<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>

#include <bits/stdc++.h>
using namespace std;

class SegmentTree {
public:
    int n;
    vector<int> tree;

    SegmentTree(int size) {
        n = size;
        tree.resize(2 * n, 0);
    }

    void update(int index, int value) {
        index += n;
        tree[index] += value;
        while (index > 1) {
            index /= 2;
            tree[index] = tree[2 * index] + tree[2 * index + 1];
        }
    }

    int query(int left, int right) {
        left += n;
        right += n;
        int sum = 0;
        while (left <= right) {
            if (left % 2 == 1) sum += tree[left++];
            if (right % 2 == 0) sum += tree[right--];
            left /= 2;
            right /= 2;
        }
        return sum;
    }
};

class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        set<long long> allSums;
        long long prefixSum = 0;
        allSums.insert(prefixSum);

        for (int num : nums) {
            prefixSum += num;
            allSums.insert(prefixSum);
            allSums.insert(prefixSum - lower);
            allSums.insert(prefixSum - upper);
        }

        unordered_map<long long, int> compressedIndex;
        int index = 0;
        for (long long sum : allSums) {
            compressedIndex[sum] = index++;
        }

        SegmentTree segTree(index);
        int count = 0;
        prefixSum = 0;
        segTree.update(compressedIndex[prefixSum], 1);

        for (int num : nums) {
            prefixSum += num;
            int leftBound = compressedIndex[prefixSum - upper];
            int rightBound = compressedIndex[prefixSum - lower];
            count += segTree.query(leftBound, rightBound);
            segTree.update(compressedIndex[prefixSum], 1);
        }

        return count;
    }
};

306336