We have an integer array that is sorted in ascending order. We also have 3 ints A, B and C. We need to apply A*x*x + B*x + C for each element x in the array and return the corresponding sorted array.
Example: Input array = -1 0 1 2 3 4 and A = -1, B = 2, C = -1
Result of applying the formula to each element = -4 -1 0 -1 -4 -9
So expected result = -9 -4 -4 -1 -1 0 (sorted)
Time complexity :o(n), no extra space
Method: Parabolic Property
The equation given is parabolic. So the result of applying it to a sorted array will result in an array that will have a maximum/minimum with the sub-arrays to its left and right sorted.
In your case the maximum is 0 and the sub array to its left [-4 -1] is sorted in ascending order and the sub-array to its right [-1 -4 -9] is sorted in descending order.
All you need to do is merge these sorted arrays which is linear in time.
So the algorithm is:
Apply equation on each element
Find maximum/minimum
Merge subarrays
Useful Link:
http://stackoverflow.com/questions/4551599/sorting-result-array
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