1. Sort the array (say arr) (O(nlgn)
2. Find the position of 0 in the array. The left of the array would be all -ve
and right of the array is all positive. Say zi is the position of zero, so
indices [0, zi) are all -ve and (zi, n-1] are all +ve. (O(lgn). If 0 is not
there in the array, we can still find its position, say it is b/w ith and
(i+1)th index. Then the -ve array would be with indices [0, i], and +ve array
would be (i, n-1].
3a. if(zi == n-1) // arr contains -ve elements only
return arr[0]*arr[1]*arr[2];
3b. if(zi == 0) // arr contains +ve elements only
return arr[n-1]*arr[n-2]*arr[n-3];
3c. return max{arr[n-1]*arr[n-2]*arr[n-3], arr[n-1]*arr[zi-1]*arr[zi-2]};
Only other cases remaining are boundry conditions, for e.g. if -ve array size
is 1, or when +ve array size is < 3.
So seems doable in O(nlgn + lgn).
________________________________
From: SP Praveen <praveen.sel...@gmail.com>
To: Algorithm Geeks <algogeeks@googlegroups.com>
Sent: Sunday, 13 September, 2009 7:04:37 PM
Subject: [algogeeks] max product of any three nos in an array of signed integers
Given an array of integers (signed integers), find three numbers in
that array which form the maximum product.
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