Given N which is the size of the N X N spiral matrix of the form:
16 15 14 13 5 4 3 12 6 1 2 11 7 8 9 10
The task is to find the sum of the diagonal elements of this matrix.
Input: N = 3 Output: 25 5 4 3 6 1 2 7 8 9 The sum of elements along its two diagonals will be 1 + 3 + 7 + 5 + 9 = 25 Input: N = 5 Output: 101
Approach: Idea behind the solution is to use the concept of Dynamic Programming. We will use array dp to store our solution. N given in the problem can either be even or odd.
When i is odd, we have to add only 4 corner elements in dp[i – 2].
dp[i] = dp[i – 2] + (i – 2) * (i – 2) + (i – 1) + (i – 2) * (i – 2) + 2 * (i – 1) + (i – 2) * (i – 2) + 3 * (i – 1) + (i – 2) * (i – 2) + 4 * (i – 1)
dp[i] = dp[i – 2] + 4 * (i – 2) * (i – 2) + 10 * (i – 1)
dp[i] = dp[i – 2] + 4 * (i) * (i) – 6 * (i – 1)
Similarly, we can check that the above formula is true when i is even.
Below is the implementation of the above approach:
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