Struggling with finding the smallest word in a TRIE

Question

Sorry in advance for any English error that I may commit. I have a school project for university and I have to use a trie to index words and have multiple functions to do multiple things. I'm programming in C. I have done a recursive function to find the biggest word in the trie and it is working. Here's the function:

int BiggestWord(ELEMENT *P)
{
    if (!P) return -1;
    int Alt_max = 0;
    for (int i = 0; i < MAX_VECTOR; i++)
        Alt_max = Biggest(BiggestWord(P->V[i]), Alt_max);
    return 1 + Alt_max;
}

'Biggest' is just a function that returns the biggest value between two values.

Now for the smallest word function. I was thinking about how to do it and tried to do check when the word ended looking for 'NULL' after every Element. Here is my attempt:

int SmallestWord(ELEMENT *P)
{
    if (!P) return -1;
    int Alt_min = 1;
    for (int i = 0; i < MAX_VECTOR; i++)
    {
        if(P->V[i] != NULL)
        {
           SmallestWord(P->V[i]);
           Alt_min++;
        }
    }
    return Alt_min;
}

I can't find a way to make it work. I also thought about trying to, after every word, point that there's the end of a word, and then try to go through every branch of the trie and find the smallest word. It's my first half-year coding and I'm finding some difficulties trying to learn it. If anyone could help me by giving me hints or trying to give me clues of where to go I would appreciate it very much since this is a very important project I must finish and do well.

Also, my data structures are the following:

#define MAX_VECTOR 26 // 26 letters of the Alphabet I'm using

typedef struct ELEMENT
{
    int occurrences_word; // this is used for counting number of occurrences of a word
    struct ELEMENT *V[MAX_VECTOR];
} ELEMENT;

typedef struct TRIE
{
    ELEMENT *root_trie;
    int num_words;
} TRIE;

Thank you in advance to everyone that contributes to helping me out Regards

Answer 1

I see no elegant way to do it. The problem is that a -1 which means a null pointer must be treated differently from a low number which means a short word.

Her is a crude but workable solution:

int SmallestWord(ELEMENT *P)
{
  if (!P) return -1; 

  if(P->occurrences_word != 0) // this is the end of a word
    return 1;

  int Alt_min = -1;      
  for (int i = 0; i < MAX_VECTOR; i++)
    {
      int n = SmallestWord(P->V[i]);
    
      if(n!=-1)
        if(n<Alt_min || Alt_min == -1)
          Alt_min = n;
    }
  return 1 + Alt_min;
}