题目
给出一个城市的地图(用邻接矩阵表示),商店设在一点,使各个地方到商店距离之和最短。
分析
最短路径,floyd或dijsktra
代码
#include <cstdio>
using namespace std;
int n,f[201][201],s,min=2147483647;
int main(){
scanf("%d",&n);
for (int i=1;i<=n;i++)
for (int j=1;j<=n;j++) {
scanf("%d",&f[i][j]);
if (!f[i][j]) f[i][j]=2147483647;
}
for (int k=1;k<=n;k++)
for (int i=1;i<=n;i++)
for (int j=1;j<=n;j++)
if (f[i][j]>f[i][k]+f[k][j]) f[i][j]=f[i][k]+f[k][j];
for (int i=1;i<=n;i++){
s=0; for (int j=1;j<=n;j++) s+=f[i][j]; if (min>s) min=s;
}
printf("%d",min); return 0;
}
floyd
#include <cstdio>
#include <cstring>
using namespace std;
int n,low[202],f[202][202],ans=2147483647; bool b[202];
int main(){
scanf("%d",&n);
for (int i=1;i<=n;i++)
for (int j=1;j<=n;j++) {
scanf("%d",&f[i][j]);
if (!f[i][j]) f[i][j]=2147483647;
}
for (int l=1;l<=n;l++){
memset(b,0,sizeof(b)); b[l]=1; int s=0;
for (int i=1;i<=n;i++) low[i]=f[l][i];
for (int i=1;i<n;i++){
int minx=2147483647,k=0;
for (int j=1;j<=n;j++)
if (!b[j]&&low[j]<minx){minx=low[j];k=j;}
if (k==0) break; b[k]=1;
for (int j=1;j<=n;j++) if ((long long)low[k]+f[k][j]<low[j]) low[j]=low[k]+f[k][j];//更新最小值
}
for (int i=1;i<=n;i++) if (low[i]!=2147483647)s+=low[i];//最短路径和
if (ans>s) ans=s;
}
printf("%d",ans);
}