1 条题解

  • 0
    @ 2025-2-25 16:02:08
    #include<bits/stdc++.h>
    using namespace std;
    typedef long long ll;
    const int N = 3e5+7,M = 3e5 + 7,MM = 3e5+7;
    const ll INF = 0x7ffffffffff;;
    int n,m;
    ll sum;
    int cnt,head[MM],ver[MM],nex[MM],edge[MM];
    int tree[MM],pre[N],ppre[N][23],depth[N],lg[N];
    ll maxf[N][23],minf[N][23];//这两个要和ans 作比较,所以用ll 
    struct E{
    	int from,to,w;
    	E(){}
    	E(int from,int to,int w) : from(from),to(to),w(w){}
    	bool operator < (const E &b)const{
    		return w < b.w;
    	}
    }e[M];
    void add(int x,int y,int w){
    	 ver[++cnt] = y;
    	 nex[cnt] = head[x];
    	 edge[cnt] = w;
    	 head[x] = cnt;
    }
    int find(int x){
    	return x == pre[x] ? x : pre[x] = find(pre[x]);
    }
    void read(){
    	scanf("%d%d",&n,&m);
    	for(int i=1;i <= m;i ++)
    		scanf("%d%d%d",&e[i].from,&e[i].to,&e[i].w);
    	
    	for(int i=0; i < N; i++)
    	pre[i] = i;
    }
    void work1(){
    	sort(e+1,e+m+1);
    	for(int i=1;i <= m;i ++){
    		int x = e[i].from,y = e[i].to,w = e[i].w;
    		int fx = find(x), fy = find(y);
    		if(fx != fy){
    			pre[fx] = fy;
    			sum += w;
    			add(x,y,w);
    			add(y,x,w);
    			tree[i] = 1;
    		}
    	}
    }
    void dfs(int f,int fa,int w){
    	depth[f] = depth[fa] + 1;
    	ppre[f][0] = fa;
    	minf[f][0] = -INF;
    	maxf[f][0] = w;
    	for(int i=1; (1<<i) <= depth[f];i++){
    		ppre[f][i] = ppre[ppre[f][i-1]][i-1];
    		maxf[f][i] = max(maxf[f][i-1],maxf[ppre[f][i-1]][i-1]);
    		minf[f][i] = max(minf[f][i-1],minf[ppre[f][i-1]][i-1]);//这里分清次小关系 
    		if(maxf[f][i-1] > maxf[ppre[f][i-1]][i-1]) minf[f][i]  = max(minf[f][i],maxf[ppre[f][i-1]][i-1]);
    		else if(maxf[f][i-1] < maxf[ppre[f][i-1]][i-1]) minf[f][i] = max(minf[f][i],maxf[f][i-1]);
    	}
    	
    	for(int i=head[f]; i ; i=nex[i]){
    		int y = ver[i],w = edge[i];
    		if(y != fa){
    			dfs(y,f,w);
    		}
    	}
    }
    int lca(int x,int y){
    	if(depth[x] < depth[y]) swap(x,y);
    	while(depth[x] > depth[y]) 
    	x = ppre[x][lg[depth[x]-depth[y]] -1];
    	
    	if(x==y) return x;
    	for(int i = lg[depth[x]]-1; i>=0; i--){
    		if(ppre[x][i] != ppre[y][i]) 
    		x= ppre[x][i],y = ppre[y][i];
    	}
    		
    	return ppre[x][0];
    }
    ll qmax(int x,int y,int maxx){
    	ll ans = -INF;
    	
    	for(int i = lg[depth[x]]-1;i>=0;i--){
    		if(depth[ppre[x][i]]>=depth[y]){
    			if(maxx != maxf[x][i]) ans = max(ans,maxf[x][i]);
    			else ans = max(ans,minf[x][i]);
    			x = ppre[x][i];
    		}
    	}
    	return ans;
    } 
    void work2(){
    	for(int i=1;i <= n;i++)
    	lg[i] = lg[i-1] + (1<<lg[i-1]==i);
     
    	dfs(1,0,0);
    	ll ans = INF;
    	for(int i = 1;i <= m;i++){
    		if(tree[i]) continue;
    		int x = e[i].from,y = e[i].to,w = e[i].w;
    		int lc = lca(x,y);
    		ll maxx = qmax(x,lc,w);
    		ll maxv = qmax(y,lc,w);
    		ans = min(ans,sum-max(maxx,maxv)+w);//找到到公共父亲节点路径中最大的那条,替换到非树边。 
    	}
    	printf("%lld\n",ans);
    }
    int main(){
    	read();
    	work1();
    	work2();
    	return 0;
    }
    
    • 1

    信息

    ID
    949
    时间
    1000ms
    内存
    512MiB
    难度
    (无)
    标签
    (无)
    递交数
    0
    已通过
    0
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