oj.uz

Submission #1077022

# Submission time Handle Problem Language Result Execution time Memory
1077022 2024-08-26T20:59:06 Z asdfgrace Palembang Bridges (APIO15_bridge) C++17
100 / 100
 262 ms 13664 KB 
#include <bits/stdc++.h>
using namespace std;
 
#define dbg(x) x
#define prt(x) dbg(cerr << x)
#define pv(x) dbg(cerr << #x << " = " << x << '\n')
#define pv2(x) dbg(cerr << #x << " = " << x.first << ',' << x.second << '\n')
#define parr(x) dbg(prt(#x << " = { "); for (auto y : x) prt(y << ' '); prt("}\n");)
#define parr2(x) dbg(prt(#x << " = { "); for (auto [y, z] : x) prt(y << ',' << z << "  "); prt("}\n");)
#define parr2d(x) dbg(prt(#x << ":\n"); for (auto arr : x) {parr(arr);} prt('\n'));
#define parr2d2(x) dbg(prt(#x << ":\n"); for (auto arr : x) {parr2(arr);} prt('\n'));
 
/*
build 1 or 2 bridges
add to baseline of sum of all distances driven without crossing bridge + n
then only consider people crossing
 
k=1:
minimize the sum of all abs(s[i] - x) + abs(t[i] - x)
one of the given locs is optimal
so here treat all s[i] and t[i] the same, sort, etc.

k=2:
starts > lb and ends < rb:
lb + rb <= x + y --> use x
else --> use y
that actually applies to everything
so you can already just sort by sum
and binary search the right bound
given the left bound
but how do you compare between left bounds

okok the hint is you just sort by sum
just iterate over the n or smth breakpoints & look for the min with 2p or smth...
HINT: the median is always optimal
*/
 
int main() {
  ios::sync_with_stdio(0); cin.tie(0);
  int k, n;
  cin >> k >> n;
  vector<array<int, 2>> a;
  long long bsl = 0;
  for (int i = 0; i < n; i++) {
    char c1, c2; int i1, i2;
    cin >> c1 >> i1 >> c2 >> i2;
    if (c1 == c2) {
      bsl += abs(i2 - i1);
    } else {
      if (i2 < i1) swap(i1, i2);
      a.push_back({i1, i2});
      bsl++;
    }
  }
  n = (int) a.size();
  if (n == 0) {
    cout << bsl << '\n';
    return 0;
  }
  vector<int> b;
  for (int i = 0; i < n; i++) {
    b.push_back(a[i][0]); b.push_back(a[i][1]);
  }
  sort(b.begin(), b.end());
  if (k == 1) {
    long long sum = 0;
    for (int i = 0; i < 2 * n; i++) {
      sum += b[i] - b[0];
    }
    long long best = sum;
    for (int i = 1; i < 2 * n; i++) {
      sum += (long long) i * (b[i] - b[i - 1]);
      sum -= (long long) (2 * n - i) * (b[i] - b[i - 1]);
      best = min(best, sum);
    }
    cout << best + bsl << '\n'; 
  } else {
    sort(a.begin(), a.end(), [&] (array<int, 2> a1, array<int, 2> a2) {
      return a1[0] + a1[1] < a2[0] + a2[1];
    });
    vector<vector<multiset<int>>> s(2, vector<multiset<int>>(2));
    vector<vector<long long>> sum(2, vector<long long>(2, 0));
    function<void(int, int)> ins = [&] (int i, int x) {
      if (s[i][0].empty() || x <= *s[i][0].rbegin()) {
        s[i][0].insert(x);
        sum[i][0] += x;
        if (s[i][0].size() > s[i][1].size() + 1) {
          int mx = *s[i][0].rbegin();
          s[i][0].erase(s[i][0].find(mx));
          sum[i][0] -= mx;
          s[i][1].insert(mx);
          sum[i][1] += mx;
        }
      } else {
        s[i][1].insert(x);
        sum[i][1] += x;
        if (s[i][1].size() > s[i][0].size()) {
          int mn = *s[i][1].begin();
          s[i][1].erase(s[i][1].find(mn));
          sum[i][1] -= mn;
          s[i][0].insert(mn);
          sum[i][0] += mn;
        }
      }
      
    };
    function<void(int, int)> del = [&] (int i, int x) {
      if (x <= *s[i][0].rbegin()) {
        s[i][0].erase(s[i][0].find(x));
        sum[i][0] -= x;
        if (s[i][1].size() > s[i][0].size()) {
          int mn = *s[i][1].begin();
          s[i][1].erase(s[i][1].find(mn));
          sum[i][1] -= mn;
          s[i][0].insert(mn);
          sum[i][0] += mn;
        }
      } else {
        s[i][1].erase(s[i][1].find(x));
        sum[i][1] -= x;
        if (s[i][0].size() > s[i][1].size() + 1) {
          int mx = *s[i][0].rbegin();
          s[i][0].erase(s[i][0].find(mx));
          sum[i][0] -= mx;
          s[i][1].insert(mx);
          sum[i][1] += mx;
        }
      }
    };
    function<long long(int)> cost = [&] (int i) {
      if (s[i][0].empty()) return 0ll;
      long long med = *s[i][0].rbegin();
      return (med * (long long) s[i][0].size() - sum[i][0])
        + (sum[i][1] - med * (long long) s[i][1].size());
    };
    for (int i = 0; i < n; i++) {
      ins(1, a[i][0]);
      ins(1, a[i][1]);
    }
    long long best = cost(1);
    for (int i = 0; i < n - 1; i++) {
      del(1, a[i][0]);
      del(1, a[i][1]);
      ins(0, a[i][0]);
      ins(0, a[i][1]);
      best = min(best, cost(0) + cost(1));
    }
    cout << best + bsl << '\n';
  }
}
 
/*
any observations help
 
check every line
IF YOUR LINES AREN'T WRONG
CHECK IF YOUR LINES ARE IN THE RIGHT ORDER
 
NEVER GIVE UP
*/

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 344 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 1 ms 468 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 15 ms 3544 KB Output is correct
13 Correct 32 ms 4872 KB Output is correct
14 Correct 21 ms 3800 KB Output is correct
15 Correct 21 ms 3124 KB Output is correct
16 Correct 17 ms 4312 KB Output is correct
17 Correct 21 ms 4980 KB Output is correct
18 Correct 23 ms 4568 KB Output is correct
19 Correct 28 ms 5032 KB Output is correct
20 Correct 21 ms 4564 KB Output is correct
21 Correct 27 ms 4824 KB Output is correct

Subtask #3
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 1 ms 344 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 456 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 344 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct

Subtask #4
32.0 / 32.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 0 ms 348 KB Output is correct
9 Correct 0 ms 348 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 2 ms 344 KB Output is correct
14 Correct 1 ms 344 KB Output is correct
15 Correct 1 ms 348 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 460 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct

Subtask #5
37.0 / 37.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 0 ms 452 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 344 KB Output is correct
9 Correct 1 ms 348 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct
12 Correct 0 ms 348 KB Output is correct
13 Correct 1 ms 348 KB Output is correct
14 Correct 1 ms 344 KB Output is correct
15 Correct 1 ms 592 KB Output is correct
16 Correct 0 ms 348 KB Output is correct
17 Correct 1 ms 348 KB Output is correct
18 Correct 1 ms 348 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 344 KB Output is correct
22 Correct 1 ms 348 KB Output is correct
23 Correct 1 ms 348 KB Output is correct
24 Correct 1 ms 348 KB Output is correct
25 Correct 146 ms 11992 KB Output is correct
26 Correct 210 ms 12112 KB Output is correct
27 Correct 262 ms 13140 KB Output is correct
28 Correct 257 ms 13664 KB Output is correct
29 Correct 253 ms 13644 KB Output is correct
30 Correct 114 ms 7384 KB Output is correct
31 Correct 124 ms 12880 KB Output is correct
32 Correct 161 ms 13600 KB Output is correct
33 Correct 89 ms 13324 KB Output is correct
34 Correct 178 ms 13648 KB Output is correct
35 Correct 154 ms 13152 KB Output is correct
36 Correct 165 ms 13276 KB Output is correct
37 Correct 147 ms 12108 KB Output is correct