Generating increasing subsequences out of n numbers of length k - c

Question

I want to generate all possible increasing subsequences of numbers (repetition allowed) from 1 to n, but of length k.
Ex. n=3, k=2
Output:
1 1
1 2
1 3
2 2
2 3
3 3
This is my code:
#include <stdio.h>
int s[100];
int n=6;
int k=4;
void subk(int prev,int index)
{
int i;
if (index==k)
{
for(int i=0; i<k; i++)
printf("%d ",s[i]);
printf("\n");
return;
}
s[index]=prev;
for (i=prev; i<=n; ++i)
{
subk(i,index+1);//,s,n,k);
}
}
int main()
{
int j;
for (j = 1; j<=n ; ++j)
{
subk(j,0);
}
return 0;
}
But this generates some unwanted repetitions. How do I eliminate those?

Answer 1

I have tested your code with n = 3 and k = 2 and got the following result:
1 1
1 1
1 1
1 2
1 2
1 3
2 2
2 2
2 3
3 3
This is obviously incorrect, as there are several identical numbers like 1 1 or 1 2.
But what exactly went wrong?
Let's write down the right results if n = 3 and k = 3. Now compare those to the result we got from the program when n = 3 and k = 2.
correct program (incorrect)
k = 3 k = 2
1 1 1 1 1
1 1 2 1 1
1 1 3 1 1
1 2 2 1 2
1 2 3 1 2
1 3 3 1 3
2 2 2 2 2
2 2 3 2 2
2 3 3 2 3
3 3 3 3 3
Now we can see that the incorrect output of the program is the same as the first two columns of the correct answer when we set k = 3. This means that the program solves the problem for 3 columns if we set k = 2, but only displays the first two columns.
You need to stop the program from writing the same number several times.
Solution 1
One way to do this is to execute the for-loop in the subk-function only once when it writes the last number (index == (k - 1)) into the buffer s.
In order to achieve this, you need to add the following two lines to the end of your for-loop.
if (index == (k - 1))
break;
(Instead of the break you could also use return)
After you added these two lines the function should look like this:
void subk(int prev, int index)
{
int i;
if (index == k)
{
for (int i = 0; i<k; i++)
printf("%d ", s[i]);
printf("\n");
return;
}
s[index] = prev;
for (i = prev; i <= n; ++i)
{
subk(i, index + 1);//,s,n,k);
if (index + 1 == k)
break;
}
}
Solution 2
Another way to solve the problem is to move the line s[index] = prev; to the beginning of the function and change the k in the if-statement to k - 1.
Now the function should look like this:
void subk(int prev, int index)
{
int i;
s[index] = prev;
if (index == k - 1)
{
for (int i = 0; i<k; i++)
printf("%d ", s[i]);
printf("\n");
return;
}
for (i = prev; i <= n; ++i)
{
subk(i, index + 1);//,s,n,k);
}
}
With this solution, the for-loop is never executed when the index shows that the program is at the last 'sub-number'. It just displays the number and exits the function because of the return.
You get the right result with both solutions, but I personally like the second solution better, because there is no additional if-statement that is executed every iteration of the for-loop and the program is (slightly) faster.