<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 NumArray {
public:
    vector<int> bit;
    int n;
    NumArray(vector<int>& nums) {
        this->n = nums.size();
        bit.assign(n, 0);

        for(int i = 0; i < n; i ++) {
            update(i, nums[i]);
        }
    }
    
    void update(int index, int val) {
        int original = sumRange(index, index);
        for(; index < n; index = index | (index + 1)) {
            bit[index] += val - original;
        }
    }
    
    int sumRange(int left, int right) {
        if(left == 0) return sumRangePrefix(right);
        return sumRangePrefix(right) - sumRangePrefix(left - 1);
    }

    int sumRangePrefix(int r) {
        int ret = 0;
        for(; r >= 0; r = (r & (r+1)) - 1) {
            ret += bit[r];
        }
        return ret;
    }
};

class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        set<long> s;
        unordered_map<long,int> m;

        long sum = 0;
        s.insert(0);
        s.insert(LONG_MAX);

        for(int i = 0; i < nums.size(); i ++) {
            sum += nums[i];
            s.insert(sum);
        }

        int i = 0;
        int zeroIndex = 0;
        for(auto &x: s) {
            if(x == 0) zeroIndex = i;
            m[x] = i ++;
        }

        vector<int> v(s.size());
        v[zeroIndex] = 1;
        NumArray* bit = new NumArray(v);

        sum = 0;
        int ans = 0;
        unordered_map<long,int> cnt;
        cnt[0] = 1;

        for(int i = 0; i < nums.size(); i ++) {
            sum += nums[i];

            int lo = m[*s.lower_bound(sum - upper)];
            int hi = m[*s.upper_bound(sum - lower)];

            ans += bit->sumRange(lo, hi-1);

            bit->update(m[sum], ++cnt[sum]);
        }

        return ans;
    }
};
194758