dfs序应用

链接 poj_3321
dfs序加树状数组维护子树和

code

---

#include<iostream>
#include<algorithm>
#include<cstring>

using namespace std;

const int N = 1e5 + 10;

int h[N], ne[N<<1], e[N<<1], w[N<<1], idx;
int in[N], out[N];
int a[N], c[N];
int time = 0;
int n, m;

//int num[N]; 记录dfs时每个节点顺序
//int id[N];记录dfs序
//int cnt = 0;

void dfs(int now, int fa)
{
    
    
	in[now] = ++ time;
	//num[time] = now;
	//id[cnt ++] = now;
	for(int i = h[now]; ~i; i = ne[i])
	{
    
    
		int j = e[i];
		if(j != fa)
		{
    
    
			dfs(j, now);
			//id[cnt ++] = now;
		}
	}
	out[now] = time;

}

void add(int a, int b)
{
    
    
	e[idx] = b;
	ne[idx] = h[a];
	h[a] = idx ++;
}

int lowbit(int x)
{
    
    
	return x & -x;
}

int sum(int x)
{
    
    
	int res = 0;
	for(int i = x; i > 0; i -= lowbit(i))
	{
    
    
		res += c[i];
	}
	return res;
}

int query(int x)
{
    
    
	int l = in[x];
	int r = out[x];
	return sum(r) - sum(l-1);
}

void change(int y)
{
    
    
	int x = in[y];
	if(a[x])
	{
    
    
		a[x] = 0;
		for(int i = x; i <= n; i += lowbit(i))
		{
    
    
			c[i] -= 1;
		}
	}
	else
	{
    
    
		a[x] = 1;
		for(int i = x; i <= n; i += lowbit(i))
		{
    
    
			c[i] += 1;
		}
	}
}

int main()
{
    
    
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	while(cin >> n)
	{
    
    
		idx = 0;
		time = 0;
		memset(h, -1, sizeof(h));
		for(int i = 0; i < n - 1; i ++)
		{
    
    
			int a, b;
			cin >> a >> b;
			add(a, b);
		}
		dfs(1, -1);
		for(int i = 1; i <= n; i ++)
		{
    
    
			a[i] = 1;
			for(int j = i; j <= n; j += lowbit(j))
			{
    
    
				c[j] += 1;
			}
		}
		cin >> m;
		while(m --)
		{
    
    
			char c;
			int x;
			cin >> c >> x;
			if(c == 'Q')
			{
    
    
				printf("%d\n", query(x));
			}
			else
			{
    
    
				change(x);
			}
		}
	}
	
	return 0;
}

---

欧拉序加ST表求lca
lca模板题

code

#include<iostream>
#include<cstring>
#include<algorithm>

using namespace std;

const int N = 5e5 + 5;

int h[N], e[N<<1], ne[N<<1], idx;
int order[N<<1], depth[N<<1], cnt;
int st[N<<1][20];
int start[N];
int lg[N<<1];
int n, m, s;

void dfs(int u, int fa)
{
    
    
	start[u] = ++ cnt;
	order[cnt] = u;
	depth[cnt] = fa + 1;
	for(int i = h[u]; i != -1; i = ne[i])
	{
    
    
		int j = e[i];
		if(start[j]) continue;
		dfs(j, fa + 1);
		order[++cnt] = u;
		depth[cnt] = fa + 1;
	}
}

void st_init()
{
    
    
	for(int i = 1; i <= cnt; i ++)
	{
    
    
		st[i][0] = i;
	}
	int a, b;
	for(int j = 1; j <= lg[cnt]; j ++)
	{
    
    
		for(int i = 1; i + (1 << j) - 1 <= cnt; i ++)
		{
    
    
			a = st[i][j-1];
			b = st[i+(1<<(j-1))][j-1];
			if(depth[a] < depth[b])
			st[i][j] = a;
			else
			st[i][j] = b;
		}
	}
}

void add(int a, int b)
{
    
    
	e[idx] = b;
	ne[idx] = h[a];
	h[a] =  idx ++;
}

int main(){
    
    
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	memset(h, -1, sizeof(h));
	cin >> n >> m >> s;
	int x, y;
	for(int i = 0; i < n-1; i ++)
	{
    
    
		cin >> x >> y;
		add(x, y);
		add(y, x);
	}
	dfs(s, 0);
	lg[0] = -1;//初始化对数
	for(int i = 1; i <= cnt; i ++)
	{
    
    
		lg[i] = lg[i>>1] + 1;
	}
	st_init();
	while(m --)
	{
    
    
		cin >> x >> y;
		x = start[x];
		y = start[y];
		if(x > y) swap(x, y);
		int k = (y - x) + 1;
		k = lg[k];
		int a, b;
		a = st[x][k];
		b = st[y - (1 << k) + 1][k];
		if(depth[a] < depth[b])
		{
    
    
			cout << order[a] << endl;
		}
		else
		{
    
    
			cout << order[b] << endl;
		}
	}
	//4 1 5 1 3 1 4 2 4
	//1 2 3 2 3 2 1 2 1
	//2 8 5 1 3
	return 0;
}