Find subsequence of given length from a given string? - c++

Question

To find the sub-sequences from a string of given length i have a recursive code (shown below) but it takes much time when the string length is big....
void F(int index, int length, string str)
{
if (length == 0) {
cout<<str<<endl;
//int l2=str.length();
//sum=0;
//for(int j=0;j<l2;j++)
//sum+=(str[j]-48);
//if(sum%9==0 && sum!=0)
//{c++;}
//sum=0;
} else {
for (int i = index; i < n; i++) {
string temp = str;
temp += S[i];
//sum+=(temp[i]-48);
F(i + 1, length - 1, temp);
}
}
}
Please help me with some idea of implementing non-recursive code or something else.

Answer 1

You mentioned your current code is too slow when the input string length is large. It would be helpful if you could provide a specific example along with your timing info so we know what you consider to be "too slow". You should also specify what you would consider to be an acceptable run time. Here's an example:
I'll start with an initial version that I believe is similar to your current algorithm. It generates all subsequences of length >= 2:
#include <iostream>
#include <string>
void subsequences(const std::string& prefix, const std::string& suffix)
{
if (prefix.length() >= 2)
std::cout << prefix << std::endl;
for (size_t i=0; i < suffix.length(); ++i)
subsequences(prefix + suffix[i], suffix.substr(i + 1));
}
int main(int argc, char* argv[])
{
subsequences("", "ABCD");
}
Running this program produces the following output:
AB
ABC
ABCD
ABD
AC
ACD
AD
BC
BCD
BD
CD
Now let's change the input string to something longer. I'll use a 26-character input string:
"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
This generates 67,108,837 subsequences. I won't list them here :-). On my machine, the code shown above takes just over 78 seconds to run (excluding output to cout) with the 26-character input string.
When I look for ways to optimize the above code, one thing that jumps out is that it's creating two new string objects for each recursive call to subsequences(). What if we could preallocate space once upfront and then simply pass pointers? Version 2:
#include <stdio.h>
#include <malloc.h>
#include <string.h>
void subsequences(char* prefix, int prefixLength, const char* suffix)
{
if (prefixLength >= 2)
printf("%s\n", prefix);
for (size_t i=0; i < strlen(suffix); ++i) {
prefix[prefixLength] = suffix[i];
prefix[prefixLength + 1] = '\0';
subsequences(prefix, prefixLength + 1, suffix + i + 1);
}
}
int main(int argc, char* argv[])
{
const char *inputString = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
char *prefix = (char*) _malloca(strlen(inputString) + 1);
subsequences(prefix, 0, inputString);
}
This generates the same 67,108,837 subsequences, but execution time is now just over 2 seconds (again, excluding output via printf).

Answer 2

Your code might be slow because your string is large. For a sequence of n unique elements there are (n over k) subsequences of length k. That means for the sequence "ABCDEFGHIJKLMNOPQRSTUVWXYZ" there are 10.400.600 different subsequences of length 13. That number grows pretty fast.
Nevertheless, since you asked, here is a non-recursive function that takes a string str and a size n and prints all subsequences of length n of that string.
void print_subsequences(const std::string& str, size_t n)
{
if (n < 1 || str.size() < n)
{
return; // there are no subsequences of the given size
}
// start with the first n characters (indexes 0..n-1)
std::vector<size_t> indexes(n);
for (size_t i = 0; i < n; ++i)
{
indexes[i] = i;
}
while (true)
{
// build subsequence from indexes
std::string subsequence(n, ' ');
for (size_t i = 0; i < n; ++i)
{
subsequence[i] = str[indexes[i]];
}
// there you are
std::cout << subsequence << std::endl;
// the last subsequence starts with n-th last character
if (indexes[0] >= str.size() - n)
{
break;
}
// find rightmost incrementable index
size_t i = n;
while (i-- > 0)
{
if (indexes[i] < str.size() - n + i)
{
break;
}
}
// increment that index and set all following indexes
size_t value = indexes[i];
for (; i < n; ++i)
{
indexes[i] = ++value;
}
}
}