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n-th number with digits in {0, 1, 2, 3, 4, 5} in C++
The numbers formed with the digits {0, 1, 2, 3, 4, 5} are
0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, etc..,
We can form the above sequence using the first 6 digits. Let's see an example of the formation of numbers.
1 * 10 + 0 = 10 1 * 10 + 1 = 11 1 * 10 + 2 = 12 1 * 10 + 3 = 13 1 * 10 + 4 = 14 1 * 10 + 5 = 15
Similarly, apply for the number 2, 3, 4, 5. You will get the next 6 numbers with 2 using the above pattern. And then 3 after that 4 and 5.
Algorithm
- Initialise the number n.
- Initialise a vector.
- Write a loop that iterates from 0 to 5.
- Push all the numbers to vector.
- We have first six numbers of the series.
- Write a loop that iterates from 0 to n / 6.
- Write a loop that iterates from 0 to 5.
- Generate remaining numbers with the above discussed pattern.
- Push them to the vector.
- Write a loop that iterates from 0 to 5.
- Return the n-th number from the sequence.
Implementation
Following is the implementation of the above algorithm in C++
#include <bits/stdc++.h>
using namespace std;
int findNthNumber(int n) {
vector<int> numbers;
for (int i = 0; i < 6; i++) {
numbers.push_back(i);
}
for (int i = 0; i <= n / 6; i++) {
for (int j = 0; j < 6; j++) {
if ((numbers[i] * 10) != 0) {
numbers.push_back(numbers[i] * 10 + numbers[j]);
}
}
}
return numbers[n - 1];
}
int main() {
int n = 7;
cout << findNthNumber(n) << endl;
return 0;
}Output
If you run the above code, then you will get the following result.
10
Updated on: 22-Oct-2021
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