再也不作死写FhqTreap作内层树了，卡的不如暴力呜呜呜……
题意翻译：给一个序列，每个下标包含两个属性$a$和$v$，求第一个属性与下标形成的所有逆序对的第二个属性和，给出$m$个交换两个下标的操作，每次操作之后查询。
考虑一下交换之后会发生什么：
假设这次要交换$x$和$y$，使$x \leq y$。
发现交换之后$x, y$和$x$的左边的数和$y$右边的数构成的逆序对产生的贡献不变，发生变化的是中间的数。
那么问题就简单了，只要先消去中间的数和$x, y$的贡献，具体来说就是$[x + 1, y - 1]$这个区间中$a_{i}$比$a_{x}$小的$b_{i}$和，以及$a_{i}$比$a_{y}$大的$b_{i}$和。
发现$(x, y)$可能也会构成一个逆序对，拎出来判一下可以保证这一对只被计算一次。
然后算一下交换之后产生的贡献，方法类似。
树套树维护即可。
时间复杂度$O(nlog^{2}n)$。
Code：
#include <cstdio>
#include <cstring>
using namespace std;
typedef long long ll; const int N = 5e4 + ;
const int M = 2e7 + ;
const ll P = 1e9 + ; int n, m, a[N];
ll v[N], ans = 0LL; template <typename T>
inline void read(T &X) {
X = ; char ch = ; T op = ;
for(; ch > '' || ch < ''; ch = getchar())
if(ch == '-') op = -;
for(; ch >= '' && ch <= ''; ch = getchar())
X = (X << ) + (X << ) + ch - ;
X *= op;
} template <typename T>
inline void swap(T &x, T &y) {
T t = x; x = y; y = t;
} namespace BinaryIndexTree {
int cnt[N]; ll s[N]; #define lowbit(x) (x & (-x)) inline void modifyS(int p, ll val) {
for(; p <= n; p += lowbit(p)) s[p] = (s[p] + val) % P;
} inline void modifyC(int p) {
for(; p <= n; p += lowbit(p)) cnt[p]++;
} inline ll getSum(int p) {
ll res = ;
for(; p > ; p -= lowbit(p)) res = (res + s[p]) % P;
return res;
} inline int getCnt(int p) {
int res = ;
for(; p > ; p -= lowbit(p)) res += cnt[p];
return res;
} #undef lowbit } using namespace BinaryIndexTree; namespace Tree {
int nodeCnt, root[N * ];
struct Node {
int lc, rc, siz;
ll sum;
} s[M]; #define mid ((l + r) >> 1) inline void up(int p) {
if(!p) return;
s[p].siz = s[s[p].lc].siz + s[s[p].rc].siz;
s[p].sum = (s[s[p].lc].sum + s[s[p].rc].sum) % P;
} void modify(int &p, int l, int r, int x, ll selV) {
if(!p) p = ++nodeCnt;
if(l == r) {
s[p].siz = (selV != -);
s[p].sum = (selV == - ? : selV % P);
return;
} if(x <= mid) modify(s[p].lc, l, mid, x, selV);
else modify(s[p].rc, mid + , r, x, selV);
up(p);
} ll query(int p, int l, int r, int x, int y, ll selV) {
if(!p) return 0LL;
if(x <= l && y >= r) return (selV * s[p].siz % P + s[p].sum) % P; ll res = 0LL;
if(x <= mid) res = (res + query(s[p].lc, l, mid, x, y, selV)) % P;
if(y > mid) res = (res + query(s[p].rc, mid + , r, x, y, selV)) % P;
return res;
} #define lowbit(p) (p & (-p)) inline void change(int p, int val, ll selV) {
for(; p <= n; p += lowbit(p))
modify(root[p], , n, val, selV);
} inline void clear(int p, int val) {
for(; p <= n; p += lowbit(p))
modify(root[p], , n, val, -);
} inline ll ask(int p, int v, ll selV, int type) {
ll res = 0LL;
for(; p > ; p -= lowbit(p)) {
if(type) res = (res + query(root[p], , n, v + , n, selV)) % P;
else res = (res + query(root[p], , n, , v - , selV)) % P;
}
return res;
} inline ll qSum(int l, int r, int v, ll selV, int type) {
return (ask(r, v, selV, type) - ask(l - , v, selV, type) + P) % P;
} } using namespace Tree; int main() {
read(n), read(m);
nodeCnt = ;
for(int i = ; i <= n; i++) {
read(a[i]), read(v[i]);
ans = (ans + (getSum(n) - getSum(a[i]) + P) % P + P + v[i] * (getCnt(n) - getCnt(a[i])) % P + P) % P;
modifyS(a[i], v[i]), modifyC(a[i]);
change(i, a[i], v[i]);
} for(int x, y; m--; ) {
read(x), read(y);
if(x == y) {
printf("%lld\n", ans);
continue;
}
if(x > y) swap(x, y); ll res = 0LL;
if(x + <= y - ) {
res = (res + qSum(x + , y - , a[y], v[y], )) % P;
res = (res + qSum(x + , y - , a[x], v[x], )) % P;
}
if(a[y] < a[x]) res = ((res + v[x]) % P + v[y]) % P; ans = (ans - res + P) % P; res = 0LL;
if(x + <= y - ) {
res = (res + qSum(x + , y - , a[y], v[y], )) % P;
res = (res + qSum(x + , y - , a[x], v[x], )) % P;
} if(a[y] > a[x]) res = ((res + v[x]) % P + v[y]) % P;
ans = (ans + res) % P; printf("%lld\n", ans); clear(x, a[x]), clear(y, a[y]);
change(x, a[y], v[y]), change(y, a[x], v[x]);
swap(a[x], a[y]), swap(v[x], v[y]);
} return ;
}
树状数组套线段树（100 pts）
// luogu-judger-enable-o2
#include <cstdio>
#include <cstring>
#include <cstdlib>
using namespace std;
typedef long long ll; const int N = 5e4 + ;
const int M = 2e7 + ;
const ll P = 1e9 + ; int n, m, a[N];
ll v[N], ans = ; namespace FhqTreap {
int root[M], nodeCnt, ch[M][], pri[M], siz[M];
ll key[M], sum[M], sel[M]; #define lc ch[p][0]
#define rc ch[p][1] inline void up(int p) {
if(p) {
siz[p] = siz[lc] + siz[rc] + ;
sum[p] = (sum[lc] % P + sum[rc] % P + sel[p] % P) % P;
}
} inline int newnode(ll val, ll selV) {
++nodeCnt;
key[nodeCnt] = val, sum[nodeCnt] = sel[nodeCnt] = selV;
pri[nodeCnt] = rand(), siz[nodeCnt] = ;
return nodeCnt;
} void split(int p, ll val, int &x, int &y) {
if(!p) x = y = ;
else {
if(val >= key[p])
x = p, split(rc, val, rc, y);
else
y = p, split(lc, val, x, lc);
up(p);
}
} int merge(int x, int y) {
if(!x || !y) return x + y;
else {
if(pri[x] < pri[y]) {
ch[x][] = merge(ch[x][], y);
up(x);
return x;
} else {
ch[y][] = merge(x, ch[y][]);
up(y);
return y;
}
}
} inline void insert(int rt, ll val, ll selV) {
if(!root[rt]) {
root[rt] = newnode(val, selV);
return;
}
int x, y;
split(root[rt], val, x, y);
root[rt] = merge(x, merge(newnode(val, selV), y));
} inline void remove(int rt, ll val) {
int x, y, z;
split(root[rt], val, x, y);
split(x, val - , x, z);
z = merge(ch[z][], ch[z][]);
root[rt] = merge(merge(x, z), y);
} inline ll ask(int rt, ll val, ll selV, int type) {
int x, y; ll res;
if(type) {
split(root[rt], val, x, y);
res = (selV * siz[x] % P + sum[x]) % P;
} else {
split(root[rt], val, x, y);
res = (selV * siz[y] % P + sum[y]) % P;
}
root[rt] = merge(x, y);
return res % P;
} void Pi(int p, int *arr) {
if(lc) Pi(lc, arr);
printf("%d ", arr[p]);
if(rc) Pi(rc, arr);
} #undef lc
#undef rc
}; namespace SegT {
using namespace FhqTreap; #define lc p << 1
#define rc p << 1 | 1
#define mid ((l + r) >> 1) void ins(int p, int l, int r, int x, ll val, ll selV) {
insert(p, val, selV);
if(l == r) return;
if(x <= mid) ins(lc, l, mid, x, val, selV);
else ins(rc, mid + , r, x, val, selV);
} void del(int p, int l, int r, int x, ll val) {
remove(p, val);
if(l == r) return;
if(x <= mid) del(lc, l, mid, x, val);
else del(rc, mid + , r, x, val);
} ll query(int p, int l, int r, int x, int y, ll val, ll selV, int type) {
if(x <= l && y >= r) return ask(p, val, selV, type) % P; ll res = ;
if(x <= mid) res = (res + query(lc, l, mid, x, y, val, selV, type)) % P;
if(y > mid) res = (res + query(rc, mid + , r, x, y, val, selV, type)) % P;
return res;
} void print(int p, int l, int r, int *arr) {
Pi(root[p], arr), printf("\n");
if(l == r) return;
print(lc, l, mid, arr), print(rc, mid + , r, arr);
} } using namespace SegT; template <typename T>
inline void swap(T &x, T &y) {
T t = x;
x = y;
y = t;
} namespace IOstream{
const int L = << ; char buffer[L], *S, *T; inline char Getchar() {
if(S == T) {
T = (S = buffer) + fread(buffer, , L, stdin);
if(S == T) return EOF;
}
return *S++;
} template <class T>
inline void read(T &X) {
char ch; T op = ;
for(ch = Getchar(); ch > '' || ch < ''; ch = Getchar())
if(ch == '-') op = -;
for(X = ; ch >= '' && ch <= ''; ch = Getchar())
X = (X << ) + (X << ) + ch - '';
X *= op;
} template <typename T>
inline void write(T x)
{
T sta[]; int len = ;
if(x < ) putchar('-'), x = -x;
if(x == ) {
putchar('');
return;
}
for(; x > ; sta[++len] = x % , x /= );
for(int i = len; i >= ; i--) putchar(sta[i] + '');
} } using namespace IOstream; namespace BinaryIndexTree {
int cnt[N]; ll s[N]; #define lowbit(x) (x & (-x)) inline void modifyS(int p, ll val) {
for(; p <= n; p += lowbit(p)) s[p] = (s[p] + val) % P;
} inline void modifyC(int p) {
for(; p <= n; p += lowbit(p)) cnt[p]++;
} inline ll getSum(int p) {
ll res = ;
for(; p > ; p -= lowbit(p)) res = (res + s[p]) % P;
return res;
} inline int getCnt(int p) {
int res = ;
for(; p > ; p -= lowbit(p)) res += cnt[p];
return res;
} } using namespace BinaryIndexTree; int main() {
// freopen("1.in", "r", stdin);
// freopen("mine.out", "w", stdout); // srand(19260817); read(n), read(m);
nodeCnt = ;
for(int i = ; i <= n; i++) {
read(a[i]), read(v[i]);
ans = (ans + (getSum(n) - getSum(a[i]) + P) % P + P + v[i] * (getCnt(n) - getCnt(a[i])) % P + P) % P;
modifyS(a[i], v[i]), modifyC(a[i]);
ins(, , n, i, a[i], v[i]);
} // printf("%d\n", ans); for(int x, y; m--; ) {
read(x), read(y);
if(x == y) {
printf("%lld\n", ans);
continue;
}
if(x > y) swap(x, y); ll res = ;
if(x + <= y - ) {
res = (res + query(, , n, x + , y - , a[y], v[y], )) % P;
res = (res + query(, , n, x + , y - , a[x], v[x], )) % P;
}
if(a[y] < a[x]) res = (res % P + v[x] % P + v[y] % P) % P;
ans = (ans - res + P) % P; res = ;
if(x + <= y - ) {
res = (res + query(, , n, x + , y - , a[y], v[y], )) % P;
res = (res + query(, , n, x + , y - , a[x], v[x], )) % P;
}
if(a[y] > a[x]) res = (v[y] % P + v[x] % P + res % P) % P;
ans = (ans + res) % P; write(ans), puts(""); del(, , n, x, a[x]), del(, , n, y, a[y]);
ins(, , n, y, a[x], v[x]), ins(, , n, x, a[y], v[y]);
swap(a[x], a[y]), swap(v[x], v[y]); /* print(1, 1, n, key), printf("\n");
print(1, 1, n, sel), printf("\n"); */
} return ;
}
线段树套fhqTreap (20 pts)