01分数规划

POJ 2976 普通的01分数规划 http://poj.org/problem?id=2976

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<queue>
using namespace std;
#define eps 1e-5
#define maxn 1005
#define INF 1999999999
typedef long long ll;
int x[maxn],y[maxn];
double u[maxn];

int main(){
int n,k;
while(scanf("%d%d",&n,&k),n!=0||k!=0){
for(int i=0;i<n;i++) scanf("%d",&x[i]);
for(int i=0;i<n;i++) scanf("%d",&y[i]);
double st=0,nd=INF;
while(st<=nd-eps)
{
double mid=(st+nd)/2;
double sum=0;
for(int i=0;i<n;i++) u[i]=100*(x[i]-y[i]*mid),sum+=u[i];

sort(u,u+n);

for(int i=0;i<k;i++){if(sum>mid) break;sum-=u[i];}

if(sum>=0) st=mid;
else nd=mid;
}
printf("%d\n",(int)(100*st+0.5));
}
}

POJ 2728 最优比率生成树 http://poj.org/showsource?solution_id=13130924

#include<iostream>
#include<cstdio>
#include<math.h>
#include<queue>
#include<string.h>
#include<vector>
#include<algorithm>
#define maxn 1005
#define INF 100000000
#define eps 1e-5
using namespace std;
struct Node
{
int x,y,h;
}node[maxn];
double w[maxn][maxn];
double h[maxn][maxn];

double ans;
double Lengh(Node a,Node b){
return sqrt(0.0+(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
int n;

double mincost[maxn];
bool used[maxn];
double prim(){
for(int i=0;i<n;i++){ //稠密图用prim
mincost[i]=INF;
used[i]=false;
}
mincost[0]=0;
double res=0;
while(1){
int v=-1;
for(int u=0;u<n;u++)
if(!used[u]&&(v==-1||mincost[u]<mincost[v]))
v=u;
if(v==-1) break;
used[v]=true;
res+=mincost[v];
for(int u=0;u<n;u++)
mincost[u]=min(mincost[u],h[v][u]-ans*w[v][u]);
}
return res;
}

int main(){
while(scanf("%d",&n),n!=0){
for(int i=0;i<n;i++)
scanf("%d%d%d",&node[i].x,&node[i].y,&node[i].h);
for(int i=0;i<n;i++)
for(int j=0;j<n;j++){
w[i][j]=Lengh(node[i],node[j]);
h[i][j]=fabs(0.0+node[i].h-node[j].h);
}

double sta=0,end=1000;
while(sta<end-eps){
double mid=(sta+end)/2;
ans=mid;
double sum=prim();
if(sum<0)
end=mid;
else
sta=mid;
}
printf("%.3f\n",ans);
}

}

POJ 3621 最优比率环 http://poj.org/problem?id=3621

#include<iostream>
#include<cstdio>
#include<queue>
#include<string.h>
#include<vector>
#define maxn 5005
#define eps 1e-5
using namespace std;
int u[maxn],v[maxn],w[maxn],next[maxn],first[maxn];
double l[maxn];
int num[maxn];
int z[maxn];
queue<int> q;
bool inq[maxn];
int n;
bool spfa(double ans){
while(!q.empty())
q.pop();
for(int i=1;i<=n;i++)
l[i]=0,num[i]=0,inq[i]=1,q.push(i);
while(!q.empty()){
int x=q.front();
q.pop();
inq[x]=0;
num[x]++;
if(num[x]>=n)
return 1;
for(int i=first[x];i!=-1;i=next[i]){
if(l[v[i]]>ans*w[i]+l[u[i]]-z[v[i]]+eps){
l[v[i]]=ans*w[i]+l[u[i]]-z[v[i]];
if(!inq[v[i]]){
q.push(v[i]);
inq[v[i]]=1;
}
}
}
}
return 0;
}

int main(){
int m;
while(scanf("%d%d",&n,&m)!=EOF){
for(int i=1;i<=n;i++)
scanf("%d",&z[i]);
memset(first,-1,sizeof(first));
for(int i=0;i<m;i++){
scanf("%d%d%d",&u[i],&v[i],&w[i]);
next[i]=first[u[i]];
first[u[i]]=i;
}

double sta=0,end=2000;
while(sta+eps<end){
double mid=(sta+end)/2;
if(spfa(mid))
sta=mid;
else
end=mid;
}
printf("%.2f\n",sta);
}
}