Monte Carlo Integration

题面

在区间 [a,b] 上使用 Monte Carlo 方法估计 ∫_a^b f(x) dx：给定随机点的函数值 y_i=f(x_i)，采用 (b-a) * (1/n) * Σ y_i 作为积分估计。

Implementation Requirements

• External libraries are not permitted
• The solve function signature must remain unchanged
• 结果写入 result；评测容差 abs/rel 1e-2

Examples

a = 0, b = 2, n=8, y = [0.0625, 0.25, 0.5625, 1.0, 1.5625, 2.25, 3.0625, 4.0]
result = 3.1875

Constraints

• 1 ≤ n_samples ≤ 100,000,000
• -1000.0 ≤ a < b ≤ 1000.0；-10000.0 ≤ y ≤ 10000.0
• Performance: n_samples = 10,000,000