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;
     }
 }