diff --git a/dsa-solutions/lc-solutions/0000-0099/0069-SqrtX.md b/dsa-solutions/lc-solutions/0000-0099/0069-SqrtX.md new file mode 100644 index 000000000..778fee4fc --- /dev/null +++ b/dsa-solutions/lc-solutions/0000-0099/0069-SqrtX.md @@ -0,0 +1,129 @@ +--- +id: sqrt-x +title: Sqrt(x) (LeetCode) +difficulty: Easy +sidebar_label: 0069-SqrtX +topics: + - Math + - Binary Search +--- + + +## Problem Description + +| Problem Statement | Solution Link | LeetCode Profile | +| :---------------- | :------------ | :--------------- | +| [Merge Two Sorted Lists](https://leetcode.com/problems/sqrtx/) | [Merge Two Sorted Lists Solution on LeetCode](https://leetcode.com/problems/sqrtx/solutions/) | [VijayShankerSharma](https://leetcode.com/u/darkknight648/) | + +## Problem Description + +Given a non-negative integer `x`, return the square root of `x` rounded down to the nearest integer. The returned integer should be non-negative as well. + +You must not use any built-in exponent function or operator. + +### Examples + +#### Example 1: + +- **Input:** `x = 4` +- **Output:** `2` +- **Explanation:** The square root of 4 is 2, so we return 2. + +#### Example 2: + +- **Input:** `x = 8` +- **Output:** `2` +- **Explanation:** The square root of 8 is approximately 2.82842..., and since we round it down to the nearest integer, 2 is returned. + +### Constraints: + +- `0 <= x <= 2^31 - 1` + +### Approach + +To find the square root of a non-negative integer `x` without using built-in functions, we can use binary search within the range `[0, x]`. + +1. Initialize variables `left` and `right` to represent the search range `[0, x]`. +2. Perform binary search within this range, updating the `mid` value as `(left + right) / 2`. +3. If `mid * mid` is greater than `x`, update `right` to `mid - 1`. +4. If `mid * mid` is less than or equal to `x`, update `left` to `mid + 1`. +5. Repeat steps 2-4 until `left` is greater than `right`. +6. Return the value of `right`, which represents the largest integer whose square is less than or equal to `x`. + +### Solution Code + +#### Python + +``` +class Solution(object): + def mySqrt(self, x): + if x < 2: + return x + left, right = 1, x + while left <= right: + mid = (left + right) // 2 + if mid * mid == x: + return mid + elif mid * mid < x: + left = mid + 1 + else: + right = mid - 1 + return right +``` + +#### C++ + +``` +class Solution { +public: + int mySqrt(int x) { + if (x == 0) { + return 0; + } + + long left = 1, right = x; + while (left <= right) { + long mid = (left + right) / 2; + if (mid * mid == x) { + return mid; + } else if (mid * mid < x) { + left = mid + 1; + } else { + right = mid - 1; + } + } + + return right; + } +}; +``` + +#### Java + +``` +class Solution { + public int mySqrt(int x) { + if (x == 0) { + return 0; + } + + long left = 1, right = x; + while (left <= right) { + long mid = (left + right) / 2; + if (mid * mid == x) { + return (int)mid; + } else if (mid * mid < x) { + left = mid + 1; + } else { + right = mid - 1; + } + } + + return (int)right; + } +} +``` + +### Conclusion + +The "Sqrt(x)" problem can be efficiently solved using binary search within the range `[0, x]`. The provided solution code implements this approach in Python, C++, and Java, providing an optimal solution to the problem. \ No newline at end of file