Friday, 3 August 2012

Maximum Product Subarray

Given an array that contains both positive and negative integers, find the product of the maximum product subarray. Expected Time complexity is O(n) and only O(1) extra space can be used.

I. The solution that came to my mind first is to "Use a way similar to Kadane's algorithm for finding the maximum sum of a sub array.", but in this case the when (prd<0) we can't just discard it like we do it fro sum, bcoz a future -ve number might make this the highest product :P.
We would have to keep an integer storing the last_neg_num_prod to store the last -ve product upto a point and then set (prd=1).

public static void main(String[] args) {
int a[] = {-2, -3, 0, -2, -40};
int max= Integer.MIN_VALUE, last_neg_prod=0, prd= 1;
for(int i=0;i<a.length;i++){
prd = prd * a[i];
if(last_neg_prod<0){ // we have an old -ve product, we can combine these to get a higher +ve product then
prd = prd*last_neg_prod;
last_neg_prod = 0;
break out;
last_neg_prod = prd;
prd = 1;
else if(prd ==0){
last_neg_prod = 0;
max = prd;

System.out.println("max prd is:"+max);



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