最小重量機問題-回溯算法

設某一機器由n個部件組成，每種部件都可以從m個不同的供應商處購得。設wij是從供應商j處購得的部件i的重量，cij是相應的價格。設計一個算法，給出總價格不超過c的最小重量機的設計。

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w[i][j] 表示供應處 j 部件 i 的重量

c[i][j] 表示供應處 j 部件 i 的價格

weight 表示當前重量，minweight表示最小重量

cost 爲當前花費， sumValue 爲價格上限

約束條件 cost + c[i][j] < sumValue && weight + w[i][j] < minweight

#include<iostream>
#include<stdio.h>
using namespace std;

int n;
int m;
int sumValue;
int weight;
int minweight = 9999;
int cost;
int** c;
int** w;
int* select;	//用來記錄分配情況
int* sign;

void backtrack(int i)
{
	if (i > n)
	{
		minweight = weight;
		for (int j = 1; j <= n; j++)
			select[j] = sign[j];
	}
	else
	{
		for (int j = 1; j <= m; j++)
		{
			if (cost + c[i][j] <= sumValue && weight + w[i][j] < minweight)
			{
				sign[i] = j;
				cost += c[i][j];
				weight += w[i][j];
				backtrack(i + 1);
				cost -= c[i][j];
				weight -= w[i][j];
			}
		}
	}
}
void initial()
{
	cout << "請輸入部件的數量：";
	cin >> n;
	sign = new int[n+1];
	select = new int[n+1];
	cout << "請輸入供應商的數量：";
	cin >> m;
	w = new int*[n+1];
	for (int i = 1; i <= m; i++)
		w[i] = new int[m+1];
	c = new int* [n+1];
	for (int i = 1; i <= m; i++)
		c[i] = new int[m+1];
	cout << "輸入部件對應的價值：";
	for (int i = 1; i <= n; i++)
	{
		for (int j = 1; j <= m; j++)
			cin >> c[i][j];
	}
	cout << "輸入部件對應的重量：";
	for (int i = 1; i <= n; i++)
	{
		for (int j = 1; j <= m; j++)
			cin >> w[i][j];
	}
	cout << "請輸入總價值：";
	cin >> sumValue;
}

int main()
{
	initial();
	backtrack(1);
	cout << "部件1-" << n << "選擇的供應商:" << endl;
	for (int i = 1; i <= n; i++)
		cout << select[i] << " ";
	return 0;
}