Lintcode: Maximum Subarray Difference

Given an array with integers.

Find two non-overlapping subarrays A and B, which |SUM(A) - SUM(B)| is the largest.

Return the largest difference.

Note
The subarray should contain at least one number

Example
For [1, 2, -3, 1], return 6

Challenge
O(n) time and O(n) space.

思路：把数组分成两部分，可以从i和i+1(0<=  i < len-1)之间分开，a[0, i] a[i+1, len-1]，然后分别求两个子数组中的最大子段和，以及最小字段和，然后求差的最大值即可。

public class Solution {
    /**
     * @param nums: A list of integers
     * @return: An integer indicate the value of maximum difference between two
     *          Subarrays
     */
    public int maxDiffSubArrays(ArrayList<Integer> nums) {
        // write your code
        if (nums==null || nums.size()==0) return 0;
        int len = nums.size();
        int[] lGlobalMax = new int[len];
        int[] lGlobalMin = new int[len];
        int lLocalMax = nums.get(0);
        int lLocalMin = nums.get(0);
        lGlobalMax[0] = lLocalMax;
        lGlobalMin[0] = lLocalMin;
        for (int i=1; i<len; i++) {
            lLocalMax = Math.max(lLocalMax+nums.get(i), nums.get(i));
            lGlobalMax[i] = Math.max(lLocalMax, lGlobalMax[i-1]);
            
            lLocalMin = Math.min(lLocalMin+nums.get(i), nums.get(i));
            lGlobalMin[i] = Math.min(lLocalMin, lGlobalMin[i-1]);
        }
        
        int[] rGlobalMax = new int[len];
        int[] rGlobalMin = new int[len];
        int rLocalMax = nums.get(len-1);
        int rLocalMin = nums.get(len-1);
        rGlobalMax[len-1] = rLocalMax;
        rGlobalMin[len-1] = rLocalMin;
        for (int i=len-2; i>=0; i--) {
            rLocalMax = Math.max(rLocalMax+nums.get(i), nums.get(i));
            rGlobalMax[i] = Math.max(rLocalMax, rGlobalMax[i+1]);
            
            rLocalMin = Math.min(rLocalMin+nums.get(i), nums.get(i));
            rGlobalMin[i] = Math.min(rLocalMin, rGlobalMin[i+1]);
        }
        
        int maxDiff = Integer.MIN_VALUE;
        for (int i=0; i<len-1; i++) {
            if (maxDiff < Math.abs(lGlobalMax[i]-rGlobalMin[i+1]))
                maxDiff = Math.abs(lGlobalMax[i]-rGlobalMin[i+1]);
                
             
            if (maxDiff < Math.abs(lGlobalMin[i]-rGlobalMax[i+1]))
                maxDiff = Math.abs(lGlobalMin[i]-rGlobalMax[i+1]);
        }
        return maxDiff;
    }
}