背包问题（贪心算法）(代码片段)

#ifndef MERGE_SORT_H
#define MERGE_SORT_H

template <class Type>
void MergeSort(Type a[], int n);

#endif

//merge_sort.template实现部分
#include "merge_sort.h"

template <class Type>
void MergeSort(Type *a , Type *v, int n)  //a是重量,v是价值

    Type *b = new Type[n];
    int s = 1;
    while (s < n)
    
        MergePass(a, b, v , s, n);  //合并到数组b
        s += s;
        MergePass(b, a, v , s, n);  //合并到数组a
        s += s;
    
    delete b;


template <class Type>
void MergePass(Type *x, Type *y, Type *v, int s, int n)

    int i = 0;
    while (i <= n - s * 2)
    
        Merge(x, y ,v , i, i + s - 1, i + 2 * s - 1);  //合并大小为s的相邻两段子数组
        i += s * 2;
    
    if (i + s < n)  //剩下的元素少于2s
        Merge(x, y, v, i, i + s - 1, n - 1);
    else for (int j = i; j <= n - 1; j++)
        y[j] = x[j];


template <class Type>
void Merge(Type *c, Type *d, Type *v , int l, int m, int r)  //合并c[l:m]和c[m+1:r]到d[l:r],其中c[l:m]和c[m+1:r]都是已经经过升序排好的数组

    int i = l, j = m + 1, k = l;
    while ((i <= m) && (j <= r))
    
        if ((v[i] / c[i]) >= (v[j] / c[j]))  //这里使用降序排序
            d[k++] = c[i++];
        else
            d[k++] = c[j++];
    
    if (i > m)
        for (int q = j; q <= r; q++)
            d[k++] = c[q];
    else for (int q = i; q <= m; q++)
        d[k++] = c[q];

//背包问题，使用贪心算法进行求解
//======================================================
#include <iostream>
#include "merge_sort.cpp"

using namespace std;


void init_data(float *v, float *w, float *x, int n)  //初始化数据

    cout << "请输入每类物体的价值：" << endl;
    for (int i = 0; i < n; i++)
    
        cin >> v[i];
    
    cout << "请输入每类物体的重量： " << endl;
    for (int i = 0; i < n; i++)
    
        cin >> w[i];
    
    for (int i = 0; i < n; i++)
        x[i] = 0;


void Knapsack(int n, float M, float *v, float *w, float *x)
//n是物体的种类数，M是背包容量，v是每类物体的价值，w是每类物体的重量,x是每类物体装入的份额，属于[0,1]

    int i = 0;
    float c = M;

    MergeSort(w , v , n);  //v[i]/w[i]是每一类物体的单位重量价值，然后对它们进行降序排序

    for (i = 0; i < n; i++)
    
        if (w[i] > c)
            break;
        x[i] = 1;
        c -= w[i];
    
    if (i < n)
        x[i] = c / w[i];


int main(void)

    float M = 0.0;  //背包容量
    cout << "请输入背包容量：  ";
    cin >> M;
    int n = 0;  //物体数量
    cout << "\n请输入物体数量 n :  ";
    cin >> n;
    float *v = new float[n];
    float *w = new float[n];
    float *x = new float[n];

    init_data(v, w, x, n);  //初始化数据
    Knapsack(n, M, v, w, x);

    cout << "排好序的w[i]:  " << endl;
    for (int i = 0; i < n; i++)
    
        cout << w[i] << "  ";
    
    cout << "\n\n输出最后的决策x[i] : " << endl;
    for (int i = 0; i < n; i++)
    
        cout << x[i] << "  ";
    

    /*MergeSort(w, v, n);
    cout << "输出排好序的w[i] : " << endl;
    for (int i = 0; i < n; i++)
    
        cout << w[i] << "  ";

    */
    system("pause");
    delete v , w , x;
    return 0;