Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Transcribed Image Text:9. Divide-and-Conquer and Dynamic Programming. This question has been on a final exam.
(a) What does dynamic programming have in common with divide-and-conquer? What is a principal
difference between them?
(b) A recurrence for the number of combinations of m things out of n, ("), for n > 1 and 0< m < n:
n
if m = 0 or m = m
(") + () if 0 < m < n
Here is a recursive function comb taking two integer parameters n and m that returns (").
int comb( int n, int m ){
0 ) || ( m ==
if( ( m ==
n ) )
return 1;
else return( C( n-1,
m ) + C( n-1, m-1 ) );
}
Though this is not an optimization problem, convince yourself that the function computes many
subproblems over and over and that a dynamic programming approach can be applied to this
problem. Consider drawing the recursion tree to see this.
i. Modify the function comb to compute () using a top-down dynamic programming approach
using memoization (i.e., , a table). The table required here is two-dimensional, n x m.
ii. Solve the problem bottom-up with memoization.
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