64 lines
1.8 KiB
C++
64 lines
1.8 KiB
C++
#include <random>
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#include <random>
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#include <vector>
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#include <iostream>
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#define MAX_N 20
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#define TIMES 1000000
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/**
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* Used to generate a uniform random distribution
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*/
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static std::random_device rd; //Will be used to obtain a seed for the random number engine
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static std::mt19937 gen(rd()); //Standard mersenne_twister_engine seeded with rd()
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static std::uniform_int_distribution<> dis;
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int randint(int n) {
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int r, rmax = RAND_MAX / n * n;
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dis=std::uniform_int_distribution<int>(0,rmax) ;
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r = dis(gen);
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return r / (RAND_MAX / n);
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}
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unsigned long long factorial(size_t n) {
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//Factorial using dynamic programming to memoize the values.
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static std::vector<unsigned long long>factorials{1,1,2};
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for (;factorials.size() <= n;)
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factorials.push_back(((unsigned long long) factorials.back())*factorials.size());
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return factorials[n];
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}
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long double expected(size_t n) {
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long double sum = 0;
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for (size_t i = 1; i <= n; i++)
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sum += factorial(n) / pow(n, i) / factorial(n - i);
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return sum;
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}
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int test(int n, int times) {
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int i, count = 0;
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for (i = 0; i < times; i++) {
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unsigned int x = 1, bits = 0;
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while (!(bits & x)) {
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count++;
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bits |= x;
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x = static_cast<unsigned int>(1 << randint(n));
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}
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}
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return count;
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}
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int main() {
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puts(" n\tavg\texp.\tdiff\n-------------------------------");
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int n;
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for (n = 1; n <= MAX_N; n++) {
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int cnt = test(n, TIMES);
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long double avg = (double)cnt / TIMES;
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long double theory = expected(static_cast<size_t>(n));
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long double diff = (avg / theory - 1) * 100;
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printf("%2d %8.4f %8.4f %6.3f%%\n", n, static_cast<double>(avg), static_cast<double>(theory), static_cast<double>(diff));
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}
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return 0;
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}
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