title: Maximum Sum Subsequence Least K Distant Elements
signature: int maximumSumSubsequenceLeastKDistantElements(vector<int> arr, int n, int k) {
test_code: #include <algorithm>
  #include <assert.h>
  #include <cstdlib>
  #include <iostream>
  #include <map>
  #include <set>
  #include <string>
  #include <tuple> 
  #include <unordered_map>
  #include <vector>
  #include <math.h>
  #include <cmath>
  #include <bits/stdc++.h>
  #include <numeric>
  #include <functional>
  
  using namespace std;
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  bool validateSolution(int actual, int expected){
      return actual == expected;
  }
  
  string driver(vector<int> arr, int n, int k, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(arr, n, k), expected)){
              return "PASSED";
          }
          return "FAILED";
      }
      catch (const std::overflow_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::runtime_error& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (const std::exception& exception_obj)
      {
          return typeid(exception_obj).name();
      }
      catch (...)
      {
          return "UNK_ERROR";
      }
  }
  
  int main() {
      string result = "";
  
      result = driver({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); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver({32, 34, -40, 90, -82, -70, 30, 26, -76, -46, -84, 76, -76}, 9, 10, 90); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver({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); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver({96, 15, 30, 25, 83}, 2, 3, 96); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver({-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); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver({1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0}, 9, 9, 1); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver({1, 2, 9, 17, 24, 31, 31, 33, 56, 57, 61, 71, 73, 74, 76, 77, 79, 83, 86, 95, 99}, 12, 10, 72); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver({-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); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver({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); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver({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); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
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 ];
  }