Minimum Perimeter of n blocks
We are given n blocks of size 1 x 1, we need to find the minimum perimeter of the grid made by these blocks.
Input : n = 4 Output : 8 Minimum possible perimeter with 4 blocks is 8. See below explanation. Input : n = 11 Output : 14 The square grid of above examples would be as
Let us take an example to see a pattern. Let us say that we have 4 blocks, following are different possibilities
+--+--+--+--+ | | | | | Perimeter = 10 +--+--+--+--+ +--+--+--+ | | | | Perimeter = 10 +--+--+--+ | | +--+ +--+--+--+ | | | | Perimeter = 10 +--+--+--+ | | +--+ +--+--+ | | | Perimeter = 8 +--+--+ | | | +--+--+
If we do some examples using pen and paper, we can notice that the perimeter becomes minimum when the shape formed is closest to a square. The reason for this is, we want maximum sides of blocks to face inside the shape so that perimeter of the shape becomes minimum.
If the Number of blocks is a perfect square then the perimeter would simply be 4*sqrt(n).
But, if the Number of blocks is not a perfect square root then we calculate number of rows and columns closest to square root. After arranging the blocks in a rectangular we still have blocks left then we will simply add 2 to the perimeter because only 2 extra side would be left.
The implementation of the above idea is given below.
Time complexity : O(logn)
Auxiliary Space : O(1)
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