> For the complete documentation index, see [llms.txt](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jimmylin1991.gitbook.io/practice-of-algorithm-problems/binary-search/69.-sqrt-x.md).

# 69. Sqrt(x)

Implement `int sqrt(int x)`.

Compute and return the square root of *x*, where *x* is guaranteed to be a non-negative integer.

Since the return type is an integer, the decimal digits are truncated and only the integer part of the result is returned.

**Example 1:**

```
Input: 4
Output: 2
```

**Example 2:**

```
Input: 8
Output: 2
Explanation: The square root of 8 is 2.82842..., and since 
             the decimal part is truncated, 2 is returned.
```

```cpp
// Binary Search
int mySqrt(int x) { // time: O(log(n)); space: O(1)
    if (x <= 1) return x;
    int l = 0, r = x;
    while(l < r) {
        int mid = l + (r - l) / 2;
        if (mid <= x / mid) l = mid + 1;
        else r = mid;
    }
    return r - 1;
}
```

```cpp
// Newton's Method
// Xi+1 = Xi + (n / Xi) / 2
int mySqrt(int x) {
    if (x <= 1) return x;
    int r = x / 2;
    while (r > x / r) {
        r = (r + x / r) / 2;
    }
    return r;
}
```