title: Dice Throw Problem 1
signature: pub fn dice_throw_problem_1(f: i32, d: i32, s: i32) -> i64 {
test_code: use std::collections::HashMap;
  use std::collections::HashSet;
  use std::cmp::*;
  use std::collections::*;
  use std::fmt::*; 
  
  
  // SOLUTION CODE
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  pub fn validate_solution(actual: i64, expected: i64)->bool{
  return actual==expected
  }
  pub fn driver(f: i32, d: i32, s: i32, expected: i64)->String{
      if validate_solution(PLACEHOLDER_FN_NAME(f, d, s), expected) {
        return "PASSED".to_string();
      };
      return "FAILED".to_string();
  
  }
  
  fn main() {
      println!("TEST-0...{}", driver(
        57, 5, 33, 
        35960
      ));
      
      println!("TEST-1...{}", driver(
        58, 45, 4, 
        0
      ));
      
      println!("TEST-2...{}", driver(
        38, 89, 9, 
        0
      ));
      
      println!("TEST-3...{}", driver(
        5, 39, 30, 
        0
      ));
      
      println!("TEST-4...{}", driver(
        91, 90, 47, 
        0
      ));
      
      println!("TEST-5...{}", driver(
        76, 56, 46, 
        0
      ));
      
      println!("TEST-6...{}", driver(
        97, 26, 52, 
        247959266474052
      ));
      
      println!("TEST-7...{}", driver(
        97, 90, 90, 
        1
      ));
      
      println!("TEST-8...{}", driver(
        99, 2, 26, 
        25
      ));
      
  }
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 ];
  }