/*
* Order of moving coins doesn't matter
*
* Manhattan distance always optimal?
* - Assume we've assigned each coin to their destination.
* - Then we move all by Manhattan distance
* - start by assigning every coin to their closest destination
* - assign N coins to N positions to minimize sum of manhattan distances
* - solve for X and Y independently
* - for 1 row version they only need to be on diff X's
* - moves for Y is fixed?
* - sum of a_y - 1
* - in 2 row version
* - exactly 2 of each X
* - N "top" and N "bottom"
* - Y would be sum of abs(Y_i - 2) for tops + abs(Y_i - 1) for bottoms
* - assign greedily
* - given N values, find min sum of N of them abs(x - 2) + abs(x - 1)
* - assign as many <= 1 as possible to abs(x - 1)
* - assign as many > 1 as possible to abs(x - 2)
* - move the remaining to wherever needed?
* - once we assign them to their Y's, we can break them up into two instances of 1 row problem
* - fairly convinced this is true?
* - how to solve 1d problem
* - assign leftmost to leftmost, second to second, etc
* - for 2 row version we can do greedy over Y's
* - then any moves to a different destination still follows Manhattan
* - nvm its not true
* - wtf its true
* - kekw
* - this constrains the problem to the box
* - so like just do some greedy in it i guess
*/
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
#define pb push_back
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define lb lower_bound
#define ub upper_bound
using pi = pair<int,int>;
#define f first
#define s second
#define mp make_pair
const int MX = 200005;
const int MOD = (int) (1e9 + 7);
const ll INF = (ll) 1e18;
int num[2][MX];
int main(){
#ifdef mikey
freopen("a.in", "r", stdin);
#endif
ios::sync_with_stdio(false);
cin.tie(0);
int n; cin >> n;
ll ans = 0;
for (int i = 0; i < 2 * n; i++) {
ll x, y; cin >> x >> y;
ll go = x - 1;
if (go < 0) ans += abs(go), go = 0;
if (go >= n) ans += go - n + 1, go = n - 1;
if (y <= 1) {
ans += abs(y - 1);
num[0][go]++;
} else {
ans += abs(y - 2);
num[1][go]++;
}
}
array<int, 2> pt;
pt[0] = 0, pt[1] = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < 2; j++) {
int &need = pt[j];
while (need < i && num[j][i] > 1) {
if (num[j][need] == 0) {
num[j][i]--;
num[j][need]++;
// dbg("MOVE", i, j, need, j);
ans += abs(i - need);
}
++need;
}
need = pt[j ^ 1];
while (need < i && num[j][i] > 1) {
if (num[j ^ 1][need] == 0) {
num[j][i]--;
num[j ^ 1][need]++;
// dbg("MOVE", i, j, need, j ^ 1);
ans += 1 + abs(i - need);
}
++need;
}
if (num[j][i] > 1 && num[j ^ 1][i] == 0) {
++ans;
num[j][i]--;
num[j ^ 1][i]++;
// dbg("MOVE", i, j, i, j ^ 1);
}
if (num[j][i] > 1 && i + 1 < n) {
num[j][i + 1] += (num[j][i] - 1);
ans += num[j][i] - 1;
num[j][i] = 1;
// dbg("MOVE", i, j, i + 1, j);
}
}
}
for (int j = 0; j < 2; j++)
for (int i = 0; i < n; i++) {
assert(num[j][i] == 1);
}
cout << ans << '\n';
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Correct |
0 ms |
364 KB |
Output is correct |
| 4 |
Correct |
1 ms |
364 KB |
Output is correct |
| 5 |
Correct |
1 ms |
364 KB |
Output is correct |
| 6 |
Correct |
1 ms |
364 KB |
Output is correct |
| 7 |
Correct |
1 ms |
364 KB |
Output is correct |
| 8 |
Correct |
1 ms |
364 KB |
Output is correct |
| 9 |
Correct |
1 ms |
364 KB |
Output is correct |
| 10 |
Correct |
1 ms |
364 KB |
Output is correct |
| 11 |
Correct |
1 ms |
364 KB |
Output is correct |
| 12 |
Correct |
1 ms |
364 KB |
Output is correct |
| 13 |
Correct |
1 ms |
364 KB |
Output is correct |
| 14 |
Incorrect |
1 ms |
364 KB |
Output isn't correct |
| 15 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Correct |
0 ms |
364 KB |
Output is correct |
| 4 |
Correct |
1 ms |
364 KB |
Output is correct |
| 5 |
Correct |
1 ms |
364 KB |
Output is correct |
| 6 |
Correct |
1 ms |
364 KB |
Output is correct |
| 7 |
Correct |
1 ms |
364 KB |
Output is correct |
| 8 |
Correct |
1 ms |
364 KB |
Output is correct |
| 9 |
Correct |
1 ms |
364 KB |
Output is correct |
| 10 |
Correct |
1 ms |
364 KB |
Output is correct |
| 11 |
Correct |
1 ms |
364 KB |
Output is correct |
| 12 |
Correct |
1 ms |
364 KB |
Output is correct |
| 13 |
Correct |
1 ms |
364 KB |
Output is correct |
| 14 |
Incorrect |
1 ms |
364 KB |
Output isn't correct |
| 15 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Correct |
0 ms |
364 KB |
Output is correct |
| 4 |
Correct |
1 ms |
364 KB |
Output is correct |
| 5 |
Correct |
1 ms |
364 KB |
Output is correct |
| 6 |
Correct |
1 ms |
364 KB |
Output is correct |
| 7 |
Correct |
1 ms |
364 KB |
Output is correct |
| 8 |
Correct |
1 ms |
364 KB |
Output is correct |
| 9 |
Correct |
1 ms |
364 KB |
Output is correct |
| 10 |
Correct |
1 ms |
364 KB |
Output is correct |
| 11 |
Correct |
1 ms |
364 KB |
Output is correct |
| 12 |
Correct |
1 ms |
364 KB |
Output is correct |
| 13 |
Correct |
1 ms |
364 KB |
Output is correct |
| 14 |
Incorrect |
1 ms |
364 KB |
Output isn't correct |
| 15 |
Halted |
0 ms |
0 KB |
- |
