Maximum Product Subarray

Question

from lintcode
Find the contiguous subarray within an array (containing at least one number) which has the largest product.
Example
For example, given the array [2,3,-2,4], the contiguous subarray [2,3] has the largest product = 6.

Idea

We all know that a max/min value can be retrieved by a loop.

You need to keep track of three things:

• global max: the final answer
• contiguous max: the max product adjacent to the current value in the loop
• contiguous min: the min product adjacent to the current value in the loop, you want to keep this because it might become next contiguous maximum (sign production rule: - * - = +)

public class Solution {
    /**
     * @param nums: an array of integers
     * @return: an integer
     */
    public int maxProduct(int[] nums) {
        // edge case
        if (nums.length == 0) {
            return 0;
        }
        // previous 
        int prevContiguousMax = nums[0], prevContiguousMin = nums[0];

        int contiguousMax, contiguousMin;

        int globalMax = nums[0];

        // for each number
        for (int i = 1; i < nums.length; i ++) {
            contiguousMax = 
                Math.max(nums[i], Math.max(prevContiguousMin * nums[i], prevContiguousMax * nums[i]));
            contiguousMin = 
                Math.min(nums[i], Math.min(prevContiguousMin * nums[i], prevContiguousMax * nums[i]));
            globalMax = Math.max(globalMax, contiguousMax);
            prevContiguousMin = contiguousMax;
            prevContiguousMax = contiguousMin;
        }
        return globalMax;
    }
}