求解0/1背包问题

动态规划

//求解0_1背包问题 
//动态规划
#include<stdio.h>
#define MaxN 20
#define MaxW 100
int knap(int f[MaxN][MaxW],int w[],int v[],int W,int n){
	//动态规划求数组f[][] 
	int i,r;
	for(i=0;i<=n;i++)
		f[i][0] = 0;
	for(r=0;r<=W;r++)
		f[0][r] = 0;
		
	for(i=1;i<=n;i++){
		for(r=1;r<=W;r++){
			if(r < w[i])
				f[i][r] = f[i-1][r];
			else{
				if(f[i-1][r] < f[i-1][r-w[i]] + v[i])
					f[i][r] = f[i-1][r-w[i]] + v[i];
				else
					f[i][r] = f[i-1][r];
			}
		} 
	} 
	return f[n][W]; 
}

int Traceback(int f[MaxN][MaxW],int w[],int x[],int W,int n){
	int i,r=W;
	int maxw = 0;
	for(i=n;i>0;i--){
		if(f[i][r] != f[i-1][r]){
			x[i] = 1;
			maxw += w[i];
			r = r - maxw;
		}
		else
			x[i] = 0; 
	}
	return maxw;
} 
void dispknap(int x[],int maxw,int maxv,int n){
	int i;
	printf("最佳背包方案是：\n");
	for(i=0;i<=n;i++){
		if(x[i] == 1)
			printf("选取第%d种物品\n",i); 
	}
	printf("总重量=%d,总价值=%d",maxw,maxv);
}
int main(){
	int f[MaxN][MaxW];
	int x[MaxN];
	int maxv;
	int maxw;
	int n=5,W=10;
	int w[MaxN] = {0,2,2,6,5,4};
	int v[MaxN] = {0,6,3,5,4,6};
	maxv = knap(f,w,v,W,n);
	maxw = Traceback(f,w,x,W,n);
	dispknap(x,maxw,maxv,n);
	return 0;
}