feat(markov): add support of supplement

calculate_one.cpp

@@ -8,8 +8,9 @@ int main ()
 {
 	int lambda;
 	double p;
-	cin >> lambda >> p;
+	int threshold;
+	cin >> lambda >> p >> threshold;
 	for ( int i = 0; i < 10; ++i ) {
-		cout << setprecision ( 13 ) << ( 1 - simulate_prob ( lambda, p, SIM_DAYS ) ) << endl;
+		cout << setprecision ( 13 ) << simulate_prob ( lambda, p, SIM_DAYS, threshold ) << endl;
 	}
 }
\ No newline at end of file

markov_chain.cpp

@@ -59,7 +59,7 @@ void State::add_coupon ( int c )
 
 
 
-double simulate_prob ( double lambda, double prob_day, int sim_times )
+double simulate_prob ( double lambda, double prob_day, int sim_times, int supplement_threshold )
 {
 	mt19937 rand_gen ( static_cast < unsigned > ( chrono::system_clock::now ().time_since_epoch ().count () ) );
 	poisson_distribution < int > poisson ( lambda );
@@ -70,10 +70,16 @@ double simulate_prob ( double lambda, double prob_day, int sim_times )
 		int day = geometric ( rand_gen ) + 1;
 		current_state.pass_day ( day );
 		int current_cost = poisson ( rand_gen );
-		total_cost += current_cost;
 		int current_coupon = current_state.use_coupon ( current_cost, static_cast < int > ( floor ( current_cost * COUPON_RATIO + 1e-9 ) ) / COUPON_VALUE );
+		int remain_cost = current_cost - current_coupon * COUPON_VALUE;
+		int need_to_ceil = COUPON_COST - remain_cost % COUPON_COST;
+		if ( need_to_ceil <= supplement_threshold ) {
+			current_cost += need_to_ceil;
+			remain_cost += need_to_ceil;
+		}
+		total_cost += current_cost;
 		used_coupon += current_coupon;
-		current_state.add_coupon ( ( current_cost - current_coupon * COUPON_VALUE ) / COUPON_COST );
+		current_state.add_coupon ( remain_cost / COUPON_COST );
 	}
 	return ( static_cast < double > ( used_coupon * COUPON_VALUE ) / total_cost );
 }

markov_chain.h

@@ -26,4 +26,4 @@ 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_times );
+double simulate_prob ( double lambda, double prob_day, int sim_times, int supplement_threshold = 0 );