[LeetCode Sync] Runtime - 1701 ms (22.25%), Memory - 52.4 MB (38.67%)

Author: NinePiece2

Solutions/0327-count-of-range-sum/README.md

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+<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>

Solutions/0327-count-of-range-sum/solution.py

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+class Solution:
+    def countRangeSum(self, nums: List[int], lower: int, upper: int) -> int:
+        n = list(accumulate(nums, initial=0))
+        sorted_array = sorted(set(val for x in n for val in (x, x - lower, x - upper)))
+        tree = BinaryIndexedTree(len(sorted_array))
+        result = 0
+
+        for x in n:
+            left = bisect_left(sorted_array, x - upper) + 1
+            right = bisect_left(sorted_array, x - lower) + 1
+            result += tree.query(right) - tree.query(left - 1)
+            tree.update(bisect_left(sorted_array, x) + 1, 1)
+
+        return result
+
+class BinaryIndexedTree:
+    def __init__(self, n):
+        self.n = n
+        self.tree = [0] * (n + 1)
+    
+    def update(self, x, v):
+        while x <= self.n:
+            self.tree[x] += v
+            x += x & -x
+    
+    def query(self, x):
+        result = 0
+        while x > 0:
+            result += self.tree[x]
+            x -= x & -x
+        return result