19 Powx,n
Problem Statement
Write a Recursive Approach to Calculate Power of Integer to N Pow(x,n).
Given an integer x and an integer n, write a recursive function to calculate the power of x to the nth power.
Example
| Sr# | x | n | Output | Description |
|---|---|---|---|---|
| 1 | 2 | 5 | 32 | 2 raised to the power of 5 equals 32. |
| 2 | 3 | 4 | 81 | 3 raised to the power of 4 equals 81. |
| 3 | 5 | 0 | 1 | Any number raised to the power of 0 equals 1 (x^0 = 1). |
Constraints:
-100.0 < x < 100.0- -231 <= n <= 231-1
nis an integer.- Either
xis not zero or n > 0. - -104 <= xn <= 104
Try it yourself
Try solving this question here:
🎯 STRICT STANDOUT — Problem cue: Pow(x,n)
1. Why
x^n via squaring in Θ(log |n|). Edges: n negative, n=0, INT_MIN negate overflow.
2. Big-O (K11)
T=T(|n|/2)+O(1) → Θ(log |n|) time/stack; naive Θ(|n|) fails n~1e93. Pattern + when-NOT
FAST EXPONENTIATION. When-NOT: small |n| trivial loop; big rational → big-num lib.
4. Edge
n=0 → 1; x=0 n>0 → 0; n=INT_MIN use long; (-2)^3=-85. Panel
Q: Odd n? A: y=pow(x,n//2); return y*y*x.
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