Given two integers R and C, the task is to find the element at the Rth row and Cth column.
- First Element of ith row =
- Every element is a Arthmetic progression increasing difference where common difference is 1.
- Intial Difference Term =
Input: R = 4, C = 4
Pattern of size 4 * 4 is –
1 3 6 10
2 5 9 14
4 8 13 19
7 12 18 25
Therefore, Element at Pat = 25
Input: R = 3, C = 3
Pattern of size 3 * 3 is –
1 3 6
2 5 9
4 8 13
Therefore, element at Pat = 13
Naive Approach: A simple solution is to generate the pattern matrix of size R * C and then finally return the element at the Rth row and Cth column.
Time Complexity: O(R*C)
Auxiliary Space: O(R*C)
Efficient Approach: The idea is to find the first term of the Rth row using the formulae and then finally compute the Cth term of that column using the help of loop.
Below is the implementation of the above approach:
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