<p>Given an integer array <code>nums</code> and two integers <code>lower</code> and <code>upper</code>, return <em>the number of range sums that lie in</em> <code>[lower, upper]</code> <em>inclusive</em>.</p>

<p>Range sum <code>S(i, j)</code> is defined as the sum of the elements in <code>nums</code> between indices <code>i</code> and <code>j</code> inclusive, where <code>i &lt;= j</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [-2,5,-1], lower = -2, upper = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three ranges are: [0,0], [2,2], and [0,2] and their respective sums are: -2, -1, 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [0], lower = 0, upper = 0
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>

class SegmentTreeNode {
public:
    long min;
    long max;
    int count; //number of values in [min, max]
    SegmentTreeNode *left;
    SegmentTreeNode *right;
    SegmentTreeNode (long min, long max, int count) {
        this->min = min;
        this->max = max;
        this->count = count;
        left = right = NULL;
    }
};

class Solution {
    SegmentTreeNode *root;
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        if (nums.size() == 0) return 0;
        unordered_set<long> ssum;
        long tmpSum = 0;
        for (auto n: nums) {
            tmpSum += n;
            ssum.insert(tmpSum);
        }
        vector<long> sum;
        for (auto s: ssum) {
            sum.push_back(s);
        }
        sort(sum.begin(), sum.end());
        root = build(sum, 0, sum.size() - 1);
        int count = 0;
        for (int i = nums.size() - 1; i >= 0; i--) {
            modify(root, tmpSum);
            tmpSum -= nums[i];
            count += query(root, lower + tmpSum, upper + tmpSum);
        }
        return count;
    }
    
    SegmentTreeNode *build(vector<long> &sum, int start, int end) {
        SegmentTreeNode *root = new SegmentTreeNode(sum[start], sum[end], 0);
        if (start == end) {
            return root;
        } else {
            int middle = (start + end) / 2;
            root->left = build(sum, start, middle);
            root->right = build(sum, middle + 1, end);
            return root;
        }
    }
    
    void modify(SegmentTreeNode *root, long value) {
        if (root == NULL || value < root->min || value > root->max) return;
        root->count += 1;
        if (root->min == root->max) {
            return;
        } else {
            modify(root->left, value);
            modify(root->right, value);
        }
    }
    
    int query(SegmentTreeNode *root, long min, long max) {
        if (root == NULL || max < root->min || min > root->max) return 0;
        if (min <= root->min && max >= root->max) return root->count;
        return query(root->left, min, max) + query(root->right, min, max);
    }
};
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