Numbers with Same Consecutive Differences in C++

Suppose we have to find all non-negative integers of length N such that the absolute difference between every two consecutive digits is K. We have to keep in mind that every number in the answer must not have leading zeros except for the number 0 itself. We may return the answer in any order. So if N = 3 and K = 7, then output will be [181,292,707,818,929], Here we can see 070 is not a valid number, because it has one leading zero.

To solve this, we will follow these steps −

• Create one matrix called dp, and its size will be n + 1, fill 1 to 9 into dp[1]

• for i in range 1 to N – 1

  • Define a set called visited

  • for j in range 0 to size of dp[i]

    • x := dp[i, j]

    • lastNum := last digit of x

    • digit := lastNum + k

    • if digit is in range 0 to 9, and (x*10 + digit) is not visited, then

      • insert (10*x + digit) into dp[i + 1]

      • insert 10*x + digit into visited array

    • digit := lastNum – K

    • if digit is in range 0 to 9, and (x*10 + digit) is not visited, then

      • insert (10*x + digit) into dp[i + 1]

      • insert 10*x + digit into visited array

• if N is 1, then insert 0 into dp[N]

• return dp[N]

Let us see the following implementation to get better understanding −

Example

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<int> v){
   cout << "[";
   for(int i = 0; i<v.size(); i++){
      cout << v[i] << ", ";
   }
   cout << "]"<<endl;
}
class Solution {
   public:
   vector<int> numsSameConsecDiff(int N, int K) {
      vector <int> dp[N + 1];
      for(int i = 1; i <= 9; i++){
         dp[1].push_back(i);
      }
      for(int i = 1; i < N; i++){
         set <int> visited;
         for(int j = 0; j < dp[i].size(); j++){
            int x = dp[i][j];
            int lastNum = x % 10;
            int digit = lastNum + K;
            if(digit >= 0 && digit <= 9 && !visited.count(x * 10 + digit)){
               dp[i + 1].push_back(x * 10 + digit);
               visited.insert(x * 10 + digit);
            }
            digit = lastNum - K;
            if(digit >= 0 && digit <= 9 && !visited.count(x * 10 + digit)){
               dp[i + 1].push_back(x * 10 + digit);
               visited.insert(x * 10 + digit);
            }
         }
      }
      if(N == 1){
         dp[N].push_back(0);
      }
      return dp[N];
   }
};
main(){
   Solution ob;
   print_vector(ob.numsSameConsecDiff(3,7));
}

Input

3
7

Output

[181,292,707,818,929]