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0-1背包问题.cpp
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0-1背包问题.cpp
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#include<bits/stdc++.h>
using namespace std;
#define C 10
int V[6][11];
int x[5];
int KnapSack(int n, int w[ ], int v[ ]);
int max(int x,int y);
int main()
{
int w[]= {2,2,6,5,4};
int v[]= {6,3,5,4,6};
cout<<"背包获得的最大价值是:"<<KnapSack(5,w,v)<<endl;
cout<<"装入背包的物品是:";
for(int i=0; i<5; i++)
if (x[i] == 1)
cout<<"物品"<<i+1<<" ";
cout<<endl;
return 0;
}
int max(int x,int y)
{
if (x > y)
return x;
else
return y;
}
int KnapSack(int n, int w[ ], int v[ ])
{
int i, j;
for (i = 0; i <= n; i++) //初始化第0列
V[i][0] = 0;
for (j = 1; j <= C; j++) //初始化第0行
V[0][j] = 0;
for (i = 1; i <= n; i++) //计算第i行,进行第i次迭代
{
for (j = 1; j <= C; j++)
{
if (j < w[i-1])
V[i][j] = V[i-1][j];
else
V[i][j] = max(V[i-1][j], V[i-1][j-w[i-1]]+v[i-1]);
}
}
for (j = C, i = n; i > 0; i--) //求装入背包的物品
{
if (V[i][j] > V[i-1][j])
{
x[i-1] = 1;
j = j - w[i-1];
}
else
x[i-1] = 0;
}
return V[n][C]; //返回背包取得的最大价值
}