#include <bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug.h>
#include "grader.cpp"
#else
#define debug(...)
#endif
#define ft front
#define bk back
#define st first
#define nd second
#define ins insert
#define ers erase
#define pb push_back
#define pf push_front
#define _pb pop_back
#define _pf pop_front
#define lb lower_bound
#define ub upper_bound
#define mtp make_tuple
#define bg begin
#define ed end
#define all(x) (x).bg(), (x).ed()
#define sz(x) (int)(x).size()
typedef long long ll; typedef unsigned long long ull;
typedef double db; typedef long double ldb;
typedef pair<int, int> pi; typedef pair<ll, ll> pll;
typedef vector<int> vi; typedef vector<ll> vll; typedef vector<pi> vpi; typedef vector<pll> vpll;
typedef string str;
template<typename T> T gcd(T a, T b) { return (b == 0? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
#define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
#define FOS(i, r, l) for (int (i) = (r); (i) >= (l); --(i))
#define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
#define FSN(i, n) for (int (i) = (n) - 1; (i) >= 0; --(i))
#define EACH(i, x) for (auto &(i) : (x))
#define WHILE while
#define file "TEST"
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
ll rand(ll l, ll r) { return uniform_int_distribution<ll>(l, r)(rd); }
/*
----------------------------------------------------------------
END OF TEMPLATE
----------------------------------------------------------------
Tran The Bao - ghostwriter
Training for VOI23 gold medal
----------------------------------------------------------------
DIT ME CHUYEN BAO LOC
----------------------------------------------------------------
*/
const int oo = 1e9 + 5;
const int M = 1e9;
namespace subtask12 {
const int MAXN = 2e3;
vi adj[MAXN];
map<pi, int> d;
vi bfs(int N, int source) {
vi d(N, oo);
queue<int> q;
d[source] = 0;
q.push(source);
WHILE(!q.empty()) {
int u = q.ft();
q.pop();
EACH(v, adj[u]) {
if (d[v] != oo) continue;
d[v] = d[u] + 1;
q.push(v);
}
}
return d;
}
int DistanceSum(int N, int *X, int *Y) {
FRN(i, N) d[{X[i], Y[i]}] = i;
FRN(i, N) {
if (d.count({X[i] - 1, Y[i]})) {
int pos = d[{X[i] - 1, Y[i]}];
adj[i].pb(pos);
adj[pos].pb(i);
}
if (d.count({X[i], Y[i] - 1})) {
int pos = d[{X[i], Y[i] - 1}];
adj[i].pb(pos);
adj[pos].pb(i);
}
}
int rs = 0;
FRN(i, N) {
vi d = bfs(N, i);
FRN(j, i) (rs += d[j]) %= M;
}
return rs;
}
}
namespace subtask3 {
const int MAXN = 1e5 + 5;
pi a[MAXN], f[MAXN];
vi v;
int getpos(int x) { return lb(all(v), x) - v.bg(); }
void upd(int pos, pi v) { ++pos; for (int i = pos; i < MAXN; i += (i & -i)) { (f[i].st += v.st) %= M; (f[i].nd += v.nd) %= M; } }
pi get(int pos) { ++pos; pi rs = {0, 0}; for (int i = pos; i > 0; i -= (i & -i)) { (rs.st += f[i].st) %= M; (rs.nd += f[i].nd) %= M; } return rs; }
int DistanceSum(int N, int *X, int *Y) {
FRN(i, N) {
a[i] = {X[i], Y[i]};
v.pb(Y[i]);
}
sort(all(v));
sort(a, a + N);
int rs = 0, sumx = 0, sumy = 0;
FRN(i, N) {
int x = a[i].st, y = a[i].nd;
int pos = getpos(y);
pi tmp = get(pos);
int cnt = tmp.st, sumy1 = tmp.nd;
rs = (rs + 1LL * x * i % M - sumx + M) % M;
rs = (rs + 1LL * y * cnt % M - sumy1 + M) % M;
rs = (rs + sumy - sumy1 - 1LL * y * (i - cnt) % M + 2LL * M) % M;
(sumx += x) %= M;
(sumy += y) %= M;
upd(pos, {1, y});
}
return rs;
}
}
namespace solution {
const int MAXN = 1e5 + 5;
int a[MAXN], a1[MAXN], s[MAXN], c[MAXN], cnt = 0, cnt1 = 0, rs = 0;
vi adj[MAXN], adj1[MAXN];
map<pi, int> d;
map<pi, bool> d1;
void dfs(int u, int p) {
s[u] = a[u];
EACH(v, adj[u]) {
if (v == p) continue;
dfs(v, u);
s[u] += s[v];
}
}
void dfs1(int u, int p) {
s[u] = a1[u];
EACH(v, adj1[u]) {
if (v == p) continue;
dfs1(v, u);
s[u] += s[v];
}
}
int DistanceSum(int N, int *X, int *Y) {
FRN(i, N) d[{X[i], Y[i]}] = i;
FRN(i, N) {
if (c[i]) continue;
++cnt;
int cntn = 0;
int x = X[i], y = Y[i];
WHILE(d.count({x, y})) {
++cntn;
int pos = d[{x, y}];
c[pos] = cnt;
--y;
}
x = X[i];
y = Y[i] + 1;
WHILE(d.count({x, y})) {
++cntn;
int pos = d[{x, y}];
c[pos] = cnt;
++y;
}
a[cnt] = cntn;
}
FRN(i, N) {
int pos = c[i];
if (d.count({X[i] - 1, Y[i]})) {
int pos1 = c[d[{X[i] - 1, Y[i]}]];
if (!d1.count({pos, pos1})) {
adj[pos].pb(pos1);
adj[pos1].pb(pos);
d1[{pos, pos1}] = d1[{pos1, pos}] = 1;
}
}
}
memset(c, 0, sizeof c);
FRN(i, N) {
if (c[i]) continue;
++cnt1;
int cntn = 0;
int x = X[i], y = Y[i];
WHILE(d.count({x, y})) {
++cntn;
int pos = d[{x, y}];
c[pos] = cnt1;
--x;
}
x = X[i] + 1;
y = Y[i];
WHILE(d.count({x, y})) {
++cntn;
int pos = d[{x, y}];
c[pos] = cnt1;
++x;
}
a1[cnt1] = cntn;
}
d1.clear();
FRN(i, N) {
int pos = c[i];
if (d.count({X[i], Y[i] - 1})) {
int pos1 = c[d[{X[i], Y[i] - 1}]];
if (!d1.count({pos, pos1})) {
adj1[pos].pb(pos1);
adj1[pos1].pb(pos);
d1[{pos, pos1}] = d1[{pos1, pos}] = 1;
}
}
}
dfs(1, 0);
FOR(i, 2, cnt) rs = (rs + 1LL * s[i] * (s[1] - s[i]) % M) % M;
dfs1(1, 0);
FOR(i, 2, cnt1) rs = (rs + 1LL * s[i] * (s[1] - s[i]) % M) % M;
return rs;
}
}
int DistanceSum(int N, int *X, int *Y) {
if (N <= 2000) return subtask12::DistanceSum(N, X, Y);
return solution::DistanceSum(N, X, Y);
}
/*
11
2 5
2 6
3 3
3 6
4 3
4 4
4 5
4 6
5 3
5 4
5 6
4
1 1
2 1
3 1
3 2
----------------------------------------------------------------
From Benq:
stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
* DON'T GET STUCK ON ONE APPROACH
----------------------------------------------------------------
*/
Compilation message
city.cpp: In function 'vi subtask12::bfs(int, int)':
city.cpp:37:31: warning: unnecessary parentheses in declaration of 'v' [-Wparentheses]
37 | #define EACH(i, x) for (auto &(i) : (x))
| ^
city.cpp:66:13: note: in expansion of macro 'EACH'
66 | EACH(v, adj[u]) {
| ^~~~
city.cpp: In function 'int subtask12::DistanceSum(int, int*, int*)':
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:75:9: note: in expansion of macro 'FRN'
75 | FRN(i, N) d[{X[i], Y[i]}] = i;
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:76:9: note: in expansion of macro 'FRN'
76 | FRN(i, N) {
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:89:9: note: in expansion of macro 'FRN'
89 | FRN(i, N) {
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'j' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:91:13: note: in expansion of macro 'FRN'
91 | FRN(j, i) (rs += d[j]) %= M;
| ^~~
city.cpp: In function 'int subtask3::DistanceSum(int, int*, int*)':
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:104:9: note: in expansion of macro 'FRN'
104 | FRN(i, N) {
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:111:9: note: in expansion of macro 'FRN'
111 | FRN(i, N) {
| ^~~
city.cpp: In function 'void solution::dfs(int, int)':
city.cpp:37:31: warning: unnecessary parentheses in declaration of 'v' [-Wparentheses]
37 | #define EACH(i, x) for (auto &(i) : (x))
| ^
city.cpp:134:9: note: in expansion of macro 'EACH'
134 | EACH(v, adj[u]) {
| ^~~~
city.cpp: In function 'void solution::dfs1(int, int)':
city.cpp:37:31: warning: unnecessary parentheses in declaration of 'v' [-Wparentheses]
37 | #define EACH(i, x) for (auto &(i) : (x))
| ^
city.cpp:142:9: note: in expansion of macro 'EACH'
142 | EACH(v, adj1[u]) {
| ^~~~
city.cpp: In function 'int solution::DistanceSum(int, int*, int*)':
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:149:9: note: in expansion of macro 'FRN'
149 | FRN(i, N) d[{X[i], Y[i]}] = i;
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:150:9: note: in expansion of macro 'FRN'
150 | FRN(i, N) {
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:171:9: note: in expansion of macro 'FRN'
171 | FRN(i, N) {
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:183:9: note: in expansion of macro 'FRN'
183 | FRN(i, N) {
| ^~~
city.cpp:35:28: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
35 | #define FRN(i, n) for (int (i) = 0; (i) < (n); ++(i))
| ^
city.cpp:205:9: note: in expansion of macro 'FRN'
205 | FRN(i, N) {
| ^~~
city.cpp:33:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
33 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
city.cpp:217:9: note: in expansion of macro 'FOR'
217 | FOR(i, 2, cnt) rs = (rs + 1LL * s[i] * (s[1] - s[i]) % M) % M;
| ^~~
city.cpp:33:31: warning: unnecessary parentheses in declaration of 'i' [-Wparentheses]
33 | #define FOR(i, l, r) for (int (i) = (l); (i) <= (r); ++(i))
| ^
city.cpp:219:9: note: in expansion of macro 'FOR'
219 | FOR(i, 2, cnt1) rs = (rs + 1LL * s[i] * (s[1] - s[i]) % M) % M;
| ^~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
4 ms |
4948 KB |
Output is correct |
| 2 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 3 |
Correct |
3 ms |
4948 KB |
Output is correct |
| 4 |
Correct |
3 ms |
5064 KB |
Output is correct |
| 5 |
Correct |
4 ms |
5076 KB |
Output is correct |
| 6 |
Correct |
4 ms |
5076 KB |
Output is correct |
| 7 |
Correct |
4 ms |
5076 KB |
Output is correct |
| 8 |
Correct |
4 ms |
5076 KB |
Output is correct |
| 9 |
Correct |
4 ms |
5076 KB |
Output is correct |
| 10 |
Correct |
4 ms |
5076 KB |
Output is correct |
| 11 |
Correct |
5 ms |
5076 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
29 ms |
5068 KB |
Output is correct |
| 2 |
Correct |
34 ms |
5164 KB |
Output is correct |
| 3 |
Correct |
60 ms |
5224 KB |
Output is correct |
| 4 |
Correct |
65 ms |
5204 KB |
Output is correct |
| 5 |
Correct |
106 ms |
5280 KB |
Output is correct |
| 6 |
Correct |
112 ms |
5284 KB |
Output is correct |
| 7 |
Correct |
111 ms |
5280 KB |
Output is correct |
| 8 |
Correct |
119 ms |
5280 KB |
Output is correct |
| 9 |
Correct |
110 ms |
5280 KB |
Output is correct |
| 10 |
Correct |
109 ms |
5280 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
32 ms |
7128 KB |
Output is correct |
| 2 |
Correct |
35 ms |
7120 KB |
Output is correct |
| 3 |
Correct |
87 ms |
9476 KB |
Output is correct |
| 4 |
Correct |
89 ms |
9540 KB |
Output is correct |
| 5 |
Correct |
197 ms |
13492 KB |
Output is correct |
| 6 |
Correct |
216 ms |
13528 KB |
Output is correct |
| 7 |
Correct |
218 ms |
13972 KB |
Output is correct |
| 8 |
Correct |
217 ms |
13300 KB |
Output is correct |
| 9 |
Correct |
214 ms |
14160 KB |
Output is correct |
| 10 |
Correct |
275 ms |
20200 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
54 ms |
8624 KB |
Output is correct |
| 2 |
Correct |
46 ms |
7984 KB |
Output is correct |
| 3 |
Correct |
161 ms |
13412 KB |
Output is correct |
| 4 |
Correct |
142 ms |
11852 KB |
Output is correct |
| 5 |
Correct |
399 ms |
21164 KB |
Output is correct |
| 6 |
Correct |
354 ms |
16368 KB |
Output is correct |
| 7 |
Correct |
422 ms |
21432 KB |
Output is correct |
| 8 |
Correct |
367 ms |
16600 KB |
Output is correct |
| 9 |
Correct |
289 ms |
15872 KB |
Output is correct |
| 10 |
Correct |
308 ms |
15436 KB |
Output is correct |
