05. Count Possible Ways to Construct Buildings

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

My Approach

The problem involves determining the total number of ways to construct buildings on plots along a road. The constraint is that no two buildings can be adjacent, and this restriction also applies to buildings on opposite sides of the road. The goal is to find a count of valid arrangements for a given number of plots.

To approach this problem:

• Initialize three variables, curr, prev, and next, which represent the count of valid arrangements for the current, previous, and next plots, respectively.

• Iterate through the plots from 1 to N, updating the next count as the sum of curr and prev, taking care of the modulo operation (mod). This step ensures that we calculate the number of valid arrangements for the current plot based on the counts of valid arrangements for the previous two plots.

• Update prev and curr for the next iteration.

• The final result is calculated as (curr * curr) % mod. This represents the total number of ways to construct buildings on both sides of the road without violating the adjacency rule.

Time and Auxiliary Space Complexity

• Time Complexity: The time complexity of this solution is O(N) since there is a single loop that iterates N times.

• Auxiliary Space Complexity: The auxiliary space complexity is O(1) since only a constant amount of extra space is used.

Code (C++)

class Solution {
public:
    int mod = 1e9 + 7;

    int TotalWays(int N) {
        long long curr, prev, next;
        curr = prev = 1;
        for (int i = 1; i <= N; ++i) {
            next = (curr + prev) % mod;
            prev = curr;
            curr = next;
        }

        return (curr * curr) % mod;
    }
};

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