CSP-S 2019 简要题解
从这里开始
又考炸了，sad.....明年应该在准备高考了，考完把坑填了好了。
一半题都被卡常，qswl。[我汤姆要报警.jpg]
dfs 怎么这么慢呀，sad.....
i7 牛逼！
写的比较混乱，可以将就着看就看吧。
Day 1
Problem A
考虑求出最高位是 1 还是 0，可以推出剩下的 $n - 1$ 位二进制数在 $n - 1$ 格雷码的排名。
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; template <typename T>
boolean chkmin(T& a, T b) {
return (a > b) ? (a = b, true) : false;
}
template <typename T>
boolean chkmax(T& a, T b) {
return (a < b) ? (a = b, true) : false;
} #define forv(_i, _vec) for (vector<int>::iterator (_i) = (_vec).begin(); (_i) != (_vec).end(); (_i)++) #define ull unsigned long long int n;
ull k; char ans[70]; int main() {
freopen("code.in", "r", stdin);
freopen("code.out", "w", stdout);
scanf("%d%llu", &n, &k);
for (int i = n; i; i--) {
ull k0 = 1ull << (i - 1);
if (k >= k0) {
k -= k0;
k = k0 - k - 1;
ans[i] = '1';
} else {
ans[i] = '0';
}
}
reverse(ans + 1, ans + n + 1);
puts(ans + 1);
return 0;
}
Problem B
考虑计算以每个位置结尾的串的个数。
把左括号看做 1，右括号看做 0，考虑充要条件是前缀和大于等于 0 且最终和为 0。
单调栈维护一下即可。
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; template <typename T>
boolean chkmin(T& a, T b) {
return (a > b) ? (a = b, true) : false;
}
template <typename T>
boolean chkmax(T& a, T b) {
return (a < b) ? (a = b, true) : false;
} #define forv(_i, _vec) for (vector<int>::iterator (_i) = (_vec).begin(); (_i) != (_vec).end(); (_i)++) typedef class Input {
public: } Input; Input& operator >> (Input& in, int& u) {
char x;
int flag = 1;
while (~(x = getchar()) && (x != '-') && !(x >= '0' && x <= '9'));
if (x == '-') {
flag = -1;
x = getchar();
}
for (u = x - '0'; ~(x = getchar()) && (x >= '0' && x <= '9'); u = u * 10+ x - '0');
u *= flag;
return in;
} Input in; #define ull unsigned long long const int N = 500005; typedef class Data {
public:
int s, c; Data() { }
Data(int s, int c) : s(s), c(c) { }
} Data; int n;
char s[N];
int sum[N];
ull g[N];
vector<int> G[N]; int tp;
Data stk[N];
void dfs(int p, int fa) {
sum[p] = sum[fa] + ((s[p] == '(') ? (1) : (-1));
int oldtp = tp;
while (tp > 1 && sum[p] < stk[tp].s)
tp--;
Data oldv;
if (stk[tp].s == sum[p]) {
oldv = stk[tp];
stk[tp].c++;
} else {
oldv = stk[tp + 1];
stk[++tp] = Data(sum[p], 1);
}
g[p] = g[fa] + stk[tp].c - 1;
// cerr << p << " " << g[p] << '\n';
forv (e, G[p]) {
dfs(*e, p);
}
stk[tp] = oldv;
tp = oldtp;
} int main() {
freopen("brackets.in", "r", stdin);
freopen("brackets.out", "w", stdout);
in >> n;
scanf("%s", s + 1);
for (int i = 2, x; i <= n; i++) {
in >> x;
G[x].push_back(i);
}
stk[tp = 1] = Data(0, 1);
dfs(1, 0);
ull ans = 0;
for (int i = 1; i <= n; i++) {
ans = ans ^ (1ull * i * g[i]);
}
printf("%llu\n", ans);
// cerr << 1.0 * clock() / CLOCKS_PER_SEC << "s";
return 0;
}
Problem C
这题都没当场过。sad.....
不知道为啥之前的做法这么复杂，看起好像绕了一个弯路。好像考虑一下菊花的情况这题就好想多了。
考虑一下一个足够强的一次交换能实现的必要条件，然后猜它是充要的那个并查集维护就没了。我应该是智障。
考虑字典序贪心。
考虑寻找一个判断是否合法的条件，考虑这样一个条件：设第 $i$ 个点上的标号最终被换到了 $p_i$，那么合法当且仅当所有 $i \rightarrow p_i$ 的路径没有交（不在边相交，一条边两个方向认为是不同边），并且每条边的正反分别被经过了 1 次。并且置换 $p$ 恰好只有 1 个环。
证明待填。
-->
当 $n = 1$ 的时候，直接输出答案就行了。
假设点 $i$ 最终要到 $p_i$，那么在树上加入一条有向路径 $i \rightarrow p_i$。
考虑每次寻找最小的合法的点，问题变成怎么判断能否加入一条路径 $i \rightarrow p_i$。
首先不难注意到任意一条边在同一方向会被经过恰好 1 次，以及当 $n > 1$ 的时候 $p_i \neq i$。
考虑进入点 $x$ 和离开点 $x$ 的路径最终大概形如：
可以发现，把当前点看成它的一个子树，那么每条路径将恰好从它的一个子树到另外一个子树。考虑把原来判断合法的变成这样一个条件：合法当且仅当每个点的所有子树恰好形成 1 个环，并且任意两条路径都没有边的相交（指同一方向）。
考虑必要性
- 不难发现周围几条边的操作顺序是唯一的，因为每次只可能操作连接 $x$ 和 $p_x$ 所在子树根的边。如果存在超过 1 个环，那么一定无解，
- 第二点比较显然。
考虑充分性，当只有 1 个点的时候显然成立。
当 $n > 1$ 的时候，考虑每次操作一条边$(x, y)$，满足 $p_x$ 在以 $x$ 为根，$y$ 的子树内，$p_y$ 在以 $y$ 为根，$x$ 的子树内。
首先证明这样一条边一定存在，考虑任取一个点 $x$，设它的 $p_x$ 在 $y$ 的子树内，如果 $(x, y)$ 不满足条件，那么我们删掉这条边（不是题目中的删除操作），令 $x' = y$。因为树是有限的，所以这一过程是有限的，所以一定会停止。
考虑找到这一条边后，操作它，不难证明新得到的两棵树仍然满足上述条件或大小等于 1。
然后用并查集判一下就好了。
时间复杂度 $O(Tn^2)$。
Code
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; const int N = 2005; typedef class Edge {
public:
int ed, nx; Edge() { }
Edge(int ed, int nx) : ed(ed), nx(nx) { }
} Edge; typedef class MapManager {
public:
int h[N];
vector<Edge> E; void init(int n) {
memset(h, -1, sizeof(int) * (n + 1));
E.clear();
} void add_edge(int u, int v) {
E.push_back(Edge(v, h[u]));
h[u] = (signed) E.size() - 1;
}
Edge& operator [] (int p) {
return E[p];
}
} MapManager; int T, n, n2;
int deg[N];
int pos[N];
MapManager g;
int uf[N * 3];
int fa[N], fe[N];
bitset<N * 2> vise;
bitset<N> occ, vis; int find(int x) {
return uf[x] == x ? x : (uf[x] = find(uf[x]));
} void dfs(int p, int fa, int fe) {
if (!occ.test(p) && fa && (deg[p] == 1 || (find(n2 + p) ^ find(fe ^ 1))))
vis.set(p);
::fa[p] = fa, ::fe[p] = fe;
for (int i = g.h[p]; ~i; i = g[i].nx) {
int e = g[i].ed;
if (e == fa)
continue;
if (vise.test(i))
continue;
if ((deg[p] != 2 - !fa || (!occ.test(p) && deg[p] == 2)) && find(fe ^ 1) == find(i))
continue;
dfs(e, p, i);
}
} void solve() {
scanf("%d", &n);
g.init(n);
for (int i = 1; i <= n; i++) {
scanf("%d", pos + i);
}
memset(deg, 0, sizeof(int) * (n + 1));
for (int i = 1, u, v; i < n; i++) {
scanf("%d%d", &u, &v);
g.add_edge(u, v);
// cerr << u << " " << v << " " << (signed) g.E.size() - 1 << '\n';
g.add_edge(v, u);
// cerr << v << " " << u << " " << (signed) g.E.size() - 1 << '\n';
deg[u] += 2;
deg[v] += 2;
}
if (n == 1) {
printf("%d\n", 1);
return;
}
occ.reset();
vise.reset();
n2 = n << 1;
for (int i = 0; i <= (3 * n); i++)
uf[i] = i;
for (int i = 1; i <= n; i++) {
int p = pos[i];
vis.reset();
dfs(p, 0, (n2 + p) ^ 1);
// assert(vis.count());
// cerr << "# " << i << " " << p << '\n';
for (int j = 1; j <= n; j++) {
if (vis.test(j)) {
printf("%d ", j);
occ.set(j);
int x = j, e1 = n2 + j, e2;
while (x ^ p) {
deg[x] -= 2 - (e1 > n2);
e2 = fe[x];
// cerr << "Link " << e1 << " " << (e2 ^ 1) << '\n';
uf[find(e1)] = find(e2 ^ 1);
vise.set(e2);
swap(e1, e2);
x = fa[x];
}
deg[p]--;
uf[find(n2 + p)] = find(e1);
// cerr << "Link " << n2 + p << " " << (e1) << '\n';
break;
}
}
}
putchar('\n');
} int main() {
// freopen("tree.in", "r", stdin);
// freopen("tree.out", "w", stdout);
scanf("%d", &T);
while (T--) {
solve();
}
// cerr << clock() << "ms";
return 0;
}
Day 2
手速慢，脑速也慢，sad....
Problem A
枚举哪一种主食材料不合法，然后 dp 记一下选择它的数量和不选的差。
时间复杂度 $O(mn^2)$。好像有点卡常。
Code
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; template <typename T>
boolean chkmin(T& a, T b) {
return (a > b) ? (a = b, true) : false;
}
template <typename T>
boolean chkmax(T& a, T b) {
return (a < b) ? (a = b, true) : false;
} #define forv(_i, _vec) for (vector<int>::iterator (_i) = (_vec).begin(); (_i) != (_vec).end(); (_i)++) const int Mod = 998244353; #define ll long long void exgcd(int a, int b, int& x, int& y) {
if (!b) {
x = 1, y = 0;
} else {
exgcd(b, a % b, y, x);
y -= (a / b) * x;
}
} int inv(int a) {
int x, y;
exgcd(a, Mod, x, y);
return (x < 0) ? (x + Mod) : (x);
} typedef class Zi {
public:
int v; Zi() : v(0) { }
Zi(int v) : v(v) { }
Zi(ll x) : v(x % Mod) { } friend Zi operator + (Zi a, Zi b) {
return ((a.v += b.v) >= Mod) ? (a.v -= Mod) : (a);
}
friend Zi operator - (Zi a, Zi b) {
return ((a.v -= b.v) < 0) ? (a.v += Mod) : (a);
}
friend Zi operator * (Zi a, Zi b) {
return 1ll * a.v * b.v;
}
friend Zi operator ~ (Zi a) {
return inv(a.v);
}
Zi& operator += (Zi b) {
return *this = *this + b;
}
Zi& operator -= (Zi b) {
return *this = *this - b;
}
Zi& operator *= (Zi b) {
return *this = *this * b;
}
} Zi; const ll Mod2 = 3ll * Mod * Mod; const int N = 105, M = 2005; int n, m;
Zi sum[N];
Zi a[N][M];
ll f[N][250]; void fix2(ll& x) {
(x >= Mod2) && (x -= Mod2);
} int main() {
freopen("meal.in", "r", stdin);
freopen("meal.out", "w", stdout);
scanf("%d%d", &n, &m);
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= m; j++) {
scanf("%d", &a[i][j].v);
sum[i] = sum[i] + a[i][j];
}
}
Zi ans = 1;
for (int i = 1; i <= n; i++)
ans *= (sum[i] + 1);
ans = ans - 1;
// cerr << "ans: " << ans.v << '\n';
const int V = 110;
for (int b = 1; b <= m; b++) {
memset(f, 0, sizeof(f));
f[0][V] = 1;
for (int i = 1; i <= n; i++) {
ll x = a[i][b].v, y = (sum[i] - a[i][b]).v;
ll *g = f[i - 1] + V, *h = f[i] + V;
for (int j = -i + 1; j < i; j++) {
ll v = g[j];
if (v) {
fix2(h[j + 1] += v * x);
fix2(h[j - 1] += v * y);
fix2(h[j] += v);
}
}
for (int j = -i; j <= i; j++) {
if (h[j]) {
h[j] %= Mod;
}
}
}
Zi tmp = 0;
for (int i = 1; i <= n; i++)
tmp += f[n][i + V];
ans -= tmp;
}
printf("%d\n", ans.v);
// cerr << 1.0 * clock() / CLOCKS_PER_SEC << '\n';
return 0;
}
Problem B
只用考虑以每个前缀，最后一段长度最小的合法划分。
我还不会证，但它看上去很对。
设第 $i$ 个前缀最后一段的和为 $f_i$，设当前考虑的前缀为 $j$，问题相当于要找出满足 $f_i - S(i + 1, j) < 0$ 的最大的 $j$。
单调队列优化即可。
高精度 rush 成功，读入 rush 失败。
Code
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; typedef class Input {
protected:
const static int limit = 65536;
FILE* file; int ss, st;
char buf[limit];
public: Input() : file(NULL) { };
Input(FILE* file) : file(file) { } void open(FILE *file) {
this->file = file;
} void open(const char* filename) {
file = fopen(filename, "r");
} char pick() {
if (ss == st)
st = fread(buf, 1, limit, file), ss = 0;//, cerr << "str: " << buf << "ed " << st << endl;
return (ss == st) ? (-1) : (buf[ss++]);
}
} Input; #define digit(_x) ((_x) >= '0' && (_x) <= '9') Input& operator >> (Input& in, unsigned& u) {
char x;
while (~(x = in.pick()) && !digit(x));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
return in;
} Input& operator >> (Input& in, unsigned long long& u) {
char x;
while (~(x = in.pick()) && !digit(x));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
return in;
} Input& operator >> (Input& in, int& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
u *= aflag;
return in;
} Input& operator >> (Input& in, long long& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
u *= aflag;
return in;
} Input& operator >> (Input& in, double& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
if (x == '.') {
double dec = 1;
for ( ; ~(x = in.pick()) && digit(x); u = u + (dec *= 0.1) * (x - '0'));
}
u *= aflag;
return in;
} Input& operator >> (Input& in, char* str) {
char x;
while (~(x = in.pick()) && x != '\n' && x != ' ')
*(str++) = x;
*str = 0;
return in;
} Input in (stdin); typedef class Output {
protected:
const static int Limit = 65536;
char *tp, *ed;
char buf[Limit];
FILE* file;
int precision; void flush() {
fwrite(buf, 1, tp - buf, file);
fflush(file);
tp = buf;
} public: Output() { }
Output(FILE* file) : tp(buf), ed(buf + Limit), file(file), precision(6) { }
Output(const char *str) : tp(buf), ed(buf + Limit), precision(6) {
file = fopen(str, "w");
}
~Output() {
flush();
} void put(char x) {
if (tp == ed)
flush();
*(tp++) = x;
} int get_precision() {
return precision;
}
void set_percision(int x) {
precision = x;
}
} Output; Output& operator << (Output& out, int x) {
static char buf[35];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
if (x < 0)
out.put('-'), x = -x;
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, long long x) {
static char buf[36];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
if (x < 0)
out.put('-'), x = -x;
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, unsigned x) {
static char buf[35];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, char x) {
out.put(x);
return out;
} Output& operator << (Output& out, const char* str) {
for ( ; *str; out.put(*(str++)));
return out;
} Output& operator << (Output& out, double x) {
int y = x;
x -= y;
out << y << '.';
for (int i = out.get_precision(); i; i--, y = x * 10, x = x * 10 - y, out.put(y + '0'));
return out;
} Output out (stdout); #define ll long long const int Base = 1e9; typedef class BigInteger {
public:
vector<ll> a; BigInteger() : BigInteger(0) { }
BigInteger(ll x) {
if (!x) {
a.resize(1);
a[0] = 0;
} else {
while (x) {
a.push_back(x % Base);
x /= Base;
}
}
} int length() const {
return a.size();
}
void resize(int newsize) {
a.resize(newsize, 0ll);
}
void shrink() {
while (length() > 1 && !a.back())
a.pop_back();
}
ll& operator [] (int p) {
return a[p];
}
ll at(int p) const {
return a[p];
} friend BigInteger operator + (BigInteger a, BigInteger b) {
BigInteger rt;
int n = max(a.length(), b.length()) + 1;
rt.resize(n);
a.resize(n);
b.resize(n);
for (int i = 0; i < n - 1; i++) {
rt[i] += a[i] + b[i];
rt[i + 1] += rt[i] / Base;
rt[i] %= Base;
}
rt.shrink();
return rt;
}
friend BigInteger operator * (BigInteger a, BigInteger b) {
BigInteger rt;
int n = a.length() + b.length();
rt.resize(n);
for (int i = 0; i < a.length(); i++) {
for (int j = 0; j < b.length(); j++) {
rt[i + j] += a[i] * b[j];
rt[i + j + 1] += rt[i + j] / Base;
rt[i + j] %= Base;
}
}
rt.shrink();
return rt;
} friend Output& operator << (Output& out, const BigInteger& x) {
static char buf[14];
out << x.a.back();
signed int n = x.length();
for (int i = n - 2; i >= 0; i--) {
char* top = buf + 12;
ll tmp = x.at(i);
*top = 0;
for (int j = 0; j < 9; j++) {
*(--top) = '0' + tmp % 10;
tmp /= 10;
}
out << top;
}
return out;
}
} BigInteger; #define uint unsigned int int n;
ll *s;
int *a, *g, *Q; ll S(int l, int r) {
return (!l) ? (s[r]) : (s[r] - s[l - 1]);
} int main() {
int op;
in >> n >> op;
a = new int[(n + 1)]; if (op == 0) {
for (int i = 1; i <= n; i++) {
in >> a[i];
}
} else {
uint x, y, z;
uint *b = new uint[(n + 1)];
int m;
in >> x >> y >> z >> b[1] >> b[2] >> m;
int *p = new int[(m + 1)];
int *l = new int[(n + 1)];
int *r = new int[(n + 1)];
for (int i = 1; i <= m; i++) {
in >> p[i] >> l[i] >> r[i];
}
uint msk = (1u << 30) - 1;
for (int i = 3; i <= n; i++) {
b[i] = (x * b[i - 1] + y * b[i - 2] + z) & msk;
}
for (int i = 1, j = 1; i <= n; i++) {
if (i > p[j])
j++;
a[i] = b[i] % (r[j] - l[j] + 1) + l[j];
}
delete[] p;
delete[] l;
delete[] r;
delete[] b;
} g = new int[(n + 1)];
s = new ll[(n + 1)];
Q = new int[(n + 10)];
s[0] = 0;
for (int i = 1; i <= n; i++) {
s[i] = s[i - 1] + a[i];
}
int st = 1, ed = 1;
Q[1] = 0, g[0] = 0;
for (int i = 1; i <= n; i++) {
while (st < ed && S(g[Q[st + 1]], Q[st + 1]) <= S(Q[st + 1] + 1, i))
st++;
g[i] = Q[st] + 1;
while (st <= ed && S(g[Q[ed]], Q[ed]) - S(Q[ed] + 1, i) >= S(g[i], i))
ed--;
Q[++ed] = i;
}
BigInteger ans (0);
for (int i = n; i; i = g[i] - 1) {
ans = ans + BigInteger(S(g[i], i)) * S(g[i], i);
}
out << ans << '\n';
return 0;
}
Problem C
先讲一下 $O(n\log n)$ 的垃圾做法：
考虑计算每个点作为中心的答案。
考虑以任意一个重心为根，重心的答案可以暴力计算，对于剩下的点必须删掉重心所在的子树中的一条边。
讨论一下这条边是在这个点到根的路径，还是其他地方。然后设删掉的边较浅一端的大小为 $x$，之后就是一个傻逼二维数点问题。树状数组维护即可。
有线性做法，我先咕着。
下面是线性做法，虽然我的线性做法比较垃圾，不开 O2 常数被吊锤。
考虑树链剖分，设根所在的重链为 $L$，如果一个点 $p$ 不在 $L$ 上，那么如果 $p$ 要成为重心，那么删掉的边必须满足下面任意条件之一，设删掉的边中较低端点为 $x$
- $x$ 是 $p$ 的祖先，并且 $x$ 和 $p$ 在同一条重链上。
- 设 $y$ 是 $p$ 的祖先中第一个在 $L$ 的点，$x$ 是 $y$ 或者 $x$ 在 $y$ 的重子树内。
对于 $L$ 上计算答案，注意到查询左端点或右端点是单调的，简单维护一下可以做到 $O(n)$。
计算不在 $L$ 上的点的第一部分答案类似，不难做到和链长线性相关的复杂度。
然后考虑计算第二部分的答案，考虑按 $L$ 上从深到浅扫描线，注意到查询总是在轻子树内，注意到查询涉及到最大的 $n - 2sz$ 中的 $sz$ 是最大轻子树的大小。考虑暴力预处理这一部分的后缀和，然后再计算轻子树内的点的答案。因为 $L$ 上每个点的轻子树不会相交，所以预处理总复杂度为 $O(n)$。
所以总复杂度 $O(n)$。
（第一份是带 log 的做法，第二份是线性）
Code1
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; typedef class Input {
protected:
const static int limit = 65536;
FILE* file; int ss, st;
char buf[limit];
public: Input() : file(NULL) { };
Input(FILE* file) : file(file) { } void open(FILE *file) {
this->file = file;
} void open(const char* filename) {
file = fopen(filename, "r");
} char pick() {
if (ss == st)
st = fread(buf, 1, limit, file), ss = 0;//, cerr << "str: " << buf << "ed " << st << endl;
return (ss == st) ? (-1) : (buf[ss++]);
}
} Input; #define digit(_x) ((_x) >= '0' && (_x) <= '9') Input& operator >> (Input& in, unsigned& u) {
char x;
while (~(x = in.pick()) && !digit(x));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
return in;
} Input& operator >> (Input& in, unsigned long long& u) {
char x;
while (~(x = in.pick()) && !digit(x));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
return in;
} Input& operator >> (Input& in, int& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
u *= aflag;
return in;
} Input& operator >> (Input& in, long long& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
u *= aflag;
return in;
} Input& operator >> (Input& in, double& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
if (x == '.') {
double dec = 1;
for ( ; ~(x = in.pick()) && digit(x); u = u + (dec *= 0.1) * (x - '0'));
}
u *= aflag;
return in;
} Input& operator >> (Input& in, char* str) {
char x;
while (~(x = in.pick()) && x != '\n' && x != ' ')
*(str++) = x;
*str = 0;
return in;
} Input in (stdin); typedef class Output {
protected:
const static int Limit = 65536;
char *tp, *ed;
char buf[Limit];
FILE* file;
int precision; void flush() {
fwrite(buf, 1, tp - buf, file);
fflush(file);
tp = buf;
} public: Output() { }
Output(FILE* file) : tp(buf), ed(buf + Limit), file(file), precision(6) { }
Output(const char *str) : tp(buf), ed(buf + Limit), precision(6) {
file = fopen(str, "w");
}
~Output() {
flush();
} void put(char x) {
if (tp == ed)
flush();
*(tp++) = x;
} int get_precision() {
return precision;
}
void set_percision(int x) {
precision = x;
}
} Output; Output& operator << (Output& out, int x) {
static char buf[35];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
if (x < 0)
out.put('-'), x = -x;
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, long long x) {
static char buf[36];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
if (x < 0)
out.put('-'), x = -x;
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, unsigned x) {
static char buf[35];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, char x) {
out.put(x);
return out;
} Output& operator << (Output& out, const char* str) {
for ( ; *str; out.put(*(str++)));
return out;
} Output& operator << (Output& out, double x) {
int y = x;
x -= y;
out << y << '.';
for (int i = out.get_precision(); i; i--, y = x * 10, x = x * 10 - y, out.put(y + '0'));
return out;
} Output out (stdout); const int N = 3e5 + 5; typedef class Fenwick {
public:
int n;
int a[N]; void init(int n) {
this->n = n;
memset(a, 0, sizeof(int) * (n + 1));
}
void add(int idx, int val) {
for ( ; idx <= n; idx += (idx & (-idx)))
a[idx] += val;
}
int query(int idx) {
int rt = 0;
for ( ; idx; idx -= (idx & (-idx)))
rt += a[idx];
return rt;
}
int query(int l, int r) {
if (l > r)
return 0;
return query(r) - query(l - 1);
}
} Fenwick; #define forv(_i, _v) for (vector<int>::iterator _i = (_v).begin(); (_i) != (_v).end(); (_i)++) #define ll long long int T, n, g;
int sz[N];
Fenwick fen;
vector<int> G[N]; int get_sz(int p, int fa) {
sz[p] = 1;
forv (e, G[p]) {
if (*e ^ fa) {
get_sz(*e, p);
sz[p] += sz[*e];
}
}
return sz[p];
}
int get_centroid(int p, int fa) {
forv (e, G[p]) {
if ((*e ^ fa) && sz[*e] > (n >> 1)) {
return get_centroid(*e, p);
}
}
return p;
} int cnt[N], mxsz[N];
void dfs1(int p, int fa) {
mxsz[p] = 0;
forv (e, G[p]) {
if (*e ^ fa) {
mxsz[p] = max(mxsz[p], sz[*e]);
}
}
int L = max(1, 2 * (n - sz[p]) - n);
int R = n - 2 * mxsz[p];
cnt[p] += fen.query(L, R);
fen.add(sz[p], -1);
L = max(2 * mxsz[p], 1);
R = min(2 * sz[p], n - 1);
cnt[p] -= fen.query(L, R);
forv (e, G[p]) {
if (*e ^ fa) {
dfs1(*e, p);
}
}
fen.add(sz[p], 1);
} void dfs2(int p, int fa) {
int L = max(1, 2 * (n - sz[p]) - n);
int R = n - 2 * mxsz[p];
cnt[p] += fen.query(L, R);
fen.add(sz[p], 1);
forv (e, G[p]) {
if (*e ^ fa) {
dfs2(*e, p);
}
}
cnt[p] -= fen.query(L, R);
} void calc(int p, int fa, int szcur, int szmx) {
int lim = ((n - sz[p]) >> 1);
cnt[g] += (szcur - sz[p] <= lim && szmx <= lim);
forv (e, G[p]) {
if (*e ^ fa) {
calc(*e, p, szcur, szmx);
}
}
} int tmp[N];
void solve() {
in >> n;
for (int i = 1; i <= n; i++)
G[i].clear();
for (int i = 1, u, v; i < n; i++) {
in >> u >> v;
G[u].push_back(v);
G[v].push_back(u);
}
get_sz(1, 0);
g = get_centroid(1, 0);
get_sz(g, 0);
memset(cnt, 0, sizeof(int) * (n + 1)); // cerr << "centroid: " << g << '\n'; // part1
fen.init(n);
// for (int i = 1; i <= n; i++)
// fen.add(sz[i], 1);
dfs1(g, 0);
memset(tmp, 0, sizeof(int) * (n + 1));
for (int i = 1; i <= n; i++)
tmp[sz[i]]++;
for (int i = 1; i <= n; i++)
tmp[i] += tmp[i - 1];
for (int p = 1; p <= n; p++) {
int L = max(1, 2 * (n - sz[p]) - n);
int R = n - 2 * mxsz[p];
if (L <= R) {
cnt[p] += tmp[R] - tmp[L - 1];
}
} // part2
fen.init(n);
dfs2(g, 0);
// for (int i = 1; i <= n; i++) {
// cerr << cnt[i] << " ";
// }
// cerr << '\n'; // part4
cnt[g] = 0;
int mx = 0, id = -1, sc = 0;
forv (p, G[g]) {
if (sz[*p] > mx) {
swap(mx, sc);
mx = sz[*p];
id = *p;
} else if (sz[*p] > sc) {
sc = sz[*p];
}
}
forv (p, G[g]) {
if (*p == id) {
calc(*p, g, mx, sc);
} else {
calc(*p, g, sz[*p], mx);
}
} ll ans = 0;
for (int i = 1; i <= n; i++) {
ans += 1ll * i * cnt[i];
// cerr << cnt[i] << " ";
}
// cerr << '\n';
out << ans << '\n';
} int main() {
in >> T;
while (T--) {
solve();
}
return 0;
}
Code2
#include <bits/stdc++.h>
using namespace std;
typedef bool boolean; typedef class Input {
protected:
const static int limit = 65536;
FILE* file; int ss, st;
char buf[limit];
public: Input() : file(NULL) { };
Input(FILE* file) : file(file) { } void open(FILE *file) {
this->file = file;
} void open(const char* filename) {
file = fopen(filename, "r");
} char pick() {
if (ss == st)
st = fread(buf, 1, limit, file), ss = 0;//, cerr << "str: " << buf << "ed " << st << endl;
return (ss == st) ? (-1) : (buf[ss++]);
}
} Input; #define digit(_x) ((_x) >= '0' && (_x) <= '9') Input& operator >> (Input& in, unsigned& u) {
char x;
while (~(x = in.pick()) && !digit(x));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
return in;
} Input& operator >> (Input& in, unsigned long long& u) {
char x;
while (~(x = in.pick()) && !digit(x));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
return in;
} Input& operator >> (Input& in, int& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
u *= aflag;
return in;
} Input& operator >> (Input& in, long long& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
u *= aflag;
return in;
} Input& operator >> (Input& in, double& u) {
char x;
while (~(x = in.pick()) && !digit(x) && x != '-');
int aflag = ((x == '-') ? (x = in.pick(), -1) : (1));
for (u = x - '0'; ~(x = in.pick()) && digit(x); u = u * 10 + x - '0');
if (x == '.') {
double dec = 1;
for ( ; ~(x = in.pick()) && digit(x); u = u + (dec *= 0.1) * (x - '0'));
}
u *= aflag;
return in;
} Input& operator >> (Input& in, char* str) {
char x;
while (~(x = in.pick()) && x != '\n' && x != ' ')
*(str++) = x;
*str = 0;
return in;
} Input in (stdin); typedef class Output {
protected:
const static int Limit = 65536;
char *tp, *ed;
char buf[Limit];
FILE* file;
int precision; void flush() {
fwrite(buf, 1, tp - buf, file);
fflush(file);
tp = buf;
} public: Output() { }
Output(FILE* file) : tp(buf), ed(buf + Limit), file(file), precision(6) { }
Output(const char *str) : tp(buf), ed(buf + Limit), precision(6) {
file = fopen(str, "w");
}
~Output() {
flush();
} void put(char x) {
if (tp == ed)
flush();
*(tp++) = x;
} int get_precision() {
return precision;
}
void set_percision(int x) {
precision = x;
}
} Output; Output& operator << (Output& out, int x) {
static char buf[35];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
if (x < 0)
out.put('-'), x = -x;
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, long long x) {
static char buf[36];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
if (x < 0)
out.put('-'), x = -x;
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, unsigned x) {
static char buf[35];
static char * const lim = buf + 34;
if (!x)
out.put('0');
else {
char *tp = lim;
for ( ; x; *(--tp) = x % 10, x /= 10);
for ( ; tp != lim; out.put(*(tp++) + '0'));
}
return out;
} Output& operator << (Output& out, char x) {
out.put(x);
return out;
} Output& operator << (Output& out, const char* str) {
for ( ; *str; out.put(*(str++)));
return out;
} Output& operator << (Output& out, double x) {
int y = x;
x -= y;
out << y << '.';
for (int i = out.get_precision(); i; i--, y = x * 10, x = x * 10 - y, out.put(y + '0'));
return out;
} Output out (stdout); const int N = 3e5 + 5; typedef class Event {
public:
int p, x, v; Event() { }
Event(int p, int x, int v) : p(p), x(x), v(v) { }
} Event; #define forv(_i, _v) for (vector<int>::iterator _i = (_v).begin(); (_i) != (_v).end(); (_i)++) #define ll long long int T, n, g;
int sz[N];
int cnt[N];
vector<int> G[N]; int get_sz(int p, int fa) {
sz[p] = 1;
forv (e, G[p]) {
if (*e ^ fa) {
get_sz(*e, p);
sz[p] += sz[*e];
}
}
return sz[p];
}
int get_centroid(int p, int fa) {
forv (e, G[p]) {
if ((*e ^ fa) && sz[*e] > (n >> 1)) {
return get_centroid(*e, p);
}
}
return p;
} int zson[N];
void dfs1(int p, int fa) {
int mx = -1, &id = zson[p];
id = 0;
forv (e, G[p]) {
if (*e ^ fa) {
dfs1(*e, p);
if (sz[*e] > mx) {
mx = sz[*e];
id = *e;
}
}
}
} int tp;
int stk[N];
void work() {
reverse(stk + 1, stk + tp + 1);
stk[tp + 1] = 0;
for (int *p = stk + 1, *q = stk + 1, *_p = stk + tp + 1; p != _p; p++) {
while (sz[*q] > (sz[*p] << 1))
q++;
cnt[*p] += p - q;
}
for (int *p = stk + 1, *q = stk + 1, *_p = stk + tp + 1; p != _p; p++) {
int sc = sz[zson[*p]];
while (q != _p && sz[*q] >= (sc << 1))
q++;
cnt[*p] -= p - q;
}
} void dfs2(int p, int fa) {
if (zson[p]) {
forv (e, G[p]) {
if ((*e ^ fa) && (*e ^ zson[p])) {
dfs2(*e, p);
work();
}
}
dfs2(zson[p], p);
} else {
tp = 0;
}
stk[++tp] = p;
} void calc(int p, int fa, int szcur, int szmx) {
int lim = ((n - sz[p]) >> 1);
cnt[g] += (szcur - sz[p] <= lim && szmx <= lim);
forv (e, G[p]) {
if (*e ^ fa) {
calc(*e, p, szcur, szmx);
}
}
} int tmp[N];
void dfs3(int p, int fa, int R, int& sum) {
tmp[sz[p]]++;
if (sz[p] <= R)
sum++;
forv (e, G[p]) {
if (*e ^ fa) {
dfs3(*e, p, R, sum);
}
}
} vector<int> P;
void dfs4(int p, int fa) {
P.push_back(p);
forv (e, G[p]) {
if (*e ^ fa) {
dfs4(*e, p);
}
}
} void solve() {
in >> n;
for (int i = 1; i <= n; i++)
G[i].clear();
for (int i = 1, u, v; i < n; i++) {
in >> u >> v;
G[u].push_back(v);
G[v].push_back(u);
}
get_sz(1, 0);
g = get_centroid(1, 0);
get_sz(g, 0);
memset(cnt, 0, sizeof(int) * (n + 1)); // cerr << "g: " << g << '\n'; dfs1(g, 0);
// cerr << "zson: ";
// for (int i = 1; i <= n; i++) {
// cerr << zson[i] << " ";
// }
// cerr << '\n';
dfs2(g, 0);
work(); memset(tmp, 0, sizeof(int) * (n + 1));
int R = 0, sum = 0;
for (int *p = stk + 1, *_p = stk + tp + 1; p != _p; p++) {
int q = n - (sz[zson[*p]] << 1);
while (R < q)
sum += tmp[++R];
cnt[*p] += sum;
forv (e, G[*p]) {
if (sz[*e] < sz[*p] && (*e ^ zson[*p])) {
dfs3(*e, *p, R, sum);
}
}
}
memset(tmp, 0, sizeof(int) * (n + 1));
R = 0, sum = 0;
for (int *p = stk + 1, *_p = stk + tp + 1; p != _p; p++) {
int q = n - (sz[*p] << 1) - 1;
while (R < q)
sum += tmp[++R];
cnt[*p] -= sum;
forv (e, G[*p]) {
if (sz[*e] < sz[*p] && (*e ^ zson[*p])) {
dfs3(*e, *p, R, sum);
}
}
} reverse(stk + 1, stk + tp + 1);
memset(tmp, 0, sizeof(int) * (n + 1));
for (int *p = stk + 1, *_p = stk + tp + 1; p != _p; p++) {
int sc = 0;
P.clear();
forv (e, G[*p]) {
if (sz[*e] < sz[*p] && (*e ^ zson[*p])) {
sc = max(sz[*e], sc);
dfs4(*e, *p);
}
}
sc = min(sc << 1 | 1, n);
for (int j = n, t = sc; t; j--, t--) {
tmp[j] += tmp[j + 1];
}
forv (e, P) {
int l = max(n - (sz[*e] << 1), 1);
int r = min(n - (sz[zson[*e]] << 1), n - 1);
cnt[*e] += tmp[l] - tmp[r + 1];
}
for (int j = n - sc + 1; j <= n; j++) {
tmp[j] -= tmp[j + 1];
}
tmp[sz[*p]]++;
forv (e, P) {
tmp[sz[*e]]++;
}
} // get the answer for the centroid
cnt[g] = 0;
int mx = 0, id = -1, sc = 0;
forv (p, G[g]) {
if (sz[*p] > mx) {
swap(mx, sc);
mx = sz[*p];
id = *p;
} else if (sz[*p] > sc) {
sc = sz[*p];
}
}
forv (p, G[g]) {
if (*p == id) {
calc(*p, g, mx, sc);
} else {
calc(*p, g, sz[*p], mx);
}
} ll ans = 0;
for (int i = 1; i <= n; i++) {
ans += 1ll * i * cnt[i];
// cerr << cnt[i] << " ";
}
// cerr << '\n';
out << ans << '\n';
} int main() {
freopen("centroid.in", "r", stdin);
freopen("centroid.out", "w", stdout);
in >> T;
while (T--) {
solve();
}
return 0;
}
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