/*
* 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;
}
}
for (int j = 0; j < 2; j++) {
int &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 |
1 ms |
364 KB |
Output is correct |
4 |
Correct |
0 ms |
364 KB |
Output is correct |
5 |
Correct |
1 ms |
364 KB |
Output is correct |
6 |
Correct |
0 ms |
364 KB |
Output is correct |
7 |
Correct |
0 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 |
0 ms |
364 KB |
Output is correct |
11 |
Correct |
0 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 |
Correct |
1 ms |
364 KB |
Output is correct |
15 |
Correct |
1 ms |
364 KB |
Output is correct |
16 |
Correct |
1 ms |
384 KB |
Output is correct |
17 |
Correct |
1 ms |
364 KB |
Output is correct |
18 |
Correct |
1 ms |
364 KB |
Output is correct |
19 |
Correct |
1 ms |
492 KB |
Output is correct |
20 |
Correct |
1 ms |
364 KB |
Output is correct |
21 |
Correct |
1 ms |
364 KB |
Output is correct |
22 |
Correct |
1 ms |
364 KB |
Output is correct |
23 |
Correct |
1 ms |
364 KB |
Output is correct |
24 |
Correct |
1 ms |
364 KB |
Output is correct |
25 |
Correct |
1 ms |
364 KB |
Output is correct |
26 |
Correct |
1 ms |
364 KB |
Output is correct |
27 |
Correct |
1 ms |
364 KB |
Output is correct |
28 |
Correct |
1 ms |
364 KB |
Output is correct |
29 |
Correct |
1 ms |
364 KB |
Output is correct |
30 |
Correct |
1 ms |
364 KB |
Output is correct |
31 |
Correct |
1 ms |
364 KB |
Output is correct |
32 |
Correct |
1 ms |
364 KB |
Output is correct |
33 |
Correct |
1 ms |
364 KB |
Output is correct |
# |
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 |
1 ms |
364 KB |
Output is correct |
4 |
Correct |
0 ms |
364 KB |
Output is correct |
5 |
Correct |
1 ms |
364 KB |
Output is correct |
6 |
Correct |
0 ms |
364 KB |
Output is correct |
7 |
Correct |
0 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 |
0 ms |
364 KB |
Output is correct |
11 |
Correct |
0 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 |
Correct |
1 ms |
364 KB |
Output is correct |
15 |
Correct |
1 ms |
364 KB |
Output is correct |
16 |
Correct |
1 ms |
384 KB |
Output is correct |
17 |
Correct |
1 ms |
364 KB |
Output is correct |
18 |
Correct |
1 ms |
364 KB |
Output is correct |
19 |
Correct |
1 ms |
492 KB |
Output is correct |
20 |
Correct |
1 ms |
364 KB |
Output is correct |
21 |
Correct |
1 ms |
364 KB |
Output is correct |
22 |
Correct |
1 ms |
364 KB |
Output is correct |
23 |
Correct |
1 ms |
364 KB |
Output is correct |
24 |
Correct |
1 ms |
364 KB |
Output is correct |
25 |
Correct |
1 ms |
364 KB |
Output is correct |
26 |
Correct |
1 ms |
364 KB |
Output is correct |
27 |
Correct |
1 ms |
364 KB |
Output is correct |
28 |
Correct |
1 ms |
364 KB |
Output is correct |
29 |
Correct |
1 ms |
364 KB |
Output is correct |
30 |
Correct |
1 ms |
364 KB |
Output is correct |
31 |
Correct |
1 ms |
364 KB |
Output is correct |
32 |
Correct |
1 ms |
364 KB |
Output is correct |
33 |
Correct |
1 ms |
364 KB |
Output is correct |
34 |
Correct |
1 ms |
364 KB |
Output is correct |
35 |
Correct |
1 ms |
364 KB |
Output is correct |
36 |
Correct |
1 ms |
364 KB |
Output is correct |
37 |
Correct |
1 ms |
364 KB |
Output is correct |
38 |
Correct |
1 ms |
364 KB |
Output is correct |
39 |
Correct |
1 ms |
364 KB |
Output is correct |
40 |
Correct |
1 ms |
364 KB |
Output is correct |
41 |
Correct |
1 ms |
364 KB |
Output is correct |
42 |
Correct |
1 ms |
364 KB |
Output is correct |
43 |
Correct |
1 ms |
364 KB |
Output is correct |
44 |
Correct |
1 ms |
364 KB |
Output is correct |
45 |
Correct |
1 ms |
364 KB |
Output is correct |
46 |
Correct |
1 ms |
364 KB |
Output is correct |
47 |
Correct |
1 ms |
364 KB |
Output is correct |
48 |
Correct |
1 ms |
512 KB |
Output is correct |
49 |
Correct |
1 ms |
364 KB |
Output is correct |
50 |
Correct |
1 ms |
364 KB |
Output is correct |
51 |
Correct |
1 ms |
364 KB |
Output is correct |
52 |
Correct |
1 ms |
364 KB |
Output is correct |
53 |
Correct |
1 ms |
364 KB |
Output is correct |
54 |
Correct |
1 ms |
364 KB |
Output is correct |
55 |
Correct |
1 ms |
364 KB |
Output is correct |
56 |
Correct |
1 ms |
364 KB |
Output is correct |
57 |
Correct |
1 ms |
364 KB |
Output is correct |
58 |
Correct |
1 ms |
364 KB |
Output is correct |
59 |
Correct |
1 ms |
364 KB |
Output is correct |
60 |
Correct |
1 ms |
364 KB |
Output is correct |
61 |
Correct |
1 ms |
364 KB |
Output is correct |
62 |
Correct |
1 ms |
364 KB |
Output is correct |
63 |
Correct |
2 ms |
364 KB |
Output is correct |
64 |
Correct |
1 ms |
364 KB |
Output is correct |
# |
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 |
1 ms |
364 KB |
Output is correct |
4 |
Correct |
0 ms |
364 KB |
Output is correct |
5 |
Correct |
1 ms |
364 KB |
Output is correct |
6 |
Correct |
0 ms |
364 KB |
Output is correct |
7 |
Correct |
0 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 |
0 ms |
364 KB |
Output is correct |
11 |
Correct |
0 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 |
Correct |
1 ms |
364 KB |
Output is correct |
15 |
Correct |
1 ms |
364 KB |
Output is correct |
16 |
Correct |
1 ms |
384 KB |
Output is correct |
17 |
Correct |
1 ms |
364 KB |
Output is correct |
18 |
Correct |
1 ms |
364 KB |
Output is correct |
19 |
Correct |
1 ms |
492 KB |
Output is correct |
20 |
Correct |
1 ms |
364 KB |
Output is correct |
21 |
Correct |
1 ms |
364 KB |
Output is correct |
22 |
Correct |
1 ms |
364 KB |
Output is correct |
23 |
Correct |
1 ms |
364 KB |
Output is correct |
24 |
Correct |
1 ms |
364 KB |
Output is correct |
25 |
Correct |
1 ms |
364 KB |
Output is correct |
26 |
Correct |
1 ms |
364 KB |
Output is correct |
27 |
Correct |
1 ms |
364 KB |
Output is correct |
28 |
Correct |
1 ms |
364 KB |
Output is correct |
29 |
Correct |
1 ms |
364 KB |
Output is correct |
30 |
Correct |
1 ms |
364 KB |
Output is correct |
31 |
Correct |
1 ms |
364 KB |
Output is correct |
32 |
Correct |
1 ms |
364 KB |
Output is correct |
33 |
Correct |
1 ms |
364 KB |
Output is correct |
34 |
Correct |
1 ms |
364 KB |
Output is correct |
35 |
Correct |
1 ms |
364 KB |
Output is correct |
36 |
Correct |
1 ms |
364 KB |
Output is correct |
37 |
Correct |
1 ms |
364 KB |
Output is correct |
38 |
Correct |
1 ms |
364 KB |
Output is correct |
39 |
Correct |
1 ms |
364 KB |
Output is correct |
40 |
Correct |
1 ms |
364 KB |
Output is correct |
41 |
Correct |
1 ms |
364 KB |
Output is correct |
42 |
Correct |
1 ms |
364 KB |
Output is correct |
43 |
Correct |
1 ms |
364 KB |
Output is correct |
44 |
Correct |
1 ms |
364 KB |
Output is correct |
45 |
Correct |
1 ms |
364 KB |
Output is correct |
46 |
Correct |
1 ms |
364 KB |
Output is correct |
47 |
Correct |
1 ms |
364 KB |
Output is correct |
48 |
Correct |
1 ms |
512 KB |
Output is correct |
49 |
Correct |
1 ms |
364 KB |
Output is correct |
50 |
Correct |
1 ms |
364 KB |
Output is correct |
51 |
Correct |
1 ms |
364 KB |
Output is correct |
52 |
Correct |
1 ms |
364 KB |
Output is correct |
53 |
Correct |
1 ms |
364 KB |
Output is correct |
54 |
Correct |
1 ms |
364 KB |
Output is correct |
55 |
Correct |
1 ms |
364 KB |
Output is correct |
56 |
Correct |
1 ms |
364 KB |
Output is correct |
57 |
Correct |
1 ms |
364 KB |
Output is correct |
58 |
Correct |
1 ms |
364 KB |
Output is correct |
59 |
Correct |
1 ms |
364 KB |
Output is correct |
60 |
Correct |
1 ms |
364 KB |
Output is correct |
61 |
Correct |
1 ms |
364 KB |
Output is correct |
62 |
Correct |
1 ms |
364 KB |
Output is correct |
63 |
Correct |
2 ms |
364 KB |
Output is correct |
64 |
Correct |
1 ms |
364 KB |
Output is correct |
65 |
Correct |
36 ms |
2668 KB |
Output is correct |
66 |
Correct |
78 ms |
5796 KB |
Output is correct |
67 |
Correct |
61 ms |
4332 KB |
Output is correct |
68 |
Correct |
54 ms |
4588 KB |
Output is correct |
69 |
Correct |
63 ms |
4332 KB |
Output is correct |
70 |
Correct |
52 ms |
4332 KB |
Output is correct |
71 |
Correct |
48 ms |
4332 KB |
Output is correct |
72 |
Correct |
59 ms |
4332 KB |
Output is correct |
73 |
Correct |
46 ms |
4332 KB |
Output is correct |
74 |
Correct |
48 ms |
4332 KB |
Output is correct |
75 |
Correct |
47 ms |
4204 KB |
Output is correct |
76 |
Correct |
46 ms |
4332 KB |
Output is correct |
77 |
Correct |
47 ms |
4332 KB |
Output is correct |
78 |
Correct |
47 ms |
4332 KB |
Output is correct |
79 |
Correct |
47 ms |
4332 KB |
Output is correct |
80 |
Correct |
47 ms |
4332 KB |
Output is correct |
81 |
Correct |
46 ms |
4332 KB |
Output is correct |
82 |
Correct |
53 ms |
4352 KB |
Output is correct |
83 |
Correct |
52 ms |
4332 KB |
Output is correct |
84 |
Correct |
47 ms |
4332 KB |
Output is correct |
85 |
Correct |
48 ms |
4332 KB |
Output is correct |
86 |
Correct |
48 ms |
4332 KB |
Output is correct |
87 |
Correct |
49 ms |
4332 KB |
Output is correct |
88 |
Correct |
51 ms |
4332 KB |
Output is correct |
89 |
Correct |
48 ms |
4332 KB |
Output is correct |
90 |
Correct |
50 ms |
4332 KB |
Output is correct |
91 |
Correct |
51 ms |
4332 KB |
Output is correct |
92 |
Correct |
48 ms |
4460 KB |
Output is correct |
93 |
Correct |
48 ms |
4460 KB |
Output is correct |
94 |
Correct |
52 ms |
4332 KB |
Output is correct |
95 |
Correct |
46 ms |
4204 KB |
Output is correct |
96 |
Correct |
47 ms |
4332 KB |
Output is correct |
97 |
Correct |
47 ms |
4332 KB |
Output is correct |
98 |
Correct |
47 ms |
4332 KB |
Output is correct |
99 |
Correct |
49 ms |
4332 KB |
Output is correct |
100 |
Correct |
47 ms |
4332 KB |
Output is correct |
101 |
Correct |
46 ms |
4332 KB |
Output is correct |
102 |
Correct |
46 ms |
4332 KB |
Output is correct |
103 |
Correct |
47 ms |
4332 KB |
Output is correct |