Algorithm to represent a sequence of numbers
I have a sequence of numbers to generate, and I want to generate it using some sort of algorithm (iterative or recursive, doesn't matter).
Contextualizing: This numbers are indexes to iterative over a list of lists. I need to do a permutation (combination, i don't know exactly), but I need to generate all combinations of all positions of that list of lists.
The sequence and the output I am trying to get is:
1 1
2 1
3 1
4 1
5 1
1 2
2 1
3 1
4 1
5 1
1 3
2 1
3 1
4 1
5 1
1 4
2 1
3 1
4 1
5 1
1 5
2 1
3 1
4 1
5 1
1 1
2 2
3 1
4 1
5 1
1 2
2 2
3 1
4 1
5 1
1 3
2 2
3 1
4 1
5 1
1 4
2 2
3 1
4 1
5 1
1 5
2 2
3 1
4 1
5 1
1 1
2 3
3 1
4 1
5 1
1 2
2 3
3 1
4 1
5 1
1 3
2 3
3 1
4 1
5 1
1 4
2 3
3 1
4 1
5 1
1 5
2 3
3 1
4 1
5 1
1 1
2 4
3 1
4 1
5 1
and so on... the last state is:
1 5
2 5
3 5
4 5
5 5
Note that at each line break is a step of iteration or recursion. The algorithm must be generic. This code that i wrote can help, but it isn't what I want. :(
List<List<int>> lstDays = new List<List<int>>
{
new List<int>{1,2,3,4,5}, //day 18
new List<int>{1,2,3,4,5}, //day 19
new List<int>{1,2,3,4,5}, //day 22
new List<int>{1,2,3,4,5}, //day 23
new List<int>{1,2,3,4,5}, //day 24
};
for(int i=0;i<lstDays.Count;i++)
{
for(int j=0;j<lstDays[i].Count;j++)
{
for(int k=0;k<lstDays.Count;k++)
{
Console.Write(k+1);
//Console.Write(j+1);
Console.Write('n');
}
Console.Write('n');
}
}
I hope that you can help me ! (:
Based on comments below by the venerable Eric Lippert, edits for the OPs original intent:
public void OutputSequence(int length){
Recurse(length-1, Enumerable.Range(1, length).ToArray(), new int[length]);
}
public void Recurse(int position, int[] arr, int[] state){
if (position == -1){
PrintState(state);
return;
}
for (int i = 0; i < arr.Length; i++)
{
state[position] = arr[i];
Recurse(position-1, arr, state);
}
}
public void PrintState(int[] state){
for (int i = 0; i < state.Length; i++)
Console.WriteLine ("{0} {1}",i+1, state[i]);
Console.WriteLine ();
}
OutputSequence(5);
will give the output the OP originally asked for.
Old Answer
What you're looking for is called a Cartesian Product. LINQ is your friend:
var pairs = from i in Enumerable.Range(1, 5)
from j in Enumerable.Range(1, 5)
select new {i, j};
foreach(var p in pairs)
Console.WriteLine ("{0} {1}", p.i, p.j);
EDIT: Just for fun, here's a way to do N-Ary cartesian products.
public IEnumerable<IEnumerable<int>> NAryCartesianProduct(int upper, int times){
if (times == 0)
return Enumerable.Empty<IEnumerable<int>>();
var nums = Enumerable.Range(1, upper);
IEnumerable<IEnumerable<int>> products = nums.Select(i => new[]{i});
for (int i = 1; i < times; i++)
{
products = from p in products
from n in nums
select p.Concat(new [] {n});
}
return products;
}
And now you can get what you had before with:
var p = NAryCartesianProduct(5, 2);
foreach(var i in p)
Console.WriteLine (i);
I'm sure there's a more efficient way than creating new arrays all of the time but I just hacked this up quick :)
Here's a much more informative answer on this: Generating all Possible Combinations
EDIT2: Apparently the original link is the origination of the answer from that SO post. I didn't read through to the end until now.
You can do it like this:
int[] second = new[] {0,0,0,0,0};
bool finish = false;
while (true) {
for (int i = 0 ; i != 5 ; i++) {
Console.WriteLine("{0} {1}", i+1, second[i]+1);
}
Console.WriteLine();
int p = 0;
do {
second[p]++;
if (second[p] == 5) {
second[p] = 0;
p++;
} else {
break;
}
} while (p != 5);
if (p == 5) break;
}
The sequence of the second digits is stored in the array "creatively" named second
. The do
/ while
loop "increments" this array as if it were a base-5 number stored as five separate digits.
Here is a demo on ideone.
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