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79d50738f2
* Add fast power Computes a^b in O(logN) time. * Change long long to int64_t * Update fast_power.cpp * Update fast_power.cpp * Add tests * Update sample tests * Update rand function * Remove extra-spaces
80 lines
2.1 KiB
C++
80 lines
2.1 KiB
C++
#include <iostream>
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#include <cstdlib>
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#include <cstdint>
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#include <cassert>
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#include <ctime>
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#include <cmath>
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/*
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Program that computes a^b in O(logN) time.
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It is based on formula that:
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case1) if b is even: a^b = a^(b/2) * a^(b/2) = (a^(b/2))ˆ2
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case2) if b is odd: a^b = a^((b-1)/2) * a^((b-1)/2) * a = (a^((b-1)/2))^2 * a
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We can compute a^b recursively using above algorithm.
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*/
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double fast_power_recursive(int64_t a, int64_t b) {
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// negative power. a^b = 1 / (a^-b)
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if (b < 0)
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return 1.0 / fast_power_recursive(a, -b);
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if (b == 0) return 1;
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int64_t bottom = fast_power_recursive(a, b >> 1);
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// Since it is integer division b/2 = (b-1)/2 where b is odd.
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// Therefore, case2 is easily solved by integer division.
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int64_t result;
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if ((b & 1) == 0) // case1
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result = bottom * bottom;
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else // case2
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result = bottom * bottom * a;
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return result;
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}
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/*
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Same algorithm with little different formula.
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It still calculates in O(logN)
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*/
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double fast_power_linear(int64_t a, int64_t b) {
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// negative power. a^b = 1 / (a^-b)
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if (b < 0)
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return 1.0 / fast_power_linear(a, -b);
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double result = 1;
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while (b) {
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if (b & 1) result = result * a;
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a = a * a;
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b = b >> 1;
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}
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return result;
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}
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int main() {
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std::srand(time(NULL));
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std::ios_base::sync_with_stdio(false);
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std::cout << "Testing..." << std::endl;
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for (int i = 0; i < 20; i++) {
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unsigned int *rand1, *rand2;
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int a = rand_r(rand1) % 20 - 10;
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int b = rand_r(rand2) % 20 - 10;
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std::cout << std::endl << "Calculating " << a << "^" << b << std::endl;
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assert(fast_power_recursive(a, b) == std::pow(a, b));
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assert(fast_power_linear(a, b) == std::pow(a, b));
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std::cout << "------ " << a << "^" << b << " = "<<
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fast_power_recursive(a, b) << std::endl;
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}
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int64_t a, b;
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std::cin >> a >> b;
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std::cout << a << "^" << b << " = "<<
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fast_power_recursive(a, b) << std::endl;
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std::cout << a << "^" << b << " = "<<
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fast_power_linear(a, b) << std::endl;
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return 0;
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}
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