# 69. Sqrt(x)

## 1.問題

* 實作sqrt

![](https://901207480-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LGKoChvN9am4__HCIRK%2F-LNbfaAKz0WhJWb-rltV%2F-LNc8t1nNPfBQt0djSh9%2F%E8%9E%A2%E5%B9%95%E5%BF%AB%E7%85%A7%202018-09-30%20%E4%B8%8A%E5%8D%889.45.56.png?alt=media\&token=032bb24f-c760-4049-81d5-45743c2fdd81)

## 2.想法

* 提問
* function header, parameter
* test input
* 說明想法 
  * edge case: x == 0
  * binary search
    * 初始狀態為left = 1, right = x
    * 當x / mid == mid, 回傳mid
    * 當x / mid > mid 時
      * 表示目標在mid右邊, 因此讓left = mid
      * 或是目標介於mid \* mid與x間, 回傳mid
    * 當x / mid < mid時
      * 表示目標在mid左邊, 因此讓right = mid
      * 或是目標介於x 與 mid \* mid間, 回傳x
* 測試計算複雜度

## 3.程式碼

```
class Solution {
public:
    int mySqrt(int x) {
        return binarySearch(1, x, x);
    }
private:
    int binarySearch(long left, long right, long target) {
        if (left > right) {
            return 0;
        }
        
        long mid = (left + right) / 2;
        long x = target / mid;
        
        if (mid == x) {
            return mid;
        }
        
        if (x > mid) {
            if (x - mid == 1) {
                return mid;
            }
            return binarySearch(mid + 1, right, target);
        } else {
            if (mid - x == 1) {
                return x;
            }
            return binarySearch(left, mid - 1, target);
        }
    }
};
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://jenhsuan.gitbook.io/algorithm/leetcode/69.-sqrt-x.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.