title: Count Possible Paths Top Left Bottom Right Nxm Matrix 2
signature: function countPossiblePathsTopLeftBottomRightNxmMatrix2($p, $q) {
test_code: <?php
  
  
  // SOLUTION CODE 
  // ============================================
  PLACEHOLDER_CODE_BODY
  
  // TESTING CODE 
  // ============================================
  function validateSolution($actual, $expected){
      return serialize($actual) == serialize($expected);
  }
  
  function driver($p, $q, $expected){
      try{
        if (validateSolution(PLACEHOLDER_FN_NAME($p, $q), $expected)){
          return "PASSED";
        }
        return "FAILED";
      }
      catch (Exception $exception_obj) {
        return get_class($exception_obj);
      }
  }
  
  function main(){
      printf("TEST-0...%s\n",driver(
        70, 5, 
        1088430));
      
      printf("TEST-1...%s\n",driver(
        9, 59, 
        5743572120));
      
      printf("TEST-2...%s\n",driver(
        54, 1, 
        1));
      
  }
  
  main();
  ?>
source_py: def count_possible_paths_top_left_bottom_right_nxm_matrix_2(p, q):
      dp = [1 for i in range(q)]
      for i in range((p - 1)):
          for j in range(1, q):
              dp[j] += dp[(j - 1)]
      return dp[(q - 1)]
source_cpp: int count_possible_paths_top_left_bottom_right_nxm_matrix_2(int m, int n) {
    int dp [ n ] = {
      1 };
      dp [ 0 ] = 1;
      for ( int i = 0;
      i < m;
      i ++ ) {
        for ( int j = 1;
        j < n;
        j ++ ) {
          dp [ j ] += dp [ j - 1 ];
        }
      }
      return dp [ n - 1 ];
    }