title: Recursively Break Number 3 Parts Get Maximum Sum 1
signature: int recursivelyBreakNumber3PartsGetMaximumSum1(int n) {
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(int n, int expected){
      try
      {
          if (validateSolution(PLACEHOLDER_FN_NAME(n), 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(50, 57); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver(83, 93); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver(18, 19); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver(24, 27); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver(31, 32); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver(38, 41); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver(94, 104); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      result = driver(24, 27); 
      cout << "TEST-" << 7 << "..."
           <<  result
           << "\n";
  
      result = driver(13, 13); 
      cout << "TEST-" << 8 << "..."
           <<  result
           << "\n";
  
      result = driver(53, 57); 
      cout << "TEST-" << 9 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
source_py: def recursively_break_number_3_parts_get_maximum_sum_1(n):
      dp = ([0] * (n + 1))
      dp[0] = 0
      dp[1] = 1
      for i in range(2, (n + 1)):
          dp[i] = max(((dp[int((i / 2))] + dp[int((i / 3))]) + dp[int((i / 4))]), i)
      return dp[n]
source_cpp: int recursively_break_number_3_parts_get_maximum_sum_1(int n) {
    int dp [ n + 1 ];
    dp [ 0 ] = 0, dp [ 1 ] = 1;
    for ( int i = 2;
    i <= n;
    i ++ ) dp [ i ] = max ( dp [ i / 2 ] + dp [ i / 3 ] + dp [ i / 4 ], i );
    return dp [ n ];
  }