Find the Longest Common Prefix with a Trie

#include <stdio.h>
#include <stdlib.h>

struct Trie { struct Trie *child[26]; int terminal, pass; };
struct Trie *new_trie(void) { struct Trie *node = calloc(1, sizeof *node); if (!node) exit(EXIT_FAILURE); return node; }
void insert_word(struct Trie *root, const char *word) { for (int i = 0; word[i]; i++) { int index = word[i] - 'a'; if (!root->child[index]) root->child[index] = new_trie(); root = root->child[index]; root->pass++; } root->terminal = 1; }
struct Trie *walk(struct Trie *root, const char *word) { for (int i = 0; word[i] && root; i++) root = root->child[word[i] - 'a']; return root; }
void free_trie(struct Trie *root) { if (root) { for (int i = 0; i < 26; i++) free_trie(root->child[i]); free(root); } }

int main(void)
{
    const char *words[] = {"flower", "flow", "flight"}; struct Trie *root = new_trie();
    for (int i = 0; i < 3; i++) { insert_word(root, words[i]); }
    char prefix[30]; int length = 0;
    while (root && !root->terminal) { int child = -1, count = 0; for (int i = 0; i < 26; i++) if (root->child[i]) { child = i; count++; } if (count != 1) break; prefix[length++] = (char) ('a' + child); root = root->child[child]; }
    prefix[length] = '\0'; printf("Prefix = %s\n", prefix); return 0;
}