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  • POJ3417 Network

    题目链接

    翻译:一棵无根树,给出m条边,把这m条边连上,每次你能毁掉两条边,规定一条是树边,一条新边。问有多少种方案能使树断裂。


    这题想一想就明白了:考虑每一条新边连接的两个点(x)(y),对于这两点间树上路径的边,如果没有和其他新边连成环,那么这条边删了后树就会断裂,否则就断不了。所以每一次我们把(x)(y)在树上的路径标记一遍,最后统计每一条边的标记情况:如果没有标记,那么随时可以删;如果只标记了一次,那么必须和对应的新边一块删;如果被标记了多次,那么任何时刻都删不了。
    记被标记了0次、1次、多次的边的数量为(n1,n2,n3),那么答案就是(n1 * m + n2)


    至于边标记,那么就要用到树上差分,而且是边差分。

    #include<cstdio>
    #include<iostream>
    #include<cmath>
    #include<algorithm>
    #include<cstring>
    #include<cstdlib>
    #include<cctype>
    #include<vector>
    #include<queue>
    #include<assert.h>
    #include<ctime>
    using namespace std;
    #define enter puts("") 
    #define space putchar(' ')
    #define Mem(a, x) memset(a, x, sizeof(a))
    #define In inline
    #define forE(i, x, y) for(int i = head[x], y; ~i && (y = e[i].to); i = e[i].nxt)
    typedef long long ll;
    typedef double db;
    const int INF = 0x3f3f3f3f;
    const db eps = 1e-8;
    const int maxn = 1e5 + 5;
    const int N = 17;
    In ll read()
    {
    	ll ans = 0;
    	char ch = getchar(), las = ' ';
    	while(!isdigit(ch)) las = ch, ch = getchar();
    	while(isdigit(ch)) ans = (ans << 1) + (ans << 3) + ch - '0', ch = getchar();
    	if(las == '-') ans = -ans;
    	return ans;
    }
    In void write(ll x)
    {
    	if(x < 0) x = -x, putchar('-');
    	if(x >= 10) write(x / 10);
    	putchar(x % 10 + '0');
    }
    In void MYFILE()
    {
    #ifndef mrclr
    	freopen(".in", "r", stdin);
    	freopen(".out", "w", stdout);
    #endif
    }
    
    int n, m;
    struct Edge
    {
    	int nxt, to;
    }e[maxn << 1];
    int head[maxn], ecnt = -1;
    In void addEdge(int x, int y)
    {
    	e[++ecnt] = (Edge){head[x], y};
    	head[x] = ecnt;
    }
    
    int fa[N + 2][maxn], dep[maxn];
    In void dfs(int now, int _f)
    {
    	for(int i = 1; (1 << i) <= dep[now]; ++i)
    		fa[i][now] = fa[i - 1][fa[i - 1][now]];
    	forE(i, now, v)
    	{
    		if(v == _f) continue;
    		dep[v] = dep[now] + 1, fa[0][v] = now;
    		dfs(v, now);
    	}
    }
    In int lca(int x, int y)
    {
    	if(dep[x] < dep[y]) swap(x, y);
    	for(int i = N; i >= 0; --i)
    		if(dep[fa[i][x]] >= dep[y]) x = fa[i][x];
    	if(x == y) return x;
    	for(int i = N; i >= 0; --i)
    		if(fa[i][x] != fa[i][y]) x = fa[i][x], y = fa[i][y];
    	return fa[0][x]; 
    }
    
    int a[maxn];
    ll ans = 0;
    In void dfs2(int now, int _f)
    {
    	forE(i, now, v)
    	{
    		if(v == _f) continue;
    		dfs2(v, now);
    		a[now] += a[v]; 
    	}
    	if(now == 1) return;
    	if(!a[now]) ans += m;
    	else if(a[now] == 1) ++ans;
    }
    
    int main()
    {
    //	MYFILE();
    	Mem(head, -1), ecnt = -1; 
    	n = read(), m = read();
    	for(int i = 1; i < n; ++i)
    	{
    		int x = read(), y = read();
    		addEdge(x, y), addEdge(y, x);
    	}
    	dep[1] = 1, dfs(1, 0);
    	for(int i = 1; i <= m; ++i)
    	{
    		int x = read(), y = read();
    		int z = lca(x, y);
    		a[x]++, a[y]++, a[z] -= 2;
    	}
    	dfs2(1, 0);
    	write(ans), enter;
    	return 0;	
    }
    
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  • 原文地址:https://www.cnblogs.com/mrclr/p/13764187.html
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