[LintCode]Maximum Subarray Difference

Solving this question by O(n) time w/ O(n) space. The basic idea is to find a appropriate cut let the difference become largest.
We keep track local max, local min, left max, left min, and right min, right max.

class Solution {public:    /**     * @param nums: A list of integers     * @return: An integer indicate the value of maximum difference between two     *          Subarrays     */    int maxDiffSubArrays(vector<int> nums) {        // write your code here        if(nums.empty()) return 0;        int n = nums.size(), localMax = 0, localMin = 0, res = INT_MIN;        vector<int> leftMax(n,0);        vector<int> leftMin(n,0);        for(int i = 0; i<n; ++i){            localMax = max(nums[i], nums[i] + localMax);            localMin = min(nums[i], nums[i] + localMin);            if(i == 0){                leftMax[i] = localMax;                leftMin[i] = localMin;            }else{                leftMax[i] = max(leftMax[i-1], localMax);                leftMin[i] = min(leftMin[i-1], localMin);            }        }        localMax = 0, localMin = 0;        int rightMax = 0, rightMin = 0;        for (int i = n-1; i>0; --i) {            localMax = max(nums[i]+localMax, nums[i]);            localMin = min(nums[i] + localMin, nums[i]);            if(i == n-1){                rightMax = localMax;                rightMin = localMin;            }else{                rightMax = max(localMax, rightMax);                rightMin = min(localMin, rightMin);            }            res = max(res, max(abs(rightMax - leftMin[i-1]),abs(leftMax[i-1]-rightMin)));        }        return res;    }};