Merge pull request #900 from debangi29/powx-n

Added solution for leetcode 50- Pow(x,n)!

Author: ajay-dhangar

dsa-solutions/lc-solutions/0000-0099/0050-pow(x,n).md

@@ -0,0 +1,139 @@
+---
+id: powx-n
+title: Pow(x,n)
+difficulty: Medium
+sidebar_label: 0050-powxn
+tags:
+  - Math
+  - Recursion
+---
+
+## Problem Description
+
+| Problem Statement | Solution Link | LeetCode Profile |
+| :---------------- | :------------ | :--------------- |
+| [Pow(x,n)](https://leetcode.com/problems/powx-n/description/) | [Pow(x,n) Solution on LeetCode](https://leetcode.com/problems/powx-n/solutions/) |  [Leetcode Profile](https://leetcode.com/u/debangi_29/) |
+
+## Problem Description
+
+Implement pow(x, n), which calculates x raised to the power n (i.e., $x^n$).
+
+ 
+
+### Examples
+
+### Example 1:
+
+**Input**: x = 2.00000, n = 10
+
+**Output**: 1024.00000
+
+
+### Example 2:
+
+**Input**: x = 2.10000, n = 3
+
+**Output**: 9.26100
+
+### Example 3:
+
+**Input**: x = 2.00000, n = -2
+
+**Output**: 0.25000
+
+**Explanation**: 2-2 = 1/22 = 1/4 = 0.25
+ 
+
+### Constraints
+
+- $-100.0 < x < 100.0$
+- $-2^{31} \leq n \leq 2^{31} - 1$
+- $n$ is an integer.
+- Either $x$ is not zero or $n > 0$.
+- $-10^{4} \leq x^{n} \leq 10^{4}$
+
+### Approach
+Initialize ans as 1.0  and store a duplicate copy of n i.e nn using to avoid overflow
+
+Check if nn is a negative number, in that case, make it a positive number.
+
+Keep on iterating until nn is greater than zero, now if nn is an odd power then multiply x with ans ans reduce nn by 1. Else multiply x with itself and divide nn by two.
+
+Now after the entire binary exponentiation is complete and nn becomes zero, check if n is a negative value we know the answer will be 1 by and.
+
+### Solution Code
+
+#### Python
+
+```
+class Solution:
+ def myPow(x: float, n: int) -> float:
+    ans = 1.0
+    nn = n
+    if nn < 0:
+        nn = -1 * nn
+    while nn:
+        if nn % 2:
+            ans = ans * x
+            nn = nn - 1
+        else:
+            x = x * x
+            nn = nn // 2
+    if n < 0:
+        ans = 1.0 / ans
+    return ans
+```
+
+#### Java
+
+```
+class Solution {
+  public static double myPow(double x, int n) {
+    double ans = 1.0;
+    long nn = n;
+    if (nn < 0) nn = -1 * nn;
+    while (nn > 0) {
+      if (nn % 2 == 1) {
+        ans = ans * x;
+        nn = nn - 1;
+      } else {
+        x = x * x;
+        nn = nn / 2;
+      }
+    }
+    if (n < 0) ans = (double)(1.0) / (double)(ans);
+    return ans;
+  }
+}
+```
+
+#### C++
+
+```
+class Solution {
+ public:
+  double myPow(double x, int n) {
+  double ans = 1.0;
+  long long nn = n;
+  if (nn < 0) nn = -1 * nn;
+  while (nn) {
+    if (nn % 2) {
+      ans = ans * x;
+      nn = nn - 1;
+    } else {
+      x = x * x;
+      nn = nn / 2;
+    }
+  }
+  if (n < 0) ans = (double)(1.0) / (double)(ans);
+  return ans;
+}
+};
+
+```
+
+### Conclusion
+
+- Time Complexity: $O(log n)$ , where n is the exponent; Using Binary exponentiation.
+
+- Space Complexity: $O(1)$ as we are not using any extra space.