Chp17: Moderate

17.1 swap a number in place.(without temporary variables)

 a = a ^ b;

 b = a ^ b;

 a = a ^ b;

17.3 Write a function which computes the number of trailing zeros in n factorial.

To count the number of zeros, we only need to count the pairs of multiples of 5 and 2. There will always be more multiples of 2 than 5 though, so, simply counting the number of multiples of 5 is sufficient.

public int count(int num){
    int count = 0;
    if(num < 0) return -1;
    for(int i = 5; num /i > 0; i *= 5)
        count += num / i;
    return count;
}

17.4 Write a method which finds the maximum of two numbers. You should not use if-else or any other comparison operator.

public int flip(int bit){
    return 1 ^ bit;
}
public int sign(int a){
    return flip((a >> 31) & 0x1);
}
public int getMax(int a, int b){
    int c = a - b;
    int sa = sign(a); //if a >= 0 : 1 other : 0
    int sb = sign(b); //if b >= 1 : 1 other : 0
    int sc = sign(c); //depends on whether a - b overflows, like a = INT_MAX, b < 0
    int use_sign_a = sa ^ sb;
    int use_sign_c = flip(sa ^ sb);
    int k = use_sign_a * sa + use_sign_c * sc;
    int q = flip(k);
    return a * k + b * q;
}

 

17.9 Design a method to find the frequency of occurrences of any given word in a book.

The first question that you should ask is if you will be doing this operation once or repeatedly. 

Solution: Single Query

go through the book, word by word, count the number of times that words appears. O(n)

Solution: Repetitive Queries

do pre-processing on the book! create a hash table which maps from a word to its frequency.

Hashtable<String, Integer> setupDic(String[] book){
    Hashtable<String, Integer> table = new Hashtable<String, Integer>();
    for(String word : book){
        word = word.toLowerCase();
        if(word.trim() != ""){
            if(!table.containsKey(word)) table.put(word, 0);
            table.put(word, table.get(word) + 1);
        }
    }
    return table;
}
int getFrequency(Hashtable<String, Integer> table, String word){
    if(table == null || word == null) return -1;
    word = word.toLowerCase();
    if(table.containsKey(word)) return table.get(word);
    return 0;
}

17.11 Implement a method rand7() given rand5(). Given a method that generates a random number between 0 and 4, write a method that generates a random number between 0 and 6.

Nondeterministic Number of Calls

public int rand7(){
    while(true){
        int num = 5 * rand5() + rand5();
        if(num < 21) return num % 7;
    }
}