title: Dice Throw Problem
signature: def diceThrowProblem(m: Int, n: Int, x: Int) = {
test_code: import scala.collection.mutable.HashMap
  import scala.collection.immutable.HashSet
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  
  // TESTING CODE 
  // ============================================
  def validateSolution(actual: Int , expected: Int): Boolean = {
      actual.toString == expected.toString
  }
  
  def driver(m: Int, n: Int, x: Int, expected: Int): String = {
      try {
          if (validateSolution(PLACEHOLDER_FN_NAME(m, n, x),expected)) {
              "PASSED"
          } else{
              "FAILED"
          }
      }catch{
          case e: Exception => {e.getClass.getName}
      }
  
  }
  object QuestionEvaluator extends App {
  
      println(s"TEST-0...${driver(
        94, 4, 69, 
        50116    
      )}")   
  
  
      println(s"TEST-1...${driver(
        7, 12, 33, 
        77635844    
      )}")   
  
  
      println(s"TEST-2...${driver(
        20, 44, 24, 
        0    
      )}")   
  
  
      println(s"TEST-3...${driver(
        90, 94, 88, 
        0    
      )}")   
  
  
      println(s"TEST-4...${driver(
        50, 58, 27, 
        0    
      )}")   
  
  
      println(s"TEST-5...${driver(
        32, 90, 29, 
        0    
      )}")   
  
  
      println(s"TEST-6...${driver(
        46, 25, 6, 
        0    
      )}")   
  
  
      println(s"TEST-7...${driver(
        43, 82, 70, 
        0    
      )}")   
  
  
      println(s"TEST-8...${driver(
        6, 83, 19, 
        0    
      )}")   
  
  }
  
source_py: def dice_throw_problem(m, n, x):
      table = [([0] * (x + 1)) for i in range((n + 1))]
      for j in range(1, min((m + 1), (x + 1))):
          table[1][j] = 1
      for i in range(2, (n + 1)):
          for j in range(1, (x + 1)):
              for k in range(1, min((m + 1), j)):
                  table[i][j] += table[(i - 1)][(j - k)]
      return table[(- 1)][(- 1)]
source_cpp: int dice_throw_problem(int m, int n, int x) {
    int table [ n + 1 ] [ x + 1 ];
    memset ( table, 0, sizeof ( table ) );
    for ( int j = 1;
    j <= m && j <= x;
    j ++ ) table [ 1 ] [ j ] = 1;
    for ( int i = 2;
    i <= n;
    i ++ ) for ( int j = 1;
    j <= x;
    j ++ ) for ( int k = 1;
    k <= m && k < j;
    k ++ ) table [ i ] [ j ] += table [ i - 1 ] [ j - k ];
    return table [ n ] [ x ];
  }