// Solution 1:

class Solution {
public:
    int maxSubArray(vector<int> &nums){
        //类似寻找最大最小值的题目，初始值一定要定义成理论上的最小最大值 
        // 或者不用初始化为理论的最小值
        //int res = INT_MIN;
        int res = nums[0];
        int n = nums.size();
        for (int i=0;i<n;i++)
        {
            int sum = 0;
            for (int j=i;j<n;j++)
            {
                sum+=nums[j];
                res = max(res,sum);
            }
        }
        return res;
    }
};


// Solution 2:
class Solution {
public:
    int maxSubArray(vector<int>& nums){
        int res = nums[0];
        int n = nums.size();
        vector<int> dp(n);
        dp[0] = nums[0];
        for (int i=1;i<n;i++)
        {
            dp[i] = max(dp[i-1]+nums[i],nums[i]);
            res = max(res,dp[i]);
        }
        return res;
    }
};


class Solution {
public:
    int maxSubArray(vector<int>& nums){
        int res = nums[0];
        int n = nums.size();
        int sum = 0;
        for (int i=0;i<n;i++)
        {
            if (sum>0)
            {
                sum+=nums[i];
            }
            else
            {
                sum = nums[i];
            }
            res = max(res,sum);
        }
        return res;
    }
};


// Solution 3:
class Solution
{
public:
    int maxSubArray(vector<int> &nums)
    {
        //类似寻找最大最小值的题目，初始值一定要定义成理论上的最小最大值
        int res = nums[0];
        int n = nums.size();
        res = maxSubArrayHelper(nums, 0, n - 1);
        return res;
    }

    int maxSubArrayHelper(vector<int> &nums, int left, int right)
    {
        if (left == right)
        {
            return nums[left];
        }
        int mid = (left + right) / 2;
        int leftSum = maxSubArrayHelper(nums, left, mid);
        //注意这里应是mid + 1，否则left + 1 = right时，会无线循环
        int rightSum = maxSubArrayHelper(nums, mid + 1, right);
        int midSum = findMaxCrossingSubarray(nums, left, mid, right);
        int res = max(leftSum, rightSum);
        res = max(res, midSum);
        return res;
    }

    int findMaxCrossingSubarray(vector<int> &nums, int left, int mid, int right)
    {
        int leftSum = INT_MIN;
        int sum = 0;
        for (int i = mid; i >= left; i--)
        {
            sum += nums[i];
            leftSum = max(leftSum, sum);
        }

        int rightSum = INT_MIN;
        sum = 0;
        //注意这里i = mid + 1，避免重复用到nums[i]
        for (int i = mid + 1; i <= right; i++)
        {
            sum += nums[i];
            rightSum = max(rightSum, sum);
        }
        return (leftSum + rightSum);
    }
};


/// C++ Solution 4:
class Solution {
public:
    int maxSubArray(vector<int> nums) {
        int res = nums[0];
        int n = nums.size();
        int sum = 0;
        for (int i=0;i<n;i++)
        {
            if (sum > 0)
                sum+=nums[i];
            else
                sum = nums[i];
            res = max(res,sum);
        }
        return res;
    }
};