feat: enhance useVirtualList for dynamic item sizing and improved scrolling behavior

core/stdlib/src/structs/FenwickTree/index.test.ts

@@ -0,0 +1,91 @@
+import { describe, expect, it } from 'vitest';
+
+import { FenwickTree } from '.';
+
+/** Deterministic LCG so failures reproduce. */
+function lcg(seed: number): () => number {
+  let state = seed;
+  return () => {
+    state = (state * 48271) % 2147483647;
+    return state / 2147483647;
+  };
+}
+
+describe('FenwickTree', () => {
+  it('should match naive sums after build', () => {
+    const rand = lcg(1);
+    const values = Array.from({ length: 137 }, () => Math.floor(rand() * 100));
+    const tree = new FenwickTree(values.length);
+    tree.build(values);
+
+    let sum = 0;
+    for (let i = 0; i <= values.length; i++) {
+      expect(tree.prefix(i)).toBe(sum);
+      if (i < values.length)
+        sum += values[i]!;
+    }
+  });
+
+  it('should keep prefix sums consistent with a naive array under updates', () => {
+    const rand = lcg(2);
+    const length = 64;
+    const naive = Array.from({ length }, () => Math.floor(rand() * 50));
+    const tree = new FenwickTree(length);
+    tree.build(naive);
+
+    for (let op = 0; op < 500; op++) {
+      const index = Math.floor(rand() * length);
+      const delta = Math.floor(rand() * 40) - 20;
+      naive[index]! += delta;
+      tree.update(index, delta);
+
+      const probe = Math.floor(rand() * (length + 1));
+      const expected = naive.slice(0, probe).reduce((a, b) => a + b, 0);
+      expect(tree.prefix(probe)).toBe(expected);
+    }
+  });
+
+  it('should match a linear scan in lowerBound, including stride and zero values', () => {
+    const rand = lcg(3);
+    for (let round = 0; round < 20; round++) {
+      const length = 1 + Math.floor(rand() * 40);
+      const values = Array.from({ length }, () => rand() < 0.2 ? 0 : Math.floor(rand() * 60));
+      const stride = round % 3 === 0 ? 0 : Math.floor(rand() * 10);
+      const tree = new FenwickTree(length);
+      tree.build(values);
+
+      const total = values.reduce((a, b) => a + b, 0) + length * stride;
+      for (const target of [-5, 0, 1, total / 3, total / 2, total - 1, total, total + 100]) {
+        let expected = 0;
+        for (let c = 0; c <= length; c++) {
+          const g = values.slice(0, c).reduce((a, b) => a + b, 0) + c * stride;
+          if (g <= target)
+            expected = c;
+          else
+            break;
+        }
+        if (target < 0)
+          expected = 0;
+        expect(tree.lowerBound(target, stride), `length=${length} stride=${stride} target=${target}`).toBe(expected);
+      }
+    }
+  });
+
+  it('should handle an empty tree', () => {
+    const tree = new FenwickTree(0);
+
+    expect(tree.prefix(0)).toBe(0);
+    expect(tree.lowerBound(0)).toBe(0);
+    expect(tree.lowerBound(100)).toBe(0);
+  });
+
+  it('should rebuild in place via build', () => {
+    const tree = new FenwickTree(4);
+    tree.build([1, 2, 3, 4]);
+    expect(tree.prefix(4)).toBe(10);
+
+    tree.build([10, 10, 10, 10]);
+    expect(tree.prefix(2)).toBe(20);
+    expect(tree.prefix(4)).toBe(40);
+  });
+});

core/stdlib/src/structs/FenwickTree/index.ts

@@ -0,0 +1,95 @@
+/**
+ * @name FenwickTree
+ * @category Data Structures
+ * @description Fenwick (Binary Indexed) tree over an array of non-negative
+ * numbers: O(log n) prefix sums, point updates, and monotonic lower-bound
+ * search, plus O(n) bulk rebuild. `lowerBound` assumes all values are
+ * non-negative (the prefix function must be non-decreasing)
+ *
+ * @example
+ * const tree = new FenwickTree(5);
+ * tree.build([10, 20, 30, 40, 50]);
+ * tree.prefix(3); // 60
+ * tree.update(1, 5); // value at index 1 becomes 25
+ * tree.lowerBound(65); // 3 — largest c with prefix(c) <= 65
+ *
+ * @since 0.0.11
+ */
+export class FenwickTree {
+  readonly size: number;
+  private readonly tree: Float64Array;
+  private readonly highBit: number;
+
+  constructor(size: number) {
+    this.size = size;
+    this.tree = new Float64Array(size + 1);
+    this.highBit = size > 0 ? 1 << (31 - Math.clz32(size)) : 0;
+  }
+
+  /**
+   * Bulk (re)initialization from raw values, O(n)
+   *
+   * @param {ArrayLike<number>} values The values to load, `values.length` must equal `size`
+   */
+  build(values: ArrayLike<number>): void {
+    const { tree, size } = this;
+    tree.fill(0);
+    for (let i = 1; i <= size; i++) {
+      tree[i]! += values[i - 1]!;
+      const parent = i + (i & -i);
+      if (parent <= size)
+        tree[parent]! += tree[i]!;
+    }
+  }
+
+  /**
+   * Add `delta` to the value at `index`, O(log n)
+   *
+   * @param {number} index Zero-based index of the value to change
+   * @param {number} delta Amount to add (may be negative)
+   */
+  update(index: number, delta: number): void {
+    for (let i = index + 1; i <= this.size; i += i & -i)
+      this.tree[i]! += delta;
+  }
+
+  /**
+   * Sum of the first `count` values, O(log n)
+   *
+   * @param {number} count How many leading values to sum
+   * @returns {number} The prefix sum
+   */
+  prefix(count: number): number {
+    let sum = 0;
+    for (let i = count; i > 0; i -= i & -i)
+      sum += this.tree[i]!;
+    return sum;
+  }
+
+  /**
+   * Largest `c` in `[0, size]` with `prefix(c) + c * stride <= target`, O(log n).
+   * `stride` models a constant per-item addition (e.g. a layout gap) without
+   * storing it in the tree
+   *
+   * @param {number} target The offset to search for
+   * @param {number} stride Constant added per item, defaults to `0`
+   * @returns {number} The largest count whose strided prefix does not exceed `target`
+   */
+  lowerBound(target: number, stride = 0): number {
+    if (target < 0)
+      return 0;
+    let pos = 0;
+    let sum = 0;
+    for (let step = this.highBit; step > 0; step >>= 1) {
+      const next = pos + step;
+      if (next <= this.size) {
+        const candidate = sum + this.tree[next]!;
+        if (candidate + next * stride <= target) {
+          pos = next;
+          sum = candidate;
+        }
+      }
+    }
+    return pos;
+  }
+}

core/stdlib/src/structs/index.ts

@@ -1,6 +1,7 @@
 export * from './BinaryHeap';
 export * from './CircularBuffer';
 export * from './Deque';
+export * from './FenwickTree';
 export * from './LinkedList';
 export * from './PriorityQueue';
 export * from './Queue';