Find order of an array using minimum memory and time - c++

Question

Let's say i have an array of 5 elements. My program knows it's always 5 elements and when sorted it's always 1,2,3,4,5 only.
As per permutations formula i.e n!/(n-r)! we can order it in 120 ways.
In C++ using std::next_permutation I can generate all those 120 orders.
Now, my program/routine accepts an input argument as a number in the range of 1 to 120 and gives the specific order of an array as output.
This works fine for small array sizes as i can repeat std::next_permutation until that matches input parameter.
The real problem is, How can i do it in less time if my array has 25 elements or more? For 25 elements, the number of possible orders are : 15511210043330985984000000.
Is there a technique that I can easily find the order of numbers using a given number as input?
Thanks in advance :)

Answer 1

This is an example c++ implementation of the algorithm mentioned in this link:
#include <vector>
#define ull unsigned long long
ull factorial(int n) {
ull fac = 1;
for (int i = 2; i <= n; i++)
fac *= i;
return fac;
}
std::vector<int> findPermutation(int len, long idx) {
std::vector<int> original = std::vector<int>(len);
std::vector<int> permutation = std::vector<int>();
for (int i = 0; i < len; i++) {
original[i] = i;
}
ull currIdx = idx;
ull fac = factorial(len);
while (original.size() > 0) {
fac /= original.size();
int next = (currIdx - 1) / fac;
permutation.push_back(original[next]);
original.erase(original.begin() + next);
currIdx -= fac * next;
}
return permutation;
}
The findPermutation function accepts the length of the original string and the index of the required permutation, and returns an array that represents that permutation. For example, [0, 1, 2, 3, 4] is the first permutation of any string with length 5, and [4, 3, 2, 1, 0] is the last (120th) permutation.

Answer 2

I have had a similar problem where I was storing lots of row in a Gtk TreeView and did not want to go over all of them every time I want to access a row by its position and not by its reference.
So, I created a map of the positions of the row so I could easily identify them by the parameter I needed.
So, my suggestion to this is you go over all permutations once and map every std::permutation in an array (I used a std::vector), so you can access it by myVector[permutation_id].
Here is my way I have done the mapping:
vector<int> FILECHOOSER_MAP;
void updateFileChooserMap() {
vector<int> map;
TreeModel::Children children = getInterface().getFileChooserModel()->children();
int i = 0;
for(TreeModel::Children::iterator iter = children.begin(); iter != children.end(); iter++) {
i++;
TreeModel::Row row = *iter;
int id = row[getInterface().getFileChooserColumns().id];
if( id >= map.size()) {
for(int x = map.size(); x <= id; x++) {
map.push_back(-1);
}
}
map[id] = i;
}
FILECHOOSER_MAP = map;
}
So in your case you would just iterate over the permutations like this and you can map them in a way that allows you accesing them by their id.
I hope this helps you :D
regards, tagelicht