Question

Maximum Value But Limited Neighbors
You are given an array a[1..n] of positive numbers and an integer k. You have to produce an array b[1..n], such that: (i) For each j, b[j] is 0 or 1, (ii) Array b has adjacent 1s at most k times, and (iii) sum_{j=1 to n} a[j]*b[j] is maximized. For example, given an array [100, 300, 400, 50] and integer k = 1, the array b can be: [0 1 1 0], which maximizes the sum to be 700. Or, given an array [10, 100, 300, 400, 50, 4500, 200, 30, 90] and k = 2, the array b can be [1, 0, 1, 1, 0, 1, 1, 0, 1] which maximizes the sum to 5500.
To be precise about the definition of adjacency: sequence [0, 1, 0, 1, 0, 1, 1, 1] has two adjacent 1s. Sequence [0, 1, 0, 0, 1, 1, 1, 1] has 3 adjacent 1s. Sequence [1, 0, 1, 1, 0, 1, 1, 1] also has 3 adjacent 1s.

MVBLN(i,m): Maximum value sum that can be achieved from the array A[1..i], using adjacent 1s at most m times.

Recurrence Relation: MVBLN(i,m) = max{MVBLN(i-1,m), MVBLN(i-1,m-1) + A[i], MVBLN(i-2,m) + A[i]}

Please use Java for programming.

Answer 1

The required JAVA code

import java.util.*;
import java.lang.*;
import java.io.*;

class Chegg{
  
public static void main (String[] args){
Scanner sc = new Scanner(System.in);
int n = Integer.parseInt(sc.nextLine());
int m = Integer.parseInt(sc.nextLine());
String line = sc.nextLine();
String[] in = line.split(" ");
int[] a = new int[n];
  
for(int i=0;i<n;i++)
a[i] = Integer.parseInt(in[i]);

int ans = MVBLN(a,n-1,m);
System.out.println(ans);
}

public static int MVBLN(int[] a,int i,int m){

if(i < 0 || m < 0)
return 0;
else{

return Math.max(Math.max(MVBLN(a,i-1,m), MVBLN(a,i-1,m-1) + a[i]),MVBLN(a,i-2,m) + a[i]);
}
}
}

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