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In this problem, we are given three variables n, s, and k and we have to print all the possible sequences that start with the number n and length s having the absolute difference between consecutive elements less than k.

Let’s take an example to understand the topic better −

Input: n = 3, s = 3 , k = 2 Output: 3 3 3 3 3 4 3 3 2 3 4 4 3 4 5 3 4 3 3 2 2 3 2 3 3 2 1

In this problem, we need to obtain the absolute difference less k. For this, we can get a sequence that has elements that are greater to obtain positive difference and lesser to obtain a negative difference.

For this, we will start with n and the make a recursive call to the elements at each consecutive position. A loop from 0 to k-1 and add it to the number to the number. Similarly going for the negative side also.

#include <bits/stdc++.h> using namespace std; void printConsicutiveNumbers(vector& v, int n, int s, int k){ if (s == 0) { for (int i = 0; i < v.size(); i++) cout<<v[i]<<" "; cout << endl; return; } for (int i = 0; i < k; i++) { v.push_back(n + i); printConsicutiveNumbers(v, n + i, s - 1, k); v.pop_back(); } for (int i = 1; i < k; i++) { v.push_back(n - i); printConsicutiveNumbers(v, n - i, s - 1, k); v.pop_back(); } } int main(){ int n = 3, s = 3, k = 2; cout<<"The sequence is :\n"; vector<int> v; v.push_back(n); printConsicutiveNumbers(v, n, s - 1, k); return 0; }

The sequence is −

3 3 3 3 3 4 3 3 2 3 4 4 3 4 5 3 4 3 3 2 2 3 2 3 3 2 1

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