title: Number N Digit Stepping Numbers
signature: long long numberNDigitSteppingNumbers(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(long long actual, long long expected){
      return actual == expected;
  }
  
  string driver(int n, long long 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(18, 547810); 
      cout << "TEST-" << 0 << "..."
           <<  result
           << "\n";
  
      result = driver(26, 100719775); 
      cout << "TEST-" << 1 << "..."
           <<  result
           << "\n";
  
      result = driver(41, 1774846161206); 
      cout << "TEST-" << 2 << "..."
           <<  result
           << "\n";
  
      result = driver(20, 2017126); 
      cout << "TEST-" << 3 << "..."
           <<  result
           << "\n";
  
      result = driver(25, 52479500); 
      cout << "TEST-" << 4 << "..."
           <<  result
           << "\n";
  
      result = driver(52, 2306507126768895); 
      cout << "TEST-" << 5 << "..."
           <<  result
           << "\n";
  
      result = driver(13, 21053); 
      cout << "TEST-" << 6 << "..."
           <<  result
           << "\n";
  
      return 0;
  }
source_py: def number_n_digit_stepping_numbers(n):
      dp = [[0 for x in range(10)] for y in range((n + 1))]
      if (n == 1):
          return 10
      for j in range(10):
          dp[1][j] = 1
      for i in range(2, (n + 1)):
          for j in range(10):
              if (j == 0):
                  dp[i][j] = dp[(i - 1)][(j + 1)]
              elif (j == 9):
                  dp[i][j] = dp[(i - 1)][(j - 1)]
              else:
                  dp[i][j] = (dp[(i - 1)][(j - 1)] + dp[(i - 1)][(j + 1)])
      sum = 0
      for j in range(1, 10):
          sum = (sum + dp[n][j])
      return sum
source_cpp: long long number_n_digit_stepping_numbers(int n) {
    int dp [ n + 1 ] [ 10 ];
    if ( n == 1 ) return 10;
    for ( int j = 0;
    j <= 9;
    j ++ ) dp [ 1 ] [ j ] = 1;
    for ( int i = 2;
    i <= n;
    i ++ ) {
      for ( int j = 0;
      j <= 9;
      j ++ ) {
        if ( j == 0 ) dp [ i ] [ j ] = dp [ i - 1 ] [ j + 1 ];
        else if ( j == 9 ) dp [ i ] [ j ] = dp [ i - 1 ] [ j - 1 ];
        else dp [ i ] [ j ] = dp [ i - 1 ] [ j - 1 ] + dp [ i - 1 ] [ j + 1 ];
      }
    }
    long long sum = 0;
    for ( int j = 1;
    j <= 9;
    j ++ ) sum += dp [ n ] [ j ];
    return sum;
  }