Recursive generation of all “words” of arbitrary length - c++

Question

I have a working function that generates all possible “words” of a specific length, i.e.
AAAAA
BAAAA
CAAAA
...
ZZZZX
ZZZZY
ZZZZZ
I want to generalize this function to work for arbitrary lengths.
In the compilable C++ code below
iterative_generation() is the working function and
recursive_generation() is the WIP replacement.
Keep in mind that the output of the two functions not only differs slightly, but is also mirrored (which doesn’t really make a difference for my implementation).
#include <iostream>
using namespace std;
const int alfLen = 26; // alphabet length
const int strLen = 5; // string length
char word[strLen]; // the word that we generate using either of the
// functions
void iterative_generation() { // all loops in this function are
for (int f=0; f<alfLen; f++) { // essentially the same
word[0] = f+'A';
for (int g=0; g<alfLen; g++) {
word[1] = g+'A';
for (int h=0; h<alfLen; h++) {
word[2] = h+'A';
for (int i=0; i<alfLen; i++) {
word[3] = i+'A';
for (int j=0; j<alfLen; j++) {
word[4] = j+'A';
cout << word << endl;
}
}
}
}
}
}
void recursive_generation(int a) {
for (int i=0; i<alfLen; i++) { // the i variable should be accessible
if (0 < a) { // in every recursion of the function
recursive_generation(a-1); // will run for a == 0
}
word[a] = i+'A';
cout << word << endl;
}
}
int main() {
for (int i=0; i<strLen; i++) {
word[i] = 'A';
}
// uncomment the function you want to run
//recursive_generation(strLen-1); // this produces duplicate words
//iterative_generation(); // this yields is the desired result
}
I think the problem might be that I use the same i variable in all the recursions. In the iterative function every for loop has its own variable.
What the exact consequences of this are, I can’t say, but the recursive function sometimes produces duplicate words (e.g. ZAAAA shows up twice in a row, and **AAA gets generated twice).
Can you help me change the recursive function so that its result is the same as that of the iterative function?
EDIT
I realised I only had to print the results of the innermost function. Here’s what I changed it to:
#include <iostream>
using namespace std;
const int alfLen = 26;
const int strLen = 5;
char word[strLen];
void recursive_generation(int a) {
for (int i=0; i<alfLen; i++) {
word[a] = i+'A';
if (0 < a) {
recursive_generation(a-1);
}
if (a == 0) {
cout << word << endl;
}
}
}
int main() {
for (int i=0; i<strLen; i++) {
word[i] = 'A';
}
recursive_generation(strLen-1);
}

Answer 1

It turns out you don't need recursion after all to generalize your algorithm to words of arbitrary length.
All you need to do is "count" through the possible words. Given an arbitrary word, how would you go to the next word?
Remember how counting works for natural numbers. If you want to go from 123999 to its successor 124000, you replace the trailing nines with zeros and then increment the next digit:
123999
|
123990
|
123900
|
123000
|
124000
Note how we treated a number as a string of digits from 0 to 9. We can use exactly the same idea for strings over other alphabets, for example the alphabet of characters from A to Z:
ABCZZZ
|
ABCZZA
|
ABCZAA
|
ABCAAA
|
ABDAAA
All we did was replace the trailing Zs with As and then increment the next character. Nothing magic.
I suggest you now go implement this idea yourself in C++. For comparison, here is my solution:
#include <iostream>
#include <string>
void generate_words(char first, char last, int n)
{
std::string word(n, first);
while (true)
{
std::cout << word << '\n';
std::string::reverse_iterator it = word.rbegin();
while (*it == last)
{
*it = first;
++it;
if (it == word.rend()) return;
}
++*it;
}
}
int main()
{
generate_words('A', 'Z', 5);
}
If you want to count from left to right instead (as your example seems to suggest), simply replace reverse_iterator with iterator, rbegin with begin and rend with end.

Answer 2

You recursive solution have 2 errors:
If you need to print in alphabetic order,'a' need to go from 0 up, not the other way around
You only need to print at the last level, otherwise you have duplicates
void recursive_generation(int a) {
for (int i=0; i<alfLen; i++)
{ // the i variable should be accessible
word[a] = i+'A';
if (a<strLen-1)
// in every recursion of the function
recursive_generation(a+1); // will run for a == 0
else
cout << word << '\n';
}
}

Answer 3

As I am inspired from #fredoverflow 's answer, I created the following code which can do the same thing at a higher speed relatively.
#include <iostream>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <cmath>
void printAllPossibleWordsOfLength(char firstChar, char lastChar, int length) {
char *word = new char[length];
memset(word, firstChar, length);
char *lastWord = new char[length];
memset(lastWord, lastChar, length);
int count = 0;
std::cout << word << " -> " << lastWord << std::endl;
while(true) {
std::cout << word << std::endl;
count += 1;
if(memcmp(word, lastWord, length) == 0) {
break;
}
if(word[length - 1] != lastChar) {
word[length - 1] += 1;
} else {
for(int i=1; i<length; i++) {
int index = length - i - 1;
if(word[index] != lastChar) {
word[index] += 1;
memset(word+index+1, firstChar, length - index - 1);
break;
}
}
}
}
std::cout << "count: " << count << std::endl;
delete[] word;
delete[] lastWord;
}
int main(int argc, char* argv[]) {
int length;
if(argc > 1) {
length = std::atoi(argv[1]);
if(length == 0) {
std::cout << "Please enter a valid length (i.e., greater than zero)" << std::endl;
return 1;
}
} else {
std::cout << "Usage: go <length>" << std::endl;
return 1;
}
clock_t t = clock();
printAllPossibleWordsOfLength('A', 'Z', length);
t = clock() - t;
std:: cout << "Duration: " << t << " clicks (" << ((float)t)/CLOCKS_PER_SEC << " seconds)" << std::endl;
return 0;
}