題意:求最長上升子序列的長度和數量。
分析:用dp求出最長上升子序列m,dp數組存的就是該元素爲子序列結尾的長度,源點與長度爲1的點建邊,長度爲m的與匯點連邊,然後枚舉任意兩個元素,ai,aj(ai>aj&&i>j&&dp[i]==dp[j]+1),j跟i連邊,因爲每個點只能選一次,所以邊的容量都爲1,求出最大流。
#include<stdio.h>
#include<string.h>
const int N=500;
const int inf=0x3fffffff;
int dis[N],gap[N],start,end,ans,dp[N],head[N],num;
struct edge
{
int st,ed,flow,next;
}e[N*5];
void addedge(int x,int y,int w)
{
e[num].st=x;e[num].ed=y;e[num].flow=w;e[num].next=head[x];head[x]=num++;
e[num].st=y;e[num].ed=x;e[num].flow=0;e[num].next=head[y];head[y]=num++;
}
int dfs(int u,int minflow)
{
if(u==end)return minflow;
int i,v,f,min_dis=ans-1,flow=0;
for(i=head[u];i!=-1;i=e[i].next)
{
v=e[i].ed;
if(e[i].flow<=0)continue;
if(dis[v]+1==dis[u])
{
f=dfs(v,e[i].flow>minflow-flow?minflow-flow:e[i].flow);
e[i].flow-=f;
e[i^1].flow+=f;
flow+=f;
if(flow==minflow)break;
if(dis[start]>=ans)return flow;
}
min_dis=min_dis>dis[v]?dis[v]:min_dis;
}
if(flow==0)
{
if(--gap[dis[u]]==0)
dis[start]=ans;
dis[u]=min_dis+1;
gap[dis[u]]++;
}
return flow;
}
int isap()
{
int maxflow=0;
memset(gap,0,sizeof(gap));
memset(dis,0,sizeof(dis));
gap[0]=ans;
while(dis[start]<ans)
maxflow+=dfs(start,inf);
return maxflow;
}
int main()
{
int i,j,n,a[N],cot;
while(scanf("%d",&n)!=-1)
{
cot=0;start=0;end=n+1;ans=end+1;num=0;
memset(head,-1,sizeof(head));
for(i=1;i<=n;i++)
{
scanf("%d",&a[i]);
dp[i]=1;
for(j=1;j<i;j++)
{if(a[i]>a[j]&&dp[i]<=dp[j]) dp[i]=dp[j]+1;}
if(cot<dp[i])cot=dp[i];
}
printf("%d\n",cot);
for(i=1;i<=n;i++)
{
if(dp[i]==1)
addedge(start,i,1);
if(dp[i]==cot)
addedge(i,end,1);
addedge(i,i,1);
}
for(i=1;i<=n;i++)
{
for(j=1;j<i;j++)
if(a[j]<a[i]&&dp[j]+1==dp[i])
addedge(j,i,1);
}
printf("%d\n",isap());
}
return 0;
}