Blog of RuSun

\begin {array}{c} \mathfrak {One Problem Is Difficult} \\\\ \mathfrak {Because You Don't Know} \\\\ \mathfrak {Why It Is Diffucult} \end {array}

CF813F Bipartite Checking

LuoGu: CF813F Bipartite Checking

CF: F. Bipartite Checking

线段树分治板子题。

将询问离线,对询问建线段树,在线段树上记录该点范围内要加的边。在线段树上遍历,在每个节点加边,回溯时撤销操作。判断二分图可以用扩展域并查集,这里要可撤销,所以要按秩合并。

查看代码
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#include <cstdio>
#include <map>
#include <vector>
#define fi first
#define se second
#define mp make_pair
using namespace std;
template <class Type>
void read(Type &x)
{
char c;
bool flag = false;
while ((c = getchar()) < '0' || c > '9')
c == '-' && (flag = true);
x = c - '0';
while ((c = getchar()) >= '0' && c <= '9')
x = (x << 3) + (x << 1) + c - '0';
if (flag) x = ~x + 1;
}
template <class Type, class ...rest>
void read(Type &x, rest &...y) { read(x), read(y...); }
template <class Type>
void write(Type x)
{
if (x < 0) putchar('-'), x = ~x + 1;
if (x > 9) write(x / 10);
putchar(x % 10 + '0');
}
typedef pair <int, int> PII;
typedef pair <int, bool> PIB;
const int N = 1e5 + 10;
vector <PIB> stk;
map <PII, int> pre;
int n, m, q, p[N << 1], d[N << 1];
struct Edge { int u, v; } e[N];
struct Node
{
int l, r;
vector <int> v;
} tr[N << 2];
void build (int l = 1, int r = q, int x = 1)
{
tr[x].l = l, tr[x].r = r;
if (l == r) return;
int mid = l + r >> 1;
build(l, mid, x << 1), build(mid + 1, r, x << 1 | 1);
}
void modify (int l, int r, int t, int x = 1)
{
if (tr[x].l >= l && tr[x].r <= r)
return tr[x].v.push_back(t);
int mid = tr[x].l + tr[x].r >> 1;
if (l <= mid) modify(l, r, t, x << 1);
if (r > mid) modify(l, r, t, x << 1 | 1);
}
int fa (int x)
{
while (x ^ p[x]) x = p[x];
return x;
}
void merge (int x, int y)
{
if (x == y) return;
if (d[x] > d[y]) swap(x, y);
stk.push_back(mp(x, d[x] == d[y]));
p[x] = y, d[y] += d[x] == d[y];
}
void dfs (int x = 1)
{
auto t = stk.size();
bool flag = true;
for (int i : tr[x].v)
{
if (!(flag &= fa(e[i].u) != fa(e[i].v))) break;
merge(fa(e[i].u + n), fa(e[i].v));
merge(fa(e[i].v + n), fa(e[i].u));
}
if (flag)
{
if (tr[x].l == tr[x].r) puts("YES");
else dfs(x << 1), dfs(x << 1 | 1);
}
else
for (int i = tr[x].l; i <= tr[x].r; ++i) puts("NO");
for (; stk.size() > t; stk.pop_back())
{
int k = stk.back().fi;
d[p[k]] -= stk.back().se, p[k] = k;
}
}
int main ()
{
read(n, q);
build();
for (int i = 1; i <= q; ++i)
{
read(e[i].u, e[i].v);
if (e[i].u > e[i].v) swap(e[i].u, e[i].v);
PII t = mp(e[i].u, e[i].v);
if (pre.count(mp(e[i].u, e[i].v)))
{
modify(pre[t], i - 1, i);
pre.erase(t);
}
else
pre[t] = i;
}
for (auto i : pre) modify(i.se, q, i.se);
for (int i = 1; i <= n << 1; ++i) p[i] = i;
dfs();
return 0;
}