14. Painting the Fence

The problem can be found at the following link: Question Link

My Approach

I'm solving this problem using a dynamic programming approach. I maintain three variables: same, diff, and total. At each step, I update these variables according to the given recurrence relation. The loop iterates from 2 to n, updating the variables in each iteration.

Time and Auxiliary Space Complexity

• Time Complexity: O(n) - The loop runs for n iterations.

• Auxiliary Space Complexity: O(1) - The algorithm uses a constant amount of space for variables regardless of the input size.

Code (C++)

class Solution {
public:
    long long countWays(int n, int k){
        long mod = 1e9 + 7;
        long same = 0;
        long diff = k;
        long total = same + diff;

        for(int i = 2; i <= n; ++i) {
            same = diff * 1;
            diff = (total * (k - 1)) % mod;
            total = same + diff;
        }
        return total % mod;
    }
};

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