129 lines
3.7 KiB
Rust
129 lines
3.7 KiB
Rust
use crate::Solution;
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impl Solution {
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/// [69.Sqrt(x)](https://leetcode-cn.com/problems/sqrtx/)
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///
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/// 2021-11-11 11:00:34
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///
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/// 给你一个非负整数 `x` ，计算并返回 `x` 的 **算术平方根** 。
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///
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/// 由于返回类型是整数，结果只保留 **整数部分** ，小数部分将被 **舍去 。**
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///
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/// **注意：** 不允许使用任何内置指数函数和算符，例如 `pow(x, 0.5)` 或者 `x * 0.5` 。
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///
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/// * **示例 1：**
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/// + **输入：** x = 4
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/// + **输出：** 2
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/// * **示例 2：**
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/// + **输入：** x = 8
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/// + **输出：** 2
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/// + **解释：** 8 的算术平方根是 2.82842..., 由于返回类型是整数，小数部分将被舍去。
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/// * **提示：**
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/// * `0 <= x <= 2^31 - 1`
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/// * Related Topics
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/// + 数学
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/// + 二分查找
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///
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/// * 👍 823
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/// * 👎 0
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/// # 方法1 内置函数
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/// ```rust
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/// pub fn my_sqrt(x: i32) -> i32 {
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/// (x as f32).sqrt() as i32
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/// }
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/// ```
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/// # 方法2 牛顿迭代法
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/// f(x) = x^2 - c 的零点，令x0=c,取f(x)在点(x0, f(x0))处切线的与x轴交点的坐标x1，迭代上一步。
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/// ## 源码
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/// ```rust
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/// pub fn my_sqrt(x: i32) -> i32 {
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/// if x == 0 {
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/// return 0;
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/// }
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/// let c = x as f64;
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/// let mut x0 = x as f64;
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/// loop {
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/// let xi = 0.5 * (x0 + c / x0);
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/// if (x0 - xi).abs() < 1e-7 {
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/// break;
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/// }
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/// x0 = xi;
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/// }
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/// x0 as i32
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/// }
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/// ```
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/// # 方法3 二分查找法
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/// 实现见源码
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/// ## 源码
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/// ```rust
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/// pub fn my_sqrt(x: i32) -> i32 {
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/// let (mut l, mut r, mut ans) = (0, x, -1);
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/// while l <= r {
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/// let mid = l + (r - l) / 2;
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/// if mid as i64 * mid as i64 <= x as i64 {
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/// ans = mid;
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/// l = mid + 1;
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/// } else {
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/// r = mid - 1;
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/// }
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/// }
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/// ans
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/// }
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/// ```
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/// # 方法4 袖珍计算器算法
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/// 使用指数函数和对数函数替换平方根函数的方法
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/// ## 源码
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/// ```rust
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/// pub fn my_sqrt(x: i32) -> i32 {
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/// let ans = (0.5f64 * (x as f64).ln()).exp() as i32;
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/// if (ans + 1) as i64 * (ans + 1) as i64 <= x as i64 {
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/// ans + 1
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/// } else {
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/// ans
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/// }
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/// }
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/// ```
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/// # 方法5 卡马克快速平方根倒数
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/// ```rust
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/// pub fn my_sqrt(x: i32) -> i32 {
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/// unsafe {
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/// union X2f {
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/// i: i64,
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/// f: f64,
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/// }
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/// let x_half = 0.5f64 * x as f64;
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/// let mut u = X2f { f: x as f64 };
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/// u.i = 0x5FE6EC85E7DE30DA_i64 - (u.i >> 1);
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/// u.f = u.f * (1.5f64 - x_half * u.f * u.f); // 牛顿迭代法
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/// u.f = u.f * (1.5f64 - x_half * u.f * u.f);
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/// u.f = u.f * (1.5f64 - x_half * u.f * u.f); // 三次迭代
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/// return (1.0f64 / u.f) as i32;
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/// }
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/// }
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/// ```
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pub fn my_sqrt(x: i32) -> i32 {
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let x_half = 0.5 * x as f64;
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let mut i = (x as f64).to_bits();
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i = 0x1FF7A3BEA91D9B1B + (i >> 1);
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let mut f = f64::from_bits(i);
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f = 0.5 * f + x_half / f;
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f = 0.5 * f + x_half / f;
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f = 0.5 * f + x_half / f;
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f as i32
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}
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}
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#[cfg(test)]
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mod test {
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use crate::Solution;
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#[test]
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fn test_q0069() {
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let x = 2147395599;
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let i = Solution::my_sqrt(x);
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assert_eq!(i, 46339);
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}
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}
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