1. all positive : [1,2,3], k = 3, array_sum = 6
    return array_sum*3
2. all negative : [-1,-2], k = 2, array_sum = -3
    return 0
3. hybrid, with array_sum <= 0, [2,1,-3], k = 4, array_sum = 0
       [ 2,  1, -3, 2, 1, -3, 2, 1, -3, 2, 1, -3]
max sum  2   3  0   2  3  0   2  3   0   2  3  0
	return max_subarray_sum between [2,1,-3,2,1,-3] which is twice of original array
	so, return max_subarray_sum = 3
4. hybrid, with array_sum > 0, [2,-6,5], k =4, array_sum = 1
       [ 2, -6, 5, 2, -6, 5, 2, -6, 5, 2, -6, 5]
max sum  2   0  5  7   1  6  8   2  7  9   3  8
a. you can notice max subarray sum is getting bigger as k grows up.
b. with first 2 array, we can get max subarray sum is 8.
c. after that, with each new array, max_subarray_sum will increase by 1, which is array_sum
==>return (max_subarray_sum when k=2) + array_sum*(k-2)

//dfs
public class Solution {
    public int pathSum(TreeNode root, int sum) {
        if(root == null)
            return 0;
        return findPath(root, sum) + pathSum(root.left, sum) + pathSum(root.right, sum);
    }
    
    public int findPath(TreeNode root, int sum){
        int res = 0;
        if(root == null)
            return res;
        if(sum == root.val)
            res++;
        res += findPath(root.left, sum - root.val);
        res += findPath(root.right, sum - root.val);
        return res;
    }
   
}

class Solution {
    public int[] twoSum(int[] nums, int target) {
        Map<Integer, Integer> map = new HashMap<>();
        for(int i=0; i<nums.length; i++)
        {
            int cur = target-nums[i];
            if(map.containsKey(cur))
                return new int[]{map.get(cur), i};
            map.put(nums[i], i);
        }
        return new int[]{};
    }
}

class Solution {
    public int maxSubArray(int[] nums) {
        int maxret = nums[0], maxcur = nums[0];
        for(int i=1; i<nums.length; i++)
        {
            maxcur = Math.max(maxcur+nums[i], nums[i]);
            maxret = Math.max(maxret, maxcur);
        }
        return maxret;
    }
}

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    public boolean isSymmetric(TreeNode root) {
        return helper(root, root);
    }
    public boolean helper(TreeNode t1, TreeNode t2){
        if(t1 == null && t2 == null) return true;
        if(t1 == null || t2 == null) return false;
        return (t1.val == t2.val) && helper(t1.left, t2.right) && helper(t1.right, t2.left);
    }
}

class Solution {
    public static int maxArea(int[] height) {
        if (height == null || height.length == 0)
            return 0;
        int len = height.length;
        int low = 0, high = len - 1, maxArea = -1;
        while (low < high) {
            int currentArea = (high - low) * (Integer.min(height[low], height[high]));
            maxArea = Integer.max(maxArea, currentArea);
            if (height[low] <= height[high])
                low++;
            else
                high--;
        }
        return maxArea;
    }
}

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    int max = 0;
    
    public int diameterOfBinaryTree(TreeNode root) {
        maxDepth(root);
        return max;
    }
    
    private int maxDepth(TreeNode root) {
        if (root == null) return 0;
        
        int left = maxDepth(root.left);
        int right = maxDepth(root.right);
        
        max = Math.max(max, left + right);
        
        return Math.max(left, right) + 1;
    }
}

class Solution {
    public int maxProfit(int[] prices) {
        if(prices == null || prices.length == 0)
            return 0;
        
        int buyPrice = prices[0];
        int max = 0;
        
        int len  = prices.length;
        for(int i=0; i<len; i++)
        {
            if(prices[i] < buyPrice)
                buyPrice = prices[i];
            else
            {
                int newProfit = prices[i]-buyPrice;
                max = (newProfit > max ? newProfit : max);
            }
        }
        return max;
    }
}

class Solution {
    public int findKthLargest(int[] nums, int k) {
      return quickSelect(nums, 0, nums.length - 1, k);
    }

    int quickSelect(int[] nums, int low, int high, int k) {
      int pivot = low;

      // use quick sort's idea
      // put nums that are <= pivot to the left
      // put nums that are  > pivot to the right
      for (int j = low; j < high; j++) {
        if (nums[j] <= nums[high]) {
          swap(nums, pivot++, j);
        }
      }
      swap(nums, pivot, high);

      // count the nums that are > pivot from high
      int count = high - pivot + 1;
      // pivot is the one!
      if (count == k) return nums[pivot];
      // pivot is too small, so it must be on the right
      if (count > k) return quickSelect(nums, pivot + 1, high, k);
      // pivot is too big, so it must be on the left
      return quickSelect(nums, low, pivot - 1, k - count);
    }
}

public class Solution {
    public void rotate(int[][] M) {
        for (int i = 0; i < (M.length+1)/2; i++) {
            for (int j = 0; j < M.length/2; j++) {
                int tmp = M[i][j];
                M[i][j] = M[M.length-j-1][i];
                M[M.length-j-1][i] = M[M.length-i-1][M.length-j-1];
                M[M.length-i-1][M.length-j-1] = M[j][M.length-i-1];
                M[j][M.length-i-1] = tmp;
            }
        }
    }
}