Print K’th element in spiral form of matrix

Given a 2D Matrix of order n X m , print K’th element in spiral form of matrix. See the following examples.

Examples:

Input: mat[][] = 
          {{1, 2, 3, 4}
           {5, 6, 7, 8}
           {9, 10, 11, 12}
           {13, 14, 15, 16}}
       k = 6
Output: 12

Input: mat[][] =
       {{1, 2, 3, 4, 5, 6}
        {7, 8, 9, 10, 11, 12}
        {13, 14, 15, 16, 17, 18}}
       k = 17
Output: 10

Simple Solution:
One simple solution is to start traversing matrix in spiral form Print Spiral Matrix and start a counter i.e; count = 0. Whenever count gets equal to K, print that element. Time complexity for this approach will be O(n^2).

Efficient Solution:
We will consider only edge of the matrix at a time and then do recursion for the sub matrix made by removing edges of main matrix.

1. If k <= m : element is in first row.
2. Else If k <= (m+n-1) : element is in last column.
3. Else If k <= (m+n-1+m-1) : element is in last row.
4. Else If k <= (m+n-1+m-1+n-2) : element is in first column.
5. Else Element lies somewhere in middle matrix.

Output:

 10

Time Complexity : O(c) where c is number of outer circular rings with respect to k’th element.
Space complexity: O(1)

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