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(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

(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

C++ Programming: From Problem Analysis to Program Design
C++ Programming: From Problem Analysis to Program Design
8th Edition
ISBN:9781337102087
Author:D. S. Malik
Publisher:D. S. Malik
Chapter15: Recursion
Section: Chapter Questions
Problem 7SA
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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.
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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