59 lines
1.0 KiB
Markdown
59 lines
1.0 KiB
Markdown
---
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title: Exponentiation
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---
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## Exponentiation
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Given two integers a and n, write a function to compute a^n.
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#### Code
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Algorithmic Paradigm: Divide and conquer.
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```C
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int power(int x, unsigned int y) {
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if (y == 0)
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return 1;
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else if (y%2 == 0)
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return power(x, y/2)*power(x, y/2);
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else
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return x*power(x, y/2)*power(x, y/2);
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}
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```
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Time Complexity: O(n) | Space Complexity: O(1)
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#### Optimized Solution: O(logn)
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```C
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int power(int x, unsigned int y) {
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int temp;
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if( y == 0)
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return 1;
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temp = power(x, y/2);
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if (y%2 == 0)
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return temp*temp;
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else
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return x*temp*temp;
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}
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```
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## Modular Exponentiation
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Given three numbers x, y, and p, compute (x^y) % p
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```C
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int power(int x, unsigned int y, int p) {
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int res = 1;
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x = x % p;
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while (y > 0) {
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if (y & 1)
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res = (res*x) % p;
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// y must be even now
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y = y>>1;
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x = (x*x) % p;
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}
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return res;
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}
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```
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Time Complexity: O(Log y).
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