title: Maximum Sum Subsequence Least K Distant Elements
signature: pub fn maximum_sum_subsequence_least_k_distant_elements(arr: Vec<i32>, n: i32, k: i32) -> i32 {
test_code: use std::collections::HashMap;
  use std::collections::HashSet;
  use std::cmp::*;
  use std::collections::*;
  use std::fmt::*; 
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  pub fn validate_solution(actual: i32, expected: i32)->bool{
  return actual==expected
  }
  pub fn driver(arr: Vec<i32>, n: i32, k: i32, expected: i32)->String{
      if validate_solution(PLACEHOLDER_FN_NAME(arr, n, k), expected) {
        return "PASSED".to_string();
      };
      return "FAILED".to_string();
  
  }
  
  fn main() {
      println!("TEST-0...{}", driver(
        Vec::from([3, 5, 20, 21, 23, 26, 27, 31, 33, 38, 39, 41, 48, 48, 50, 51, 56, 57, 64, 68, 69, 70, 71, 74, 76, 86, 97]), 23, 15, 
        98
      ));
      
      println!("TEST-1...{}", driver(
        Vec::from([32, 34, -40, 90, -82, -70, 30, 26, -76, -46, -84, 76, -76]), 9, 10, 
        90
      ));
      
      println!("TEST-2...{}", driver(
        Vec::from([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]), 22, 34, 
        0
      ));
      
      println!("TEST-3...{}", driver(
        Vec::from([96, 15, 30, 25, 83]), 2, 3, 
        96
      ));
      
      println!("TEST-4...{}", driver(
        Vec::from([-90, -82, -80, -76, -62, -58, -50, -48, -46, -38, -38, -38, -38, -38, -34, -32, -24, -22, -16, -16, -4, -2, 10, 10, 20, 26, 26, 32, 38, 38, 44, 44, 46, 48, 58, 62, 64, 66, 76, 78, 78, 82, 92, 96, 96, 98]), 27, 30, 
        26
      ));
      
      println!("TEST-5...{}", driver(
        Vec::from([1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0]), 9, 9, 
        1
      ));
      
      println!("TEST-6...{}", driver(
        Vec::from([1, 2, 9, 17, 24, 31, 31, 33, 56, 57, 61, 71, 73, 74, 76, 77, 79, 83, 86, 95, 99]), 12, 10, 
        72
      ));
      
      println!("TEST-7...{}", driver(
        Vec::from([-12, 52, -44, 80, -66, 34, 42, -46, 8, 12, -22, -56, 74, -98, -44, 2, -24, -14, -54, -56, -26, -18, -72]), 13, 19, 
        80
      ));
      
      println!("TEST-8...{}", driver(
        Vec::from([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]), 13, 13, 
        1
      ));
      
      println!("TEST-9...{}", driver(
        Vec::from([65, 1, 34, 38, 15, 6, 55, 21, 32, 90, 39, 25, 43, 48, 64, 66, 88, 70, 82, 75, 25, 56, 23, 27, 41, 33, 33, 55, 60, 90, 41, 58, 42, 53, 38, 90, 7, 15]), 37, 33, 
        155
      ));
      
  }
source_py: def maximum_sum_subsequence_least_k_distant_elements(arr, N, k):
      MS = [0 for i in range(N)]
      MS[(N - 1)] = arr[(N - 1)]
      for i in range((N - 2), (- 1), (- 1)):
          if (((i + k) + 1) >= N):
              MS[i] = max(arr[i], MS[(i + 1)])
          else:
              MS[i] = max((arr[i] + MS[((i + k) + 1)]), MS[(i + 1)])
      return MS[0]
source_cpp: int maximum_sum_subsequence_least_k_distant_elements(vector<int> arr, int N, int k) {
    int MS [ N ];
    MS [ N - 1 ] = arr [ N - 1 ];
    for ( int i = N - 2;
    i >= 0;
    i -- ) {
      if ( i + k + 1 >= N ) MS [ i ] = max ( arr [ i ], MS [ i + 1 ] );
      else MS [ i ] = max ( arr [ i ] + MS [ i + k + 1 ], MS [ i + 1 ] );
    }
    return MS [ 0 ];
  }