#include <iostream.h>
#include<iomanip.h>
#include<string.h>
int min(int w,int c)
{int temp;
if (w<c) temp=w;
else
temp=c;
return temp;
}
int max(int w,int c)
{
int temp;
if (w>c) temp=w;
else
temp=c;
return temp;
}
void knapsack(int v[],int w[],int c,int n,int**m) //求最优值
{
int jmax=min(w[n]-1,c);
for(int j=0;j<=jmax;j++)
m[n][j]=0;
for(int jj=w[n];jj<=c;jj++)
m[n][jj]=v[n];
for(int i=n-1;i>1;i--){ //递归部分
jmax=min(w[i]-1,c);
for(int j=0;j<=jmax;j++)
m[i][j]=m[i+1][j];
for(int jj=w[i];jj<=c;jj++)
m[i][jj]=max(m[i+1][jj],m[i+1][jj-w[i]]+v[i]);
}
m[1][c]=m[2][c];
if(c>=w[1])
m[1][c]=max(m[1][c],m[2][c-w[1]]+v[1]);
cout<<"最优值："<<m[1][c]<<endl;
for(int l=2;l<=n;l++)
for(int j=0;j<=c;j++)
{
cout<<m[l][j]<<setw(c-1);
}
cout<<endl;
cout<<"*******************************************"<<endl;
}
int traceback(int **m,int w[],int c,int n,int x[]) //回代，求最优解
{
cout<<"得到的一组最优解如下:"<<endl;
for(int i=1;i<n;i++)
if(m[i][c]==m[i+1][c]) x[i]=0;
else {x[i]=1;
c-=w[i];}
x[n]=(m[n][c])?1:0;
for(int y=1;y<=n;y++)
{
cout<<setw(5)<<x[y];
}
return x[n];
}
void main()
{
int n,c;
int **m;
cout<<"&&&&&&&&&&&&&&&&&&&&& 欢迎使用0-1背包问题程序&&&&&&&&&&&&&&&&&&&"<<endl;
cout<<"请输入物品个数和重量上限:";
cin>>n>>c;
int *v=new int[n+1];
cout<<"Pls input the property (v[i]):"<<endl;
for(int i=1;i<=n;i++)
cin>>v[i];
int *w=new int[n+1];
cout<<"Pls input the weight (w[i]):"<<endl;
for(int j=1;j<=n;j++)
cin>>w[j];
int *x=new int[n+1];
m=new int*[n+1]; //动态的分配二维数组
for(int p=0;p<n+1;p++)
{
m[p]=new int[c+1];
}
knapsack(v,w,c,n,m);
traceback(m,w,c,n,x);
}
static void Main()
{
int[] values = { 100, 200, 300, 400, 500, 600, 700, 600 };
//int[] values = { 1, 1, 1 , 1,2};
double x = 1, y = 3, z = 4;
int maxValue = 0;
int sumTotal = 0;
foreach (int val in values)
{
sumTotal += val;
if (val > maxValue) maxValue = val;
}
int len = values.Length;
double xyz = x + y + z;
x = (x * sumTotal) / xyz;
y = (y * sumTotal) / xyz;
z = (z * sumTotal) / xyz;
double offset = maxValue;
int[] x1 = new int[0], y1 = new int[0], z1 = new int[0];
for (int countX = 1; countX <= len - 2; countX++)
{
Combination(len, countX, delegate(int[] indexesX)
{
int sumX = Sum(values, indexesX);
double offsetX = Math.Abs(sumX - x);
if (offsetX <= maxValue)
{
int[] arrayYZ = CopyArrayByExclude(values, indexesX);
int lenYZ = arrayYZ.Length;
for (int countY = 1; countY <= lenYZ - 1; countY++)
{
Combination(lenYZ, countY, delegate(int[] indexesY)
{
int sum2 = Sum(values, indexesY);
double offsetY = Math.Abs(sum2 - y);
if (offsetY <= maxValue)
{
int[] arrayZ = CopyArrayByExclude(arrayYZ, indexesY);
int sumZ = Sum(arrayZ);
double offsetZ = Math.Abs(sumZ - z);
if ((offsetX + offsetY + offsetZ) / 2 <= offset)
{
offset = (offsetX + offsetY + offsetZ) / 2;
x1 = CopyArrayByInclude(values, indexesX);
y1 = CopyArrayByInclude(arrayYZ, indexesY);
z1 = arrayZ;
}
}
});
}
}
});
}
Console.WriteLine("运算结果");
Console.Write("Offset: " + offset);
Console.Write("\nX: ");
foreach (int i in x1) Console.Write(i + " ");
Console.Write("\nY: ");
foreach (int i in y1) Console.Write(i + " ");
Console.Write("\nZ: ");
foreach (int i in z1) Console.Write(i + " ");
Console.ReadKey();
}
static int Sum(int[] values)
{
int total = 0;
for (int i = 0; i < values.Length; i++)
{
total += values[i];
}
return total;
}
static int Sum(int[] values, int[] sumIndexs)
{
int total = 0;
for (int i = 0; i < sumIndexs.Length; i++)
{
total += values[sumIndexs[i]];
}
return total;
}
static int[] CopyArrayByExclude(int[] array, int[] excludeIndexes)
{
int[] newArray = new int[array.Length - excludeIndexes.Length];
int newArrayIndex = 0;
for (int i = 0; i < array.Length; i++)
{
bool pass = false;
foreach (int index in excludeIndexes)
{
if (i == index)
{
pass = true;
break;
}
}
if (!pass)
{
newArray[newArrayIndex] = array[i];
newArrayIndex++;
}
}
return newArray;
}
static int[] CopyArrayByInclude(int[] array, int[] includeIndexes)
{
int[] newArray = new int[includeIndexes.Length];
for (int i = 0; i < includeIndexes.Length; i++)
{
newArray[i] = array[includeIndexes[i]];
}
return newArray;
}
static void Combination(int len, int count, Action<int[]> process)
{
int[] indexes = new int[count];
int pos = 0;
while (true)
{
if (pos == count - 1)
{
process(indexes);
if (indexes[pos] < len - 1)
{
indexes[pos]++;
}
else
{
bool isEnd = true;
for (int i = count - 2; i >= 0; i--)
{
if (indexes[i] < len - count + i)
{
pos = i;
indexes[pos]++;
isEnd = false;
break;
}
}
if (isEnd) break;
}
}
else
{
indexes[pos + 1] = indexes[pos] + 1;
pos++;
}
}
}
