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  • [JLOI2016/SHOI2016]侦察守卫

    CXIII.[JLOI2016/SHOI2016]侦察守卫

    神题。

    见代码即可。

    #include<bits/stdc++.h>
    using namespace std;
    int n,m,p,a[500100],f[500100][25],g[500100][25],res=0x3f3f3f3f;
    //f[i,j]:minimum cost when there're at most j layers left uncovered
    //g[i,j]:minimum cost when there're at least j layers outside the subtree covered
    bool sp[500100];
    vector<int>v[500100];
    void dfs(int x,int fa){
    	if(sp[x])f[x][0]=g[x][0]=a[x];//at special points, empty state still need a guard; at normal points, empty state doesn't need a guard.
    	for(int i=1;i<=m;i++)g[x][i]=a[x];//at whatever points, a state which can spread outside the subtree need a guard.
    	g[x][m+1]=0x3f3f3f3f;//avoiding transferring outside bounds
    	for(auto y:v[x]){
    		if(y==fa)continue;
    		dfs(y,x);
    		for(int i=m;i>=0;i--)g[x][i]=min(g[x][i]+f[y][i],f[x][i+1]+g[y][i+1]);
    		//in this case transferring order doesn't matter.
    		//but g's transferring must take place before f since it needs f in transferring.
    		//case 1:guards in x spread into y, where there are i layers downwards y is covered from x.
    		//case 2:guards in y spread into x, where there are i+1 layers downward x is covered from y, and y can also cover upper levels.
    		for(int i=m;i>=0;i--)g[x][i]=min(g[x][i],g[x][i+1]);
    		//in this case it is getting a suffix minimum, where transferring order matters.
    		f[x][0]=g[x][0];//in fact f[x][0] and g[x][0] have the same meaning(which is a full subtree covered and nothing more)
    		for(int i=1;i<=m;i++)f[x][i]+=f[y][i-1];
    		//if there are at most i layers downwards, there should be at most i-1 layers downwards.
    		for(int i=1;i<=m;i++)f[x][i]=min(f[x][i],f[x][i-1]);
    		//getting a prefix minimum.
    	}
    }
    int main(){
    	scanf("%d%d",&n,&m);
    	for(int i=1;i<=n;i++)scanf("%d",&a[i]);
    	scanf("%d",&p);
    	for(int i=1,x;i<=p;i++)scanf("%d",&x),sp[x]=true;
    	for(int i=1,x,y;i<n;i++)scanf("%d%d",&x,&y),v[x].push_back(y),v[y].push_back(x);
    	dfs(1,0);
    	printf("%d\n",f[1][0]);
    	return 0;
    }
    

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  • 原文地址:https://www.cnblogs.com/Troverld/p/14601317.html
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