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;
     }
 }