feat(markov): add markov chain simulator

.gitignore

+main
+Debug
+.vs
+*.vcxproj*

consts.cpp

+/**
+* consts.cpp
+* Define the constants
+*/
+
+#include "consts.h"
+
+const int EXPIRE_DAYS = 30;
+const int COUPON_COST = 100;
+const int COUPON_VALUE = 50;

consts.h

+/**
+ * consts.h
+ * Define the constants
+ */
+
+#pragma once
+
+extern const int EXPIRE_DAYS;
+extern const int COUPON_COST;
+extern const int COUPON_VALUE;

main.cpp

+#include <bits/stdc++.h>
+#include "markov_chain.h"
+using namespace std;
+
+const int SIM_DAYS = 10000000;
+
+int main ()
+{
+	int lambda;
+	double p;
+	cin >> lambda >> p;
+	for ( int i = 0; i < 10; ++i ) {
+		cout << setprecision ( 13 ) << ( 1 - simulate_prob ( lambda, p, SIM_DAYS ) ) << endl;
+	}
+}
\ No newline at end of file

markov_chain.cpp

+/**
+ * markov_chain.cpp
+ * Calculate the percentage of the off-sale
+ */
+
+#include "markov_chain.h"
+#include "consts.h"
+
+#include <algorithm>
+#include <numeric>
+#include <random>
+#include <chrono>
+using namespace std;
+
+
+
+State::State ()
+	: coupon_count ( EXPIRE_DAYS )
+{
+
+}
+
+int State::operator [] ( int i ) const
+{
+	return coupon_count[i];
+}
+
+int & State::operator [] ( int i )
+{
+	return coupon_count[i];
+}
+
+pair<State, int> State::use_coupon ( int c ) const
+{
+	State result = *this;
+	int use_count = 0, current_use_count;
+	for ( int i = 0; i < EXPIRE_DAYS; ++i ) {
+		current_use_count = min ( result[i], c / COUPON_COST );
+		c -= COUPON_COST * current_use_count;
+		result[i] -= current_use_count;
+		use_count += current_use_count;
+	}
+	return make_pair ( result, use_count );
+}
+
+State State::pass_day ( int c ) const
+{
+	State result;
+	for ( int i = 1; i < EXPIRE_DAYS; ++i ) {
+		result[i - 1] = coupon_count[i];
+	}
+	result[EXPIRE_DAYS - 1] = c;
+	return result;
+}
+
+
+
+double simulate_prob ( double lambda, double prob_day, int sim_days )
+{
+	mt19937 rand_gen ( static_cast < unsigned > ( chrono::system_clock::now ().time_since_epoch ().count () ) );
+	poisson_distribution < int > poisson ( lambda );
+	uniform_real_distribution < double > uniform ( 0.0, 1.0 );
+	State current_state;
+	long long total_cost = 0, used_coupon = 0;
+	for ( int day = 0; day < sim_days; ++day ) {
+		int current_cost = ( uniform ( rand_gen ) < prob_day ) ? poisson ( rand_gen ) : 0;
+		total_cost += current_cost;
+		auto return_val = current_state.use_coupon ( current_cost );
+		used_coupon += return_val.second;
+		current_state = return_val.first.pass_day ( ( current_cost - return_val.second * COUPON_VALUE ) / COUPON_COST );
+	}
+	return ( static_cast < double > ( used_coupon * COUPON_VALUE ) / total_cost );
+}

markov_chain.h

+/**
+ * markov_chain.h
+ * Calculate the percentage of the off-sale
+ */
+
+#pragma once
+
+#include <utility>
+#include <vector>
+
+class State
+{
+public:
+	State ();
+
+	int operator [] ( int i ) const;
+	int & operator [] ( int i );
+
+	std::pair < State, int > use_coupon ( int c ) const;
+
+	State pass_day ( int c ) const;
+
+private:
+	std::vector < int > coupon_count;   // i-th term indicates the number of coupons expired in the i-th day
+};
+
+double simulate_prob ( double lambda, double prob_day, int sim_days );