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d58954523f
* fix: Integer overflow of least_common_multiple. * Update the typing (linter warning).
82 lines
2.3 KiB
C++
82 lines
2.3 KiB
C++
/**
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* Copyright 2020 @author tjgurwara99
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* @file
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*
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* A basic implementation of LCM function
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*/
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#include <cassert>
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#include <iostream>
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/**
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* Function for finding greatest common divisor of two numbers.
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* @params two integers x and y whose gcd we want to find.
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* @return greatest common divisor of x and y.
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*/
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unsigned int gcd(unsigned int x, unsigned int y) {
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if (x == 0) {
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return y;
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}
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if (y == 0) {
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return x;
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}
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if (x == y) {
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return x;
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}
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if (x > y) {
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// The following is valid because we have checked whether y == 0
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unsigned int temp = x / y;
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return gcd(y, x - temp * y);
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}
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// Again the following is valid because we have checked whether x == 0
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unsigned int temp = y / x;
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return gcd(x, y - temp * x);
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}
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/**
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* Function for finding the least common multiple of two numbers.
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* @params integer x and y whose lcm we want to find.
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* @return lcm of x and y using the relation x * y = gcd(x, y) * lcm(x, y)
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*/
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unsigned int lcm(unsigned int x, unsigned int y) {
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return x / gcd(x, y) * y;
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}
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/**
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* Function for testing the lcm() functions with some assert statements.
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*/
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void tests() {
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// First test on lcm(5,10) == 10
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assert(((void)"LCM of 5 and 10 is 10 but lcm function gives a different "
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"result.\n",
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lcm(5, 10) == 10));
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std::cout << "First assertion passes: LCM of 5 and 10 is " << lcm(5, 10)
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<< std::endl;
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// Second test on lcm(2,3) == 6 as 2 and 3 are coprime (prime in fact)
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assert(((void)"LCM of 2 and 3 is 6 but lcm function gives a different "
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"result.\n",
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lcm(2, 3) == 6));
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std::cout << "Second assertion passes: LCM of 2 and 3 is " << lcm(2, 3)
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<< std::endl;
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// Testing an integer overflow.
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// The algorithm should work as long as the result fits into integer.
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assert(((void)"LCM of 987654321 and 987654321 is 987654321 but lcm function"
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" gives a different result.\n",
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lcm(987654321, 987654321) == 987654321));
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std::cout << "Third assertion passes: LCM of 987654321 and 987654321 is "
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<< lcm(987654321, 987654321)
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<< std::endl;
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}
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/**
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* Main function
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*/
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int main() {
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tests();
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return 0;
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}
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