title: Subsequences Size Three Array Whose Sum Divisible M 1
signature: function subsequences_size_three_array_whose_sum_divisible_m_1(a, n, m)
source_py: def subsequences_size_three_array_whose_sum_divisible_m_1(A, N, M):
      ans = 0
      h = ([0] * M)
      for i in range(0, N):
          A[i] = (A[i] % M)
          h[A[i]] = (h[A[i]] + 1)
      for i in range(0, M):
          for j in range(i, M):
              rem = ((M - ((i + j) % M)) % M)
              if (rem < j):
                  continue
              if ((i == j) and (rem == j)):
                  ans = (ans + (((h[i] * (h[i] - 1)) * (h[i] - 2)) / 6))
              elif (i == j):
                  ans = (ans + (((h[i] * (h[i] - 1)) * h[rem]) / 2))
              elif (i == rem):
                  ans = (ans + (((h[i] * (h[i] - 1)) * h[j]) / 2))
              elif (rem == j):
                  ans = (ans + (((h[j] * (h[j] - 1)) * h[i]) / 2))
              else:
                  ans = (ans + ((h[i] * h[j]) * h[rem]))
          return ans
source_cpp: int subsequences_size_three_array_whose_sum_divisible_m_1(vector<int> A, int N, int M) {
    int ans = 0;
    int h [ M ] = {
      0 };
      for ( int i = 0;
      i < N;
      i ++ ) {
        A [ i ] = A [ i ] % M;
        h [ A [ i ] ] ++;
      }
      for ( int i = 0;
      i < M;
      i ++ ) {
        for ( int j = i;
        j < M;
        j ++ ) {
          int rem = ( M - ( i + j ) % M ) % M;
          if ( rem < j ) continue;
          if ( i == j && rem == j ) ans += h [ i ] * ( h [ i ] - 1 ) * ( h [ i ] - 2 ) / 6;
          else if ( i == j ) ans += h [ i ] * ( h [ i ] - 1 ) * h [ rem ] / 2;
          else if ( i == rem ) ans += h [ i ] * ( h [ i ] - 1 ) * h [ j ] / 2;
          else if ( rem == j ) ans += h [ j ] * ( h [ j ] - 1 ) * h [ i ] / 2;
          else ans = ans + h [ i ] * h [ j ] * h [ rem ];
        }
      }
      return ans;
    }
question_info.test_code: 
  
  -- SOLUTION CODE
  -- ============================================
  PLACEHOLDER_CODE_BODY
  
  -- TESTING CODE 
  -- ============================================
  function isCorrect(actual, expected)
      if type(expected) ~= type(actual) then
          return false
      end
      
      if type(expected) == 'table' then
          for k,v_expected in pairs(expected) do
              
              if actual[k] == nil then
                  return false
              end
              local v_actual = actual[k]
              if not isCorrect(v_actual, v_expected) then
                  return false
              end
              actual[k]=nil
          end
      
          if next(actual) then 
              return false
          end
          return true
      else
          return actual == expected
      end
  end
  
  function validateSolution(actual, expected)
      return math.abs(actual - expected) < 1e-06
  end
  
  function driver(a, n, m, expected)
      local exec_result;
      local status, error_msg = pcall(function () 
          exec_result=PLACEHOLDER_FN_NAME(a, n, m) 
      end)
      if status then
          if validateSolution(exec_result,expected) then
              return "PASSED"
          end
          return "FAILED"
      else
          return string.format("ERROR=%s",string.gsub(error_msg,".*:[%d]+: ",""))
      end
  end
      
  function main()
      result = driver({6, 7, 13, 16, 19, 20, 0, 4, 7, 10, 15, 17, 0, 2, 8, 12, 13, 14, 0, 0, 0, 2, 2, 2, 4, 8, 10, 73, 76, 78, 87, 90, 91, 99}, 27, 21, 75.0)
      print(string.format("TEST-0...%s",result))
  
      result = driver({7, 13, 19, 15, 14, 11, 19, 4, 1, 18, 7, 5, 15, 9, 5, 11, 6, 18, 5, 19, 9, 7, 9, 19, 9, 12, 20, 12, 2, 66, 94, 12, 10, 4, 40, -72, 20, -2, -90, -90}, 29, 21, 0.0)
      print(string.format("TEST-1...%s",result))
  
      result = driver({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, 1, 1}, 29, 43, 1140.0)
      print(string.format("TEST-2...%s",result))
  
      result = driver({1, 2, 3, 37, 91}, 3, 4, 0.0)
      print(string.format("TEST-3...%s",result))
  
      result = driver({8, 6, 10, 10, 4, 2, 10, 2, 2, 10, 0, 8, 10, 86, 88}, 13, 12, 17.0)
      print(string.format("TEST-4...%s",result))
  
      result = driver({1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1}, 11, 15, 56.0)
      print(string.format("TEST-5...%s",result))
  
      result = driver({1, 2, 0, 2, 3, 0, 1, 58, 78}, 7, 4, 6.0)
      print(string.format("TEST-6...%s",result))
  
      result = driver({0, 2, 2, 12, 4, 8, 8, 6, 10, 12, 10, 4, 4, -2, -4}, 13, 14, 12.0)
      print(string.format("TEST-7...%s",result))
  
      result = driver({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, 1, 1}, 37, 34, 286.0)
      print(string.format("TEST-8...%s",result))
  
      result = driver({27, 1, 31, 14, 20, 8, 23, 12, 15, 0, 15, 26, 3, 8, 3, 26, 15, 31, 97, 90, 1, 69, 77, 20, 68, 11, 2, 92, 50, 8, 23, 83, 76, 6, 32, 43, 92}, 18, 35, 6.0)
      print(string.format("TEST-9...%s",result))
  
  end
  
  main()
question_info.entry_cls_name: Solution
question_info.test_list: [{"idx": 0, "outputs": 75.0, "inputs": {"a": [6, 7, 13, 16, 19, 20, 0, 4, 7, 10, 15, 17, 0, 2, 8, 12, 13, 14, 0, 0, 0, 2, 2, 2, 4, 8, 10, 73, 76, 78, 87, 90, 91, 99], "n": 27, "m": 21}}, {"idx": 1, "outputs": 0.0, "inputs": {"a": [7, 13, 19, 15, 14, 11, 19, 4, 1, 18, 7, 5, 15, 9, 5, 11, 6, 18, 5, 19, 9, 7, 9, 19, 9, 12, 20, 12, 2, 66, 94, 12, 10, 4, 40, -72, 20, -2, -90, -90], "n": 29, "m": 21}}, {"idx": 2, "outputs": 1140.0, "inputs": {"a": [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, 1, 1], "n": 29, "m": 43}}, {"idx": 3, "outputs": 0.0, "inputs": {"a": [1, 2, 3, 37, 91], "n": 3, "m": 4}}, {"idx": 4, "outputs": 17.0, "inputs": {"a": [8, 6, 10, 10, 4, 2, 10, 2, 2, 10, 0, 8, 10, 86, 88], "n": 13, "m": 12}}, {"idx": 5, "outputs": 56.0, "inputs": {"a": [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1], "n": 11, "m": 15}}, {"idx": 6, "outputs": 6.0, "inputs": {"a": [1, 2, 0, 2, 3, 0, 1, 58, 78], "n": 7, "m": 4}}, {"idx": 7, "outputs": 12.0, "inputs": {"a": [0, 2, 2, 12, 4, 8, 8, 6, 10, 12, 10, 4, 4, -2, -4], "n": 13, "m": 14}}, {"idx": 8, "outputs": 286.0, "inputs": {"a": [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, 1, 1], "n": 37, "m": 34}}, {"idx": 9, "outputs": 6.0, "inputs": {"a": [27, 1, 31, 14, 20, 8, 23, 12, 15, 0, 15, 26, 3, 8, 3, 26, 15, 31, 97, 90, 1, 69, 77, 20, 68, 11, 2, 92, 50, 8, 23, 83, 76, 6, 32, 43, 92], "n": 18, "m": 35}}]
question_info.extension: lua
question_info.entry_fn_name: subsequences_size_three_array_whose_sum_divisible_m_1
question_info.test_case_ids: 0 1 2 3 4 5 6 7 8 9
question_info.commands: lua __FILENAME__