I currently have a vector and need to find the n largest numbers in it. For example, a user enters 5, i gotta run through it and output the 5 largest. Problem is, i can not sort this vector due to other constraints. Whats the best way to go about this?
Thanks!
Based on your description of not modifying the original vector and my assumption that you want the order to matter, I suggest std::partial_sort_copy:
//assume vector<int> as source
std::vector<int> dest(n); //largest n numbers; VLA or std::dynarray in C++14
std::partial_sort_copy(
std::begin(source), std::end(source), //.begin/.end in C++98/C++03
std::begin(dest), std::end(dest),
std::greater<int>() //remove "int" in C++14
);
//output dest however you want, e.g., std::copy
Is copying and sorting an option? I mean if your application is not that performance critical, this is the simplest (and asymptotically not too bad) way to go!
Something like this (A is incoming vector, N the number largest you want to find, v becomes the result vector):
vector<T> v(N, 0);
for each element in A:
if (element > v[N-1])
for(i = N-1; i > 0 && v[i] < element; i--)
v[i] = v[i-1];
v[i] = element;
This is some sort of "pseudo-C++", not exactly C++, but hopefully describes how you'd do this.
Related
I think this is a fairly common question but I didn't find any answer for this using hashing in C++.
I have two arrays, both of the same lengths, which contain some elements, for example:
A={5,3,5,4,2}
B={3,4,1,2,1}
Here, the uncommon elements are: {5,5,1,1}
I have tried this approach- iterating a while loop on both the arrays after sorting:
while(i<n && j<n) {
if(a[i]<b[j])
uncommon[k++]=a[i++];
else if (a[i] > b[j])
uncommon[k++]=b[j++];
else {
i++;
j++;
}
}
while(i<n && a[i]!=b[j-1])
uncommon[k++]=a[i++];
while(j < n && b[j]!=a[i-1])
uncommon[k++]=b[j++];
and I am getting the correct answer with this. However, I want a better approach in terms of time complexity since sorting both arrays every time might be computationally expensive.
I tried to do hashing but couldn't figure it out entirely.
To insert elements from arr1[]:
set<int> uncommon;
for (int i=0;i<n1;i++)
uncommon.insert(arr1[i]);
To compare arr2[] elements:
for (int i = 0; i < n2; i++)
if (uncommon.find(arr2[i]) != uncommon.end())
Now, what I am unable to do is to send only those elements to the uncommon array[] which are uncommon to both of them.
Thank you!
First of all, std::set does not have anything to do with hashing. Sets and maps are ordered containers. Implementations may differ, but most likely it is a binary search tree. Whatever you do, you wont get faster that nlogn with them - the same complexity as sorting.
If you're fine with nlogn and sorting, I'd strongly advice just using set_symmetric_difference algorithm https://en.cppreference.com/w/cpp/algorithm/set_symmetric_difference , it requires two sorted containers.
But if you insist on an implementation relying on hashing, you should use std::unordered_set or std::unordered_map. This way you can be faster than nlogn. You can get your answer in nm time, where n = a.size() and m = b.size(). You should create two unordered_set`s: hashed_a, hashed_b and in two loops check what elements from hashed_a are not in hashed_b, and what elements in hashed_b are not in hashed_a. Here a pseudocode:
create hashed_a and hashed_b
create set_result // for the result
for (a_v : hashed_a)
if (a_v not in hashed_b)
set_result.insert(a_v)
for (b_v : hashed_b)
if (b_v not in hashed_a)
set_result.insert(b_v)
return set_result // it holds the symmetric diference, which you need
UPDATE: as noted in the comments, my answer doesn't count for duplicates. The easiest way to modify it for duplicates would be to use unordered_map<int, int> with the keys for elements in the set and values for number of encounters.
First, you need to find a way to distinguish between the same values contained in the same array (for ex. 5 and 5 in the first array, and 1 and 1 in the second array). This is the key to reducing the overall complexity, otherwise you can't do better than O(nlogn). A good possible algorithm for this task is to create a wrapper object to hold your actual values, and put in your arrays pointers to those wrapper objects with actual data, so your pointer addresses will serve as a unique identifier for objects. This wrapping will cost you just O(n1+n2) operations, but also an additional O(n1+n2) space.
Now your problem is that you have in both arrays only elements unique to each of those arrays, and you want to find the uncommon elements. This means the (Union of both array elements) - (Intersection of both array elements). Therefore, all you need to do is to push all the elements of the first array into a hash-map (complexity O(n1)), and then start pushing all the elements of the second array into the same hash-map (complexity O(n2)), by detecting the collisions (equality of an element from first array with an element from the second array). This comparison step will require O(n2) comparisons in the worst case. So for the maximum performance optimization you could have checked the size of the arrays before starting pushing the elements into the hash-map, and swap the arrays so that the first push will take place with the longest array. Your overall algorithm complexity would be O(n1+n2) pushes (hashings) and O(n2) comparisons.
The implementation is the most boring stuff, so I let it to you ;)
A solution without sorting (and without hashing but you seem to care more about complexity then the hashing itself) is to notice the following : an uncommon element e is an element that is in exactly one multiset.
This means that the multiset of all uncommon elements is the union between 2 multisets:
S1 = The element in A that are not in B
S2 = The element in B that are not in A
Using the std::set_difference, you get:
#include <set>
#include <vector>
#include <iostream>
#include <algorithm>
int main() {
std::multiset<int> ms1{5,3,5,4,2};
std::multiset<int> ms2{3,4,1,2,1};
std::vector<int> v;
std::set_difference( ms1.begin(), ms1.end(), ms2.begin(), ms2.end(), std::back_inserter(v));
std::set_difference( ms2.begin(), ms2.end(), ms1.begin(), ms1.end(), std::back_inserter(v));
for(int e : v)
std::cout << e << ' ';
return 0;
}
Output:
5 5 1 1
The complexity of this code is 4.(N1+N2 -1) where N1 and N2 are the size of the multisets.
Links:
set_difference: https://en.cppreference.com/w/cpp/algorithm/set_difference
compiler explorer: https://godbolt.org/z/o3KGbf
The Question can Be solved in O(nlogn) time-complexity.
ALGORITHM
Sort both array with merge sort in O(nlogn) complexity. You can also use sort-function. For example sort(array1.begin(),array1.end()).
Now use two pointer method to remove all common elements on both arrays.
Program of above Method
int i = 0, j = 0;
while (i < array1.size() && j < array2.size()) {
// If not common, print smaller
if (array1[i] < array2[j]) {
cout << array1[i] << " ";
i++;
}
else if (array2[j] < array1[i]) {
cout << array2[j] << " ";
j++;
}
// Skip common element
else {
i++;
j++;
}
}
Complexity of above program is O(array1.size() + array2.size()). In worst case say O(2n)
The above program gives the uncommon elements as output. If you want to store them , just create a vector and push them into vector.
Original Problem LINK
Question
I have two arrays of integers A[] and B[]. Array B[] is fixed, I need to to find the permutation of A[] which is lexiographically smaller than B[] and the permutation is nearest to B[]. Here what I mean is:
for i in (0 <= i < n)
abs(B[i]-A[i]) is minimum and A[] should be smaller than B[] lexiographically.
For Example:
A[]={1,3,5,6,7}
B[]={7,3,2,4,6}
So,possible nearest permutation of A[] to B[] is
A[]={7,3,1,6,5}
My Approach
Try all permutation of A[] and then compare that with B[]. But the time complexity would be (n! * n)
So is there any way to optimize this?
EDIT
n can be as large as 10^5
For better understanding
First, build an ordered map of the counts of the distinct elements of A.
Then, iterate forward through array indices (0 to n−1), "withdrawing" elements from this map. At each point, there are three possibilities:
If i < n-1, and it's possible to choose A[i] == B[i], do so and continue iterating forward.
Otherwise, if it's possible to choose A[i] < B[i], choose the greatest possible value for A[i] < B[i]. Then proceed by choosing the largest available values for all subsequent array indices. (At this point you no longer need to worry about maintaining A[i] <= B[i], because we're already after an index where A[i] < B[i].) Return the result.
Otherwise, we need to backtrack to the last index where it was possible to choose A[i] < B[i], then use the approach in the previous bullet-point.
Note that, despite the need for backtracking, the very worst case here is three passes: one forward pass using the logic in the first bullet-point, one backward pass in backtracking to find the last index where A[i] < B[i] was possible, and then a final forward pass using the logic in the second bullet-point.
Because of the overhead of maintaining the ordered map, this requires O(n log m) time and O(m) extra space, where n is the total number of elements of A and m is the number of distinct elements. (Since m ≤ n, we can also express this as O(n log n) time and O(n) extra space.)
Note that if there's no solution, then the backtracking step will reach all the way to i == -1. You'll probably want to raise an exception if that happens.
Edited to add (2019-02-01):
In a now-deleted answer, גלעד ברקן summarizes the goal this way:
To be lexicographically smaller, the array must have an initial optional section from left to right where A[i] = B[i] that ends with an element A[j] < B[j]. To be closest to B, we want to maximise the length of that section, and then maximise the remaining part of the array.
So, with that summary in mind, another approach is to do two separate loops, where the first loop determines the length of the initial section, and the second loop actually populates A. This is equivalent to the above approach, but may make for cleaner code. So:
Build an ordered map of the counts of the distinct elements of A.
Initialize initial_section_length := -1.
Iterate through the array indices 0 to n−1, "withdrawing" elements from this map. For each index:
If it's possible to choose an as-yet-unused element of A that's less than the current element of B, set initial_section_length equal to the current array index. (Otherwise, don't.)
If it's not possible to choose an as-yet-unused element of A that's equal to the current element of B, break out of this loop. (Otherwise, continue looping.)
If initial_section_length == -1, then there's no solution; raise an exception.
Repeat step #1: re-build the ordered map.
Iterate through the array indices from 0 to initial_section_length-1, "withdrawing" elements from the map. For each index, choose an as-yet-unused element of A that's equal to the current element of B. (The existence of such an element is ensured by the first loop.)
For array index initial_section_length, choose the greatest as-yet-unused element of A that's less than the current element of B (and "withdraw" it from the map). (The existence of such an element is ensured by the first loop.)
Iterate through the array indices from initial_section_length+1 to n−1, continuing to "withdraw" elements from the map. For each index, choose the greatest element of A that hasn't been used yet.
This approach has the same time and space complexities as the backtracking-based approach.
There are n! permutations of A[n] (less if there are repeating elements).
Use binary search over range 0..n!-1 to determine k-th lexicographic permutation of A[] (arbitrary found example) which is closest lower one to B[].
Perhaps in C++ you can exploit std::lower_bound
Based on the discussion in the comment section to your question, you seek an array made up entirely of elements of the vector A that is -- in lexicographic ordering -- closest to the vector B.
For this scenario, the algorithm becomes quite straightforward. The idea is the same as as already mentioned in the answer of #ruakh (although his answer refers to an earlier and more complicated version of your question -- that is still displayed in the OP -- and is therefore more complicated):
Sort A
Loop over B and select the element of A that is closest to B[i]. Remove that element from the list.
If no element in A is smaller-or-equal than B[i], pick the largest element.
Here is the basic implementation:
#include <string>
#include <vector>
#include <algorithm>
auto get_closest_array(std::vector<int> A, std::vector<int> const& B)
{
std::sort(std::begin(A), std::end(A), std::greater<>{});
auto select_closest_and_remove = [&](int i)
{
auto it = std::find_if(std::begin(A), std::end(A), [&](auto x) { return x<=i;});
if(it==std::end(A))
{
it = std::max_element(std::begin(A), std::end(A));
}
auto ret = *it;
A.erase(it);
return ret;
};
std::vector<int> ret(B.size());
for(int i=0;i<(int)B.size();++i)
{
ret[i] = select_closest_and_remove(B[i]);
}
return ret;
}
Applied to the problem in the OP one gets:
int main()
{
std::vector<int> A ={1,3,5,6,7};
std::vector<int> B ={7,3,2,4,6};
auto C = get_closest_array(A, B);
for(auto i : C)
{
std::cout<<i<<" ";
}
std::cout<<std::endl;
}
and it displays
7 3 1 6 5
which seems to be the desired result.
Create a function that checks whether an array has two opposite elements or not for less than n^2 complexity. Let's work with numbers.
Obviously the easiest way would be:
bool opposite(int* arr, int n) // n - array length
{
for(int i = 0; i < n; ++i)
{
for(int j = 0; j < n; ++j)
{
if(arr[i] == - arr[j])
return true;
}
}
return false;
}
I would like to ask if any of you guys can think of an algorithm that has a complexity less than n^2.
My first idea was the following:
1) sort array ( algorithm with worst case complexity: n.log(n) )
2) create two new arrays, filled with negative and positive numbers from the original array
( so far we've got -> n.log(n) + n + n = n.log(n))
3) ... compare somehow the two new arrays to determine if they have opposite numbers
I'm not pretty sure my ideas are correct, but I'm opened to suggestions.
An important alternative solution is as follows. Sort the array. Create two pointers, one initially pointing to the front (smallest), one initially pointing to the back (largest). If the sum of the two pointed-to elements is zero, you're done. If it is larger than zero, then decrement the back pointer. If it is smaller than zero, then increment the front pointer. Continue until the two pointers meet.
This solution is often the one people are looking for; often they'll explicitly rule out hash tables and trees by saying you only have O(1) extra space.
I would use an std::unordered_set and check to see if the opposite of the number already exist in the set. if not insert it into the set and check the next element.
std::vector<int> foo = {-10,12,13,14,10,-20,5,6,7,20,30,1,2,3,4,9,-30};
std::unordered_set<int> res;
for (auto e : foo)
{
if(res.count(-e) > 0)
std::cout << -e << " already exist\n";
else
res.insert(e);
}
Output:
opposite of 10 alrready exist
opposite of 20 alrready exist
opposite of -30 alrready exist
Live Example
Let's see that you can simply add all of elements to the unordered_set and when you are adding x check if you are in this set -x. The complexity of this solution is O(n). (as #Hurkyl said, thanks)
UPDATE: Second idea is: Sort the elements and then for all of the elements check (using binary search algorithm) if the opposite element exists.
You can do this in O(n log n) with a Red Black tree.
t := empty tree
for each e in A[1..n]
if (-e) is in t:
return true
insert e into t
return false
In C++, you wouldn't implement a Red Black tree for this purpose however. You'd use std::set, because it guarantees O(log n) search and insertion.
std::set<int> s;
for (auto e : A) {
if (s.count(-e) > 0) {
return true;
}
s.insert(e);
}
return false;
As Hurkyl mentioned, you could do better by just using std::unordered_set, which is a hashtable. This gives you O(1) search and insertion in the average case, but O(n) for both operations in the worst case. The total complexity of the solution in the average case would be O(n).
I have a vector< vector <int> > matrix of size n and I want to get the minimum value for each i and it indexs [i][j] and put it on a vector but I don't want to get any indexs repeated.
I've found a theoretical way but I cannot write it in code.
Make 2 vectors U←{1,...,n}, L←{1,...,n}
Repeat n times
Be (u,l)∈U×L from matrix[u,l] ≤ matrix[i,j], ∀i∈U, ∀j∈L
S[u] ← l
Do U←U-{u} y L←L-{l}
You can code this algorithm directly
typedef vector<vector<int>> Matrix;
typedef pair<size_t, size_t> Index;
typedef vector<Index> IndexList;
IndexList MinimalSequence(const Matrix& matrix) {
IndexList result;
set<size_t> U, L;
for (size_t i = 0; i < matrix.size(); ++i) { // consider square
U.insert(i);
L.insert(i);
}
while (U.size()) { // same as L.size()
int min = numeric_limits<int>::max();
Index minIndex;
for (auto u: U)
for (auto l: L)
if (matrix[u][l] < min) {
minIndex = make_pair(u, l);
min = matrix[u][l];
}
U.erase(minIndex.first);
L.erase(minIndex.second);
result.push_back(minIndex);
}
return result;
}
also your question is not clear in this way: do you want to start from the overall smallest element of the matrix (as your formula said) and then move to the next smallest?
or do you want to move through the columns from left to right? I implemented it according to formulas.
Note that set of non-negative integers in your formula is set<size_t> on which insert() and erase() are available. For all is while-loop
I would also suggest to try alternative algorithm - sort a list of matrix indices by there corresponding values and then iterate over it removing indices you dont want anymore.
edit: code actually differs from algorithm in few ways to be precise. That seemed more practical.
process is repeated until set of indices is exhausted - that is equal to n
return structure is list of 2d indices and encodes more information than array
You already have accepted an answer, but aren't you facing the Assignment problem that can be solved using the Hugarian algorithm, and maybe even more efficient algorithms that exists and are already implemented?
I have
vector<int> my_vector;
vector<int> other_vector;
with my_vector.size() == 20 and other_vector.size() == 5.
Given int n, with 0 < n < 14, I would like to replace the subvector (my_vector[n], myvector[n+1], ..., myvector[n+4]) with other_vector.
For sure with the stupid code
for(int i=0; i<5; i++)
{
my_vector[n+i] = other_vector[i];
}
I'm done, but I was wondering if is there a more efficient way to do it. Any suggestion?
(Of course the numbers 20 and 5 are just an example, in my case I have bigger size!)
In C++11, a friendly function std::copy_n is added, so you can use it:
std::copy_n(other_vector.begin(), 5, &my_vector[n]);
In C++03, you could use std::copy as other answers has already mentioned.
You could use std::copy:
// Get the first destination iterator
auto first = std::advance(std::begin(my_vector), n);
// Do the copying
std::copy(std::begin(other_vector), std::end(other_vector), first);
Although this basically is the same as your naive solution.
I dont know about performance, but a cleaner version would be to use std::copy
std::copy(other_vector.begin(),other_vector.end(),my_vector.begin()+n);
For min-max performance, perhaps(?) memcpy is the answer..
memcpy(my_vector.begin()+n, other_vector.begin(), sizeof(int) *other_vector.size());