title: Dice Throw Problem 1
signature: function diceThrowProblem1($f, $d, $s) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($f, $d, $s, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($f, $d, $s), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        57, 5, 33, 
        35960));
      
      printf("TEST-1...%s\n",driver(
        58, 45, 4, 
        0));
      
      printf("TEST-2...%s\n",driver(
        38, 89, 9, 
        0));
      
      printf("TEST-3...%s\n",driver(
        5, 39, 30, 
        0));
      
      printf("TEST-4...%s\n",driver(
        91, 90, 47, 
        0));
      
      printf("TEST-5...%s\n",driver(
        76, 56, 46, 
        0));
      
      printf("TEST-6...%s\n",driver(
        97, 26, 52, 
        247959266474052));
      
      printf("TEST-7...%s\n",driver(
        97, 90, 90, 
        1));
      
      printf("TEST-8...%s\n",driver(
        99, 2, 26, 
        25));
      
  }
  
  main();
  ?>
source_py: def dice_throw_problem_1(f, d, s):
      mem = [[0 for i in range((s + 1))] for j in range((d + 1))]
      mem[0][0] = 1
      for i in range(1, (d + 1)):
          for j in range(1, (s + 1)):
              mem[i][j] = (mem[i][(j - 1)] + mem[(i - 1)][(j - 1)])
              if (((j - f) - 1) >= 0):
                  mem[i][j] -= mem[(i - 1)][((j - f) - 1)]
      return mem[d][s]
source_cpp: long dice_throw_problem_1(int f, int d, int s) {
    long mem [ d + 1 ] [ s + 1 ];
    memset ( mem, 0, sizeof mem );
    mem [ 0 ] [ 0 ] = 1;
    for ( int i = 1;
    i <= d;
    i ++ ) {
      for ( int j = i;
      j <= s;
      j ++ ) {
        mem [ i ] [ j ] = mem [ i ] [ j - 1 ] + mem [ i - 1 ] [ j - 1 ];
        if ( j - f - 1 >= 0 ) mem [ i ] [ j ] -= mem [ i - 1 ] [ j - f - 1 ];
      }
    }
    return mem [ d ] [ s ];
  }