle in C++. I managed to find a recursive algorithm that given an array of size n, generates and prints all possible combinations of r elements in array. I've employed this function using Rcpp in R. I've then written a loop around this function to get all the subsets of combinations r to r + n.
#include <Rcpp.h>
using namespace Rcpp;
// [[Rcpp::export]]
int recursive(IntegerVector arr, IntegerVector data, int start, int end, int index, int r)
{
if (index == r)
{
for (int j=0; j<r; j++)
printf("%d ", data[j]);
printf("\n");
}
for (int i=start; i<=end && end-i+1 >= r-index; i++)
{
data[index] = arr[i];
recursive(arr, data, i+1, end, index+1, r);
}
}
R code with five groups:
Rcpp::sourceCpp('recursive2.cpp')
nComm <- 5
r <- c(2:nComm)
n <- nComm
arr <- c(1:nComm)
dat <- c(1:nComm)
for(i in 1:(n-1)){
recursive(arr, dat, 0, n-1, 0, r[i])
}
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5
1 2 3
1 2 4
1 2 5
1 3 4
1 3 5
1 4 5
2 3 4
2 3 5
2 4 5
3 4 5
1 2 3 4
1 2 3 5
1 2 4 5
1 3 4 5
2 3 4 5
1 2 3 4 5
Currently, this just prints the subsets of combinations I need to estimate my dissimilarities. I'd like to be able to remove the loop and use it as a single Rcpp function/script. With the end goal to be able to use the subsets (currently printed combinations) as way to subset rows in an array. Which will be used to calculate the intersect between vectors. So 1 2 will be used to compare rows 1 and 2 in an array. And so forth.
I've created a map having a vector as below:
map<int,vector<int>> mymap;
How can I sort this map according to the nth value of the vector contained by map?
You can't. You can provide a custom comparator to make the underlying data get sorted another way than the default, but this only relates to keys, not values. If you have a requirement for your container's elements to exist in some specific, value-defined order, then you're using the wrong container.
You can switch to a set, and take advantage of the fact that there is no distinction there between "key" and "value", and hack the underlying sorting yourself:
template <std::size_t N>
struct MyComparator
{
typedef std::pair<int, std::vector<int>> value_type;
bool operator()(const value_type& lhs, const value_type& rhs)
{
return lhs.second.at(N) < rhs.second.at(N);
}
};
/**
* A set of (int, int{2,}) pairs, sorted by the 2nd element in
* the 2nd item of each pair.
*/
std::set<std::pair<int, std::vector<int>>, MyComparator<1>> my_data;
int main()
{
my_data.insert(std::make_pair(1, std::vector<int>{0,5,0,0}));
my_data.insert(std::make_pair(2, std::vector<int>{0,2,0,0}));
my_data.insert(std::make_pair(3, std::vector<int>{0,1,0,0}));
my_data.insert(std::make_pair(4, std::vector<int>{0,9,0,0}));
for (const auto& el : my_data)
std::cout << el.first << ' ';
}
// Output: 3 2 1 4
(live demo)
However, if you still need to perform lookup on key as well, then you're really in trouble and need to rethink some things. You may need to duplicate your data or provide an indexing vector.
map<int,vector<int>> mymap;
How can i sort this map according to the nth value of the vector contained by map?
That's only possible if you're prepared to use that nth value as the integer key too, as in consistently assigning:
mymap[v[n - 1]] = v;
If you're doing that, you might consider a set<vector<int>>, which removes the redundant storage of that "key" element - you would then need to provide a custom comparison though....
If you envisage taking an existing populated map that doesn't have that ordering, then sorting its elements - that's totally impossible. You'll have to copy the elements out to another container, such as a set that's ordered on the nth element, or a vector that you std::sort after populating.
If I have understood correctly you can (build) add elements to the map the following way
std::vector<int> v = { 1, 2, 3 };
std::vector<int>::size_type n = 2;
mymap[v[n]] = v;
Here is an example
#include <iostream>
#include <vector>
#include <map>
#include <algorithm>
#include <cstdlib>
#include <ctime>
int main()
{
std::srand( ( unsigned )time( 0 ) );
const size_t N = 10;
std::map<int, std::vector<int>> m;
for ( size_t i = 0; i < N; i++ )
{
std::vector<int> v( N );
std::generate( v.begin(), v.end(), []{ return std::rand() % N; } );
m[v[0]] = v;
}
for ( auto &p : m )
{
for ( int x : p.second ) std::cout << x << ' ';
std::cout << std::endl;
}
return 0;
}
The output is
0 1 7 8 1 2 9 0 0 9
1 6 3 1 3 5 0 3 1 5
3 8 0 0 0 7 1 2 9 7
5 9 5 0 7 1 2 0 6 3
6 4 7 5 4 0 0 4 2 0
7 9 8 6 5 5 9 9 4 5
8 3 8 0 5 9 6 6 8 3
9 5 4 7 4 0 3 5 1 9
Take into account that as there can be duplicated vectors (that is that have the same value of the n-th element (in my example n is equal to 0) then some vectors will not be added to the map. If you want to have duplicates then you should use for example std::multimap
Also you can build a new map according to the criteria based on an existent map.
You can abuse the fact a c++ map uses a tree sorted by its keys. This means that you can either create a new map, with as keys the values you wish it to be sorted on, but you can also create a vector with references to the items in your map, and sort that vector (or the other way around: you could have a sorted vector, and use a map to create an index on your vector). Be sure to use a multimap in the case of duplicate keys.