Lec-32 Recursion - Divide and Conquer in Queue

Lec-32 Recursion - Divide and Conquer in Queue

• 1.
  Example 1  Writetwo recursive functions to display numbers from 1 to n (a positive integer) in both ascending and descending order void displayAscending(int n) { if (n==1) { cout<<n<<“,”; return; } displayAscending(n-1); cout<<n<<“,”; } 1
• 2.
  void displayDescending (intn) { cout<<n<<“,”; if (n==1) return; displayDescending( n-1); } void main(void) { int num = 15; displayDescending(num); cout<<endl; displayAscending(num); } 2
• 3.
  Example 2  Writea recursive function which adds first n positive integers int add_n_integers(int n) { if (n==1) return 1; else return n + add_n_integers(n-1); } void main(void) { int num = 4; cout<<“sum of first “<<num <<“ positive integers is: “ <<add_n_integers(num); } 3
• 4.
  Counting Digits  Recursivedefinition digits(n) = 1 if (–9 <= n <= 9) 1 + digits(n/10) otherwise  Example digits(321) = 1 + digits(321/10) = 1 +digits(32) = 1 + [1 + digits(32/10)] = 1 + [1 + digits(3)] = 1 + [1 + (1)] = 3
• 5.
  Counting Digits inC++ int numberofDigits(int n) { if ((-10 < n) && (n < 10)) return 1 else return 1 + numberofDigits(n/10); }
• 6.
  Evaluating Exponents Recurisivley int power(intk, int n) { // raise k to the power n if (n == 0) return 1; else return k * power(k, n – 1); }
• 7.
  Divide and Conquer Using this method each recursive subproblem is about one-half the size of the original problem  If we could define power so that each subproblem was based on computing kn/2 instead of kn – 1 we could use the divide and conquer principle  Recursive divide and conquer algorithms are often more efficient than iterative algorithms
• 8.
  Evaluating Exponents Using Divideand Conquer int power(int k, int n) { // raise k to the power n if (n == 0) return 1; else{ int t = power(k, n/2); if ((n % 2) == 0) return t * t; else return k * t * t; }
• 9.
  Stacks  Every recursivefunction can be implemented using a stack and iteration.  Every iterative function which uses a stack can be implemented using recursion.
• 10.
  Disadvantages  May runslower. Compilers Inefficient Code  May use more space.
• 11.
  Advantages  More natural. Easier to prove correct.  Easier to analysis.  More flexible.