#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <ctype.h>

#define MAX_WORD_LENGTH 100
#define MAX_DICTIONARY_SIZE 10000
#define VOWELS "aeiou"

typedef struct {
    char word[MAX_WORD_LENGTH];
    int frequency;
} Word;

typedef struct {
    char word[MAX_WORD_LENGTH];
    int index;
} DictionaryEntry;

Word words[MAX_DICTIONARY_SIZE];
DictionaryEntry dictionary[MAX_DICTIONARY_SIZE];
int dictionarySize = 0;

void addWord(char *word) {
    int found = 0;
    for (int i = 0; i < dictionarySize; i++) {
        if (strcmp(dictionary[i].word, word) == 0) {
            dictionary[i].frequency++;
            found = 1;
            break;
        }
    }
    if (!found) {
        strcpy(words[dictionarySize].word, word);
        words[dictionarySize].frequency = 1;
        dictionary[dictionarySize].index = dictionarySize;
        dictionarySize++;
    }
}

double logProbability(char *context, char *word) {
    int contextLength = strlen(context);
    int wordLength = strlen(word);
    int totalWordsInContext = contextLength + wordLength;
    int totalVowelsInContext = countVowels(context);
    int totalVowelsInWord = countVowels(word);
    int totalConsonantsInWord = totalWordsInContext - totalVowelsInWord;
    int totalConsonantsInContext = totalWordsInContext - totalVowelsInContext;
    int totalLettersInWord = totalConsonantsInWord + totalVowelsInWord;
    int totalLettersInContext = totalConsonantsInContext + totalVowelsInContext;
    int wordIndex = findWordIndex(word);
    int contextIndex = findWordIndex(context);
    double probability = exp((-1.0 * log(words[wordIndex].frequency)) * (totalLettersInWord));
    double contextFrequency = exp((-1.0 * log(words[contextIndex].frequency)) * (totalLettersInContext));
    double wordFrequency = exp((-1.0 * log(words[wordIndex].frequency)) * (totalLettersInWord));
    double coOccurrenceFrequency = (contextFrequency * wordFrequency) / (totalLettersInContext * totalLettersInWord);
    return probability * coOccurrenceFrequency;
}

int findWordIndex(char *word) {
    int index = binarySearch(&dictionary[0], dictionarySize, word);
    if (index >= 0) {
        return dictionary[index].index;
    } else {
        return index;
    }
}

int binarySearch(DictionaryEntry *array, int size, char *value) {
    int low = 0;
    int high = size - 1;
    int mid;
    int comparisonResult;
    while (low <= high) {
        mid = (low + high) >> 1;
        comparisonResult = strcmp(array[mid].word, value);
        if (comparisonResult == 0) {
            return array[mid].index;
        } else if (comparisonResult < 0) {
            low = mid + 1;
        } else if (comparisonResult > 0) {
            high = mid - 1;