From 7d8ba0b3d18b7db7f5127e317c7072248b1a06e7 Mon Sep 17 00:00:00 2001
From: Ishita Mukherjee <ishitam299@gmail.com>
Date: Mon, 22 Jul 2024 18:17:31 +0530
Subject: [PATCH] Solution of Square Rooot Problem from gfg is added

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+---
+id: square-root
+title: Square Root
+sidebar_label: Square-Root
+tags:
+- Math
+- Binary Search
+description: "This document provides solutions to the problem of finding the Square Root of an integer."
+---
+
+## Problem
+
+Given an integer `x`, find the square root of `x`. If `x` is not a perfect square, then return the floor value of √x.
+
+### Examples
+
+**Example 1:**
+
+```
+Input: x = 5
+Output: 2
+Explanation: Since 5 is not a perfect square, the floor of the square root of 5 is 2.
+```
+
+**Example 2:**
+
+```
+Input: x = 4
+Output: 2
+Explanation: Since 4 is a perfect square, its square root is 2.
+```
+
+### Your Task
+
+You don't need to read input or print anything. The task is to complete the function `floorSqrt()` which takes `x` as the input parameter and returns its square root. Note: Try solving the question without using the sqrt function. The value of `x` ≥ 0.
+
+**Expected Time Complexity:** $O(log N)$
+**Expected Auxiliary Space:** $O(1)$
+
+**Constraints**
+- `1 ≤ x ≤ 10^7`
+
+## Solution
+
+### Intuition & Approach
+
+To find the square root of a number without using the built-in `sqrt` function, we can use binary search. This approach leverages the fact that the square root of `x` must lie between `0` and `x`. By repeatedly narrowing down the range using binary search, we can efficiently find the floor value of the square root.
+
+### Implementation
+
+<Tabs>
+  <TabItem value="python" label="Python">
+
+```python
+class Solution:
+    def floorSqrt(self, x: int) -> int:
+        if x == 0 or x == 1:
+            return x
+        start, end = 1, x
+        ans = 0
+        while start <= end:
+            mid = (start + end) // 2
+            if mid * mid == x:
+                return mid
+            if mid * mid < x:
+                start = mid + 1
+                ans = mid
+            else:
+                end = mid - 1
+        return ans
+```
+
+  </TabItem>
+  <TabItem value="java" label="Java">
+
+```java
+class Solution {
+    long floorSqrt(long x) {
+        if (x == 0 || x == 1) {
+            return x;
+        }
+        long start = 1, end = x, ans = 0;
+        while (start <= end) {
+            long mid = (start + end) / 2;
+            if (mid * mid == x) {
+                return mid;
+            }
+            if (mid * mid < x) {
+                start = mid + 1;
+                ans = mid;
+            } else {
+                end = mid - 1;
+            }
+        }
+        return ans;
+    }
+}
+```
+
+  </TabItem>
+  <TabItem value="cpp" label="C++">
+
+```cpp
+class Solution {
+public:
+    long long int floorSqrt(long long int x) {
+        if (x == 0 || x == 1)
+            return x;
+        long long int start = 1, end = x, ans = 0;
+        while (start <= end) {
+            long long int mid = (start + end) / 2;
+            if (mid * mid == x)
+                return mid;
+            if (mid * mid < x) {
+                start = mid + 1;
+                ans = mid;
+            } else {
+                end = mid - 1;
+            }
+        }
+        return ans;
+    }
+};
+```
+
+  </TabItem>
+  <TabItem value="javascript" label="JavaScript">
+
+```javascript
+class Solution {
+    floorSqrt(x) {
+        if (x === 0 || x === 1) {
+            return x;
+        }
+        let start = 1, end = x, ans = 0;
+        while (start <= end) {
+            let mid = Math.floor((start + end) / 2);
+            if (mid * mid === x) {
+                return mid;
+            }
+            if (mid * mid < x) {
+                start = mid + 1;
+                ans = mid;
+            } else {
+                end = mid - 1;
+            }
+        }
+        return ans;
+    }
+}
+```
+
+  </TabItem>
+  <TabItem value="typescript" label="TypeScript">
+
+```typescript
+class Solution {
+    floorSqrt(x: number): number {
+        if (x === 0 || x === 1) {
+            return x;
+        }
+        let start = 1, end = x, ans = 0;
+        while (start <= end) {
+            let mid = Math.floor((start + end) / 2);
+            if (mid * mid === x) {
+                return mid;
+            }
+            if (mid * mid < x) {
+                start = mid + 1;
+                ans = mid;
+            } else {
+                end = mid - 1;
+            }
+        }
+        return ans;
+    }
+}
+```
+
+  </TabItem>
+</Tabs>
+
+## Complexity Analysis
+
+The provided solutions efficiently find the floor value of the square root of a given integer `x` using binary search. This approach ensures a time complexity of $ O(log N) and an auxiliary space complexity of $O(1)$. The algorithms are designed to handle large values of `x` up to 10^7 efficiently without relying on built-in square root functions.
+
+**Time Complexity:** $O(log N)$
+**Auxiliary Space:** $O(1)$
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