# Find maximum points which can be obtained by deleting elements from array

Given an array A having N elements and two integers L and R where, and . You can choose any element of the array (let’s say ax) and delete it, and also delete all elements equal to ax+1, ax+2ax+R and ax-1, ax-2ax-L from the array. This step will cost ax points. The task is to maximize the total cost after deleting all the elements from the array.

Examples:

Input : 2 1 2 3 2 2 1
L = 1, R = 1
Output : 8
We select 2 to delete, then (2-1)=1 and (2+1)=3 will need to be deleted,
for given L and R range respectively.
Repeat this until 2 is completely removed. So, total cost = 2*4 = 8.

Input : 2 4 2 9 5
L = 1, R = 2
Output : 18
We select 2 to delete, then 5 and then 9.
So total cost = 2*2 + 5 + 9 = 18.


## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: We will find the count of all the elements. Now let’s say an element X is selected then, all elements in the range [X-L, X+R] will be deleted. Now we select the minimum range from L and R and finds up to which elements are to be deleted when element X is selected. Our results will be maximum of previously deleted elements and when element X is deleted. We will use dynamic programming to store the result of previously deleted elements and use it further.

 // C++ program to find maximum cost after  // deleting all the elements form the array  #include  using namespace std;     // function to return maximum cost obtained  int maxCost(int a[], int n, int l, int r)  {         int mx = 0, k;      // find maximum element of the array.      for (int i = 0; i < n; ++i)          mx = max(mx, a[i]);         // initialize count of all elements to zero.      int count[mx + 1];      memset(count, 0, sizeof(count));         // calculate frequency of all elements of array.      for (int i = 0; i < n; i++)          count[a[i]]++;         // stores cost of deleted elements.      int res[mx + 1];      res = 0;         // selecting minimum range from L and R.      l = min(l, r);         for (int num = 1; num <= mx; num++) {             // finds upto which elements are to be          // deleted when element num is selected.          k = max(num - l - 1, 0);             // get maximum when selecting element num or not.          res[num] = max(res[num - 1], num * count[num] + res[k]);      }         return res[mx];  }     // Driver program  int main()  {      int a[] = { 2, 1, 2, 3, 2, 2, 1 }, l = 1, r = 1;         // size of array      int n = sizeof(a) / sizeof(a);         // function call to find maximum cost      cout << maxCost(a, n, l, r);         return 0;  }

 //Java program to find maximum cost after  //deleting all the elements form the array     public class GFG {             //function to return maximum cost obtained      static int maxCost(int a[], int n, int l, int r)      {          int mx = 0, k;       // find maximum element of the array.       for (int i = 0; i < n; ++i)           mx = Math.max(mx, a[i]);          // initialize count of all elements to zero.       int[] count = new int[mx + 1];       for(int i = 0; i < count.length; i++)           count[i] = 0;          // calculate frequency of all elements of array.       for (int i = 0; i < n; i++)           count[a[i]]++;          // stores cost of deleted elements.       int[] res = new int[mx + 1];       res = 0;          // selecting minimum range from L and R.       l = Math.min(l, r);          for (int num = 1; num <= mx; num++) {              // finds upto which elements are to be           // deleted when element num is selected.           k = Math.max(num - l - 1, 0);              // get maximum when selecting element num or not.           res[num] = Math.max(res[num - 1], num * count[num] + res[k]);       }          return res[mx];      }         //Driver program      public static void main(String[] args) {                     int a[] = { 2, 1, 2, 3, 2, 2, 1 }, l = 1, r = 1;              // size of array           int n = a.length;              // function call to find maximum cost           System.out.println(maxCost(a, n, l, r));      }  }

 # Python 3 Program to find maximum cost after   # deleting all the elements form the array      # function to return maximum cost obtained   def maxCost(a, n, l, r) :         mx = 0        # find maximum element of the array.      for i in range(n) :          mx = max(mx, a[i])         # create and initialize count of all elements to zero.      count =  * (mx + 1)         # calculate frequency of all elements of array.      for i in range(n) :          count[a[i]] += 1        # stores cost of deleted elements.      res =  * (mx + 1)      res = 0        # selecting minimum range from L and R.      l = min(l, r)         for num in range(1, mx + 1) :             # finds upto which elements are to be           # deleted when element num is selected.          k = max(num - l - 1, 0)             # get maximum when selecting element num or not.           res[num] = max(res[num - 1], num * count[num] + res[k])         return res[mx]     # Driver code  if __name__ == "__main__" :         a = [2, 1, 2, 3, 2, 2, 1 ]      l, r = 1, 1        # size of array       n =  len(a)         # function call to find maximum cost       print(maxCost(a, n, l, r))     # This code is contributed by ANKITRAI1

 // C# program to find maximum cost   // after deleting all the elements   // form the array  using System;     class GFG   {     // function to return maximum   // cost obtained  static int maxCost(int []a, int n,                      int l, int r)  {      int mx = 0, k;             // find maximum element      // of the array.      for (int i = 0; i < n; ++i)          mx = Math.Max(mx, a[i]);             // initialize count of all      // elements to zero.      int[] count = new int[mx + 1];      for(int i = 0; i < count.Length; i++)          count[i] = 0;             // calculate frequency of all      // elements of array.      for (int i = 0; i < n; i++)          count[a[i]]++;             // stores cost of deleted elements.      int[] res = new int[mx + 1];      res = 0;             // selecting minimum range      // from L and R.      l = Math.Min(l, r);             for (int num = 1; num <= mx; num++)       {                 // finds upto which elements           // are to be deleted when           // element num is selected.          k = Math.Max(num - l - 1, 0);                 // get maximum when selecting           // element num or not.          res[num] = Math.Max(res[num - 1], num *                            count[num] + res[k]);      }     return res[mx];  }     // Driver Code  public static void Main()  {      int []a = { 2, 1, 2, 3, 2, 2, 1 };      int l = 1, r = 1;         // size of array      int n = a.Length;         // function call to find maximum cost      Console.WriteLine(maxCost(a, n, l, r));  }  }     // This code is contributed   // by inder_verma

Output:
8


Time Complexity: O(max(A))

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