回溯法

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#include<iostream>
#define N 10010
using namespace std;
double c;//背包容量
int n;//物品数量
double w[N];//物品重量数组
double v[N];//物品价值数组
double cw;//当前重量
double cv;//当前价值
double bestv;//当前最优价值
double best_x[N];//记录最好的情况
int x[N];//记录回溯的情况
double Bound(int i);
void BackTrack(int i);
int main(void) {

	double weight_sum=0, best_value=0;
	cout<<"Please input the number of goods:";
	cin >> n;
	cout<<"Please input the capacity of bag:";
	cin >> c;
	cout<<"Please input the weight and value of each goods:"<<endl;
	for (int i = 0; i < n; i++) {
		cin >> w[i] >> v[i];
		weight_sum += w[i];
		best_value += v[i];
	}
	if (weight_sum <= c) cout << "All goods can be put into the bag\n" << "The best value is" << best_value << endl;
	else {
		BackTrack(0);
		cout << "The best_x is : ";
		for (int i = 0; i < n; i++) {
			cout << best_x[i] << " ";
		}
		cout << endl << "The bestv is :";
		cout << bestv << endl;
	}
	return 0;
}
double Bound(int i) {
	double cleft_value=0;
	double cleft = c - cw;
	while (i <=n-1&&w[i]<=cleft) {
		cleft_value += v[i];
		cleft -= w[i];
		i++;
	}
	if(i<n)
	cleft_value += v[i] / w[i] * cleft;
	return (cleft_value + cv);
}
void BackTrack(int i) {
	if (i > n-1) {//只要能到达叶子节点，一定是最好的情况
		for (int t = 0; t < n; t++) {
			best_x[t] = x[t];//记录解向量
		}
		bestv = cv;
		return;
	}
	if (cw + w[i] <= c) {
		x[i] = 1;
		cw += w[i];
		cv += v[i];
		BackTrack(i+1);
		cw -= w[i];//回溯，
		cv -= v[i];
	}
	if (Bound(i + 1) >bestv) {
		x[i] = 0;
		BackTrack(i + 1);
	}
}

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