title: Maximum Subsequence Sum Such That No Three Are Consecutive
signature: function maximumSubsequenceSumSuchThatNoThreeAreConsecutive(arr: Array<number>, n: number): number {
source_py: def maximum_subsequence_sum_such_that_no_three_are_consecutive(arr, n):
      sum = [0 for k in range(n)]
      if (n >= 1):
          sum[0] = arr[0]
      if (n >= 2):
          sum[1] = (arr[0] + arr[1])
      if (n > 2):
          sum[2] = max(sum[1], max((arr[1] + arr[2]), (arr[0] + arr[2])))
      for i in range(3, n):
          sum[i] = max(max(sum[(i - 1)], (sum[(i - 2)] + arr[i])), ((arr[i] + arr[(i - 1)]) + sum[(i - 3)]))
      return sum[(n - 1)]
source_cpp: int maximum_subsequence_sum_such_that_no_three_are_consecutive(vector<int> arr, int n) {
    int sum [ n ];
    if ( n >= 1 ) sum [ 0 ] = arr [ 0 ];
    if ( n >= 2 ) sum [ 1 ] = arr [ 0 ] + arr [ 1 ];
    if ( n > 2 ) sum [ 2 ] = max ( sum [ 1 ], max ( arr [ 1 ] + arr [ 2 ], arr [ 0 ] + arr [ 2 ] ) );
    for ( int i = 3;
    i < n;
    i ++ ) sum [ i ] = max ( max ( sum [ i - 1 ], sum [ i - 2 ] + arr [ i ] ), arr [ i ] + arr [ i - 1 ] + sum [ i - 3 ] );
    return sum [ n - 1 ];
  }
question_info.test_list: [{"idx": 0, "outputs": 832, "inputs": {"arr": [5, 6, 8, 9, 10, 10, 16, 17, 17, 20, 21, 22, 23, 28, 29, 32, 36, 37, 40, 41, 42, 43, 47, 47, 48, 48, 49, 49, 52, 52, 53, 59, 61, 64, 65, 79, 79, 81, 87, 91, 92, 98], "n": 35}}, {"idx": 1, "outputs": 308, "inputs": {"arr": [98, 76, -80, -30, 82, 52, -14, 28, 98, 18, 82, 52, 26, -62, -8], "n": 7}}, {"idx": 2, "outputs": 2, "inputs": {"arr": [0, 0, 0, 0, 0, 1, 1, 1, 1], "n": 7}}, {"idx": 3, "outputs": 419, "inputs": {"arr": [21, 26, 85, 73, 47, 10, 54, 9, 11, 70, 42, 95, 44, 91], "n": 12}}, {"idx": 4, "outputs": -182, "inputs": {"arr": [-94, -92, -90, -84, -76, -68, -60, -50, -34, -34, -20, -16, -6, 18, 50, 54, 66, 70, 96], "n": 9}}, {"idx": 5, "outputs": 7, "inputs": {"arr": [1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], "n": 16}}, {"idx": 6, "outputs": 895, "inputs": {"arr": [2, 3, 4, 4, 14, 14, 18, 21, 24, 26, 29, 31, 32, 34, 36, 37, 38, 40, 42, 44, 44, 54, 63, 69, 77, 77, 82, 82, 86, 87, 90, 93, 95], "n": 31}}, {"idx": 7, "outputs": 450, "inputs": {"arr": [-46, 64, -44, 88, -74, 54, 40, -2, -24, 94, 40, -44, 56, -54, -60, -86, -58, 48, -90, 12, -76, -30, 94, -34, 14, 12, 80, -40, 60], "n": 22}}, {"idx": 8, "outputs": 0, "inputs": {"arr": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1], "n": 7}}, {"idx": 9, "outputs": 895, "inputs": {"arr": [4, 32, 63, 23, 44, 57, 59, 69, 88, 61, 66, 61, 65, 33, 79, 58, 71, 2, 80, 41, 83, 12, 20, 9, 7, 40, 36, 97, 10, 98, 66, 78, 71, 37, 53], "n": 26}}]
question_info.entry_cls_name: Solution
question_info.test_code: 
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function convertToString(value: any): string{
      return JSON.stringify(value, function (key, val) {
          if (val instanceof Set) {
              return Array.from(val);
          } return val;});
  }
  
  function validateSolution(actual: number, expected: number): boolean {
      return convertToString(actual) === convertToString(expected);
  }
  
  function driver(arr: Array<number>, n: number, expected:number): string {
      try{
          if (validateSolution(PLACEHOLDER_FN_NAME(arr, n),expected)){
              return "PASSED";
          }
          return "FAILED";
      } catch (error) {
        return error.name;
      }
      
  }
      
  function main(){
    let result = '';
    result = driver([5, 6, 8, 9, 10, 10, 16, 17, 17, 20, 21, 22, 23, 28, 29, 32, 36, 37, 40, 41, 42, 43, 47, 47, 48, 48, 49, 49, 52, 52, 53, 59, 61, 64, 65, 79, 79, 81, 87, 91, 92, 98], 35, 832);
    console.log(`TEST-0...${result}`);
  
    result = driver([98, 76, -80, -30, 82, 52, -14, 28, 98, 18, 82, 52, 26, -62, -8], 7, 308);
    console.log(`TEST-1...${result}`);
  
    result = driver([0, 0, 0, 0, 0, 1, 1, 1, 1], 7, 2);
    console.log(`TEST-2...${result}`);
  
    result = driver([21, 26, 85, 73, 47, 10, 54, 9, 11, 70, 42, 95, 44, 91], 12, 419);
    console.log(`TEST-3...${result}`);
  
    result = driver([-94, -92, -90, -84, -76, -68, -60, -50, -34, -34, -20, -16, -6, 18, 50, 54, 66, 70, 96], 9, -182);
    console.log(`TEST-4...${result}`);
  
    result = driver([1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1], 16, 7);
    console.log(`TEST-5...${result}`);
  
    result = driver([2, 3, 4, 4, 14, 14, 18, 21, 24, 26, 29, 31, 32, 34, 36, 37, 38, 40, 42, 44, 44, 54, 63, 69, 77, 77, 82, 82, 86, 87, 90, 93, 95], 31, 895);
    console.log(`TEST-6...${result}`);
  
    result = driver([-46, 64, -44, 88, -74, 54, 40, -2, -24, 94, 40, -44, 56, -54, -60, -86, -58, 48, -90, 12, -76, -30, 94, -34, 14, 12, 80, -40, 60], 22, 450);
    console.log(`TEST-7...${result}`);
  
    result = driver([0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1], 7, 0);
    console.log(`TEST-8...${result}`);
  
    result = driver([4, 32, 63, 23, 44, 57, 59, 69, 88, 61, 66, 61, 65, 33, 79, 58, 71, 2, 80, 41, 83, 12, 20, 9, 7, 40, 36, 97, 10, 98, 66, 78, 71, 37, 53], 26, 895);
    console.log(`TEST-9...${result}`);
  
  };
  
  main();
question_info.extension: ts
question_info.entry_fn_name: maximumSubsequenceSumSuchThatNoThreeAreConsecutive
question_info.test_case_ids: 0 1 2 3 4 5 6 7 8 9
question_info.commands: tsc --target es2020 --lib es5,dom,es2015,es2020 __FILENAME__
question_info.commands: node __FILENAME__.js