Question

1. What does dynamic programming have in common with divide-and-conquer? What is a principal difference between them?

2. Solve the instance 10, 25, 1, 1, 5, 1, 25, 10, 10 of the coin-row problem using the dynamic programming algorithm technique. Show the solution array and also the final output.(NO PSUEDO CODE ACTUALLY WORK IT OUT)

Answer 1

Dynamic programming and Divide-and-conquer:

Similarity:

1 Dynamic programming is an extension of Divide and Conquer.

2. Both work by breaking down the problem into a smaller subproblem,

3.Solution to the problem gets combine to find the original problem.

Difference:

Divide and Conquer

1. The subproblem is independent of each other.

2. Recursive

3. Consume more running time

4. Not very efficient

Dynamic program:

1. The subproblem is interrelated on each other.

2. Non-recursive

3. Consume less running time

4. Very efficient

package dp;

public class CoinRow {
   public static int coinRow(int ar[]){
  
       int n=ar.length + 1;
       int temp[]= new int[n];
       for (int i = 0; i < ar.length; i++) {//initialize temp array with ar element but from index 1
           temp[i + 1] = ar[i];
       }

           int[] dp = new int[n]; //carry result
           dp[0] = 0; //first element 0
           dp[1] = temp[1]; //second element is first element of ar

   for (int i = 2; i <n; i++) {
       int s=temp[i] + dp[i - 2]; //take sum of present element and two element behind, and prev element
       //of dp
   dp[i] = Integer.max(s, dp[i - 1]); //which is greater will be present result
   }
   //printing solution array
   for (int i = 0; i < n; i++) {
       System.out.print(dp[i]+" ");
   }
      return dp[ar.length]; //last element of dp will be result
       }

   public static void main(String[] args) {
      

           int ar[]={ 10, 25, 1, 1, 5, 1, 25, 10, 10};
           int res=coinRow(ar);
           System.out.println();
           System.out.print("Res= ");
           System.out.println(res);
          
   }

}

output

0 10 25 25 26 30 30 55 55 65
Res= 65