Question

Design a linear algorithm to rearrange the elements of a given array of n elements so that all its negative numbers precede any zeroes, and any zeroes precede any positive numbers. It should also be space efficient so that it doesn’t require more than a constant amount of additional space.

Everything I am thinking of is much bigger than O(n), and would love some tips/hints/help/java code!

Answer 1

Help? Hint: Quicksort’s partition part with pivot as 0. See this Wikipedia article, look for in-place version.

---

I just realized if you implement teh exact version given in the link above it may not help if you have dupes of zero. My statement is still true that you need to use partition part of Quicksort, but the partition is going to be done by Dutch National Flag problem or three way partitioning. Here is the pseudo code for you

//assume index based 1
A[1..n]
p = 0
q = n+1
i = 1

while i < q
  if A[i] < 0
   swap(i, ++p)
  else if A[i] > 0
   swap(i, --q)
  else
   i++

Time complexity:    O(n)
Space complexity: O(1)