Submission #249749

#	Submission time	Handle	Problem	Language	Result	Execution time	Memory
249749	2020-07-15T16:46:41 Z	AMO5	Palembang Bridges (APIO15_bridge)	C++17	100 / 100	289 ms	12908 KB

bridge

#include <bits/stdc++.h>
 
using namespace std;
 
#define fi first
#define se second
#define eb emplace_back
#define mt make_tuple
#define all(x) (x).begin(), (x).end()  
#define sz(x) int(x.size()) 
#define MOD 1000000007
 
typedef long long ll;
typedef pair <int, int> ii;
typedef pair <ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef long double ld;
 
const int mxn = 1e5+5;
bool DEBUG=0;
ll pref[mxn],suff[mxn];
bool cmp(const pll &a, const pll &b){
	if(a.fi+a.se!=b.fi+b.se)return a.fi+a.se<b.fi+b.se;
	else return a.fi<b.fi;
}
int main()
{
    ios_base::sync_with_stdio(0); cin.tie(0);
	ll k,n;
	vll coor;
	vector<pll>str;
	cin >> k >> n;
	ll ans = 0ll;
	for(int i=0; i<n; i++){
		char p,q; ll s,t;
		cin >> p >> s >> q >> t;
		if(p==q){
			ans += abs(s-t);
		}else{
			if(s>t)swap(s,t);
			ans+=1ll;
			str.eb(s,t);
		}
	}
	n=sz(str);
	if(n==0){
		//no bridge is needed
		cout << ans << endl;
		return 0;
	}
	if(k==1){
		//k=1
		for(ii x:str){
			coor.eb(x.fi);
			coor.eb(x.se);
		}
		sort(all(coor));
		ll bridge1=coor[n-1],bridge2=coor[n]; //bridge 2 is unnecessarily as long as bridge is median 
		ll res1=0ll,res2=0ll;
		for(int i=0; i<n; i++){
			if(bridge1<str[i].fi){
				res1 += 2ll*(str[i].fi-bridge1);
			}else if(bridge1>str[i].se){
				res1 += 2ll*(bridge1-str[i].se);
			}
			if(bridge2<str[i].fi){
				res2 += 2ll*(str[i].fi-bridge2);
			}else if(bridge2>str[i].se){
				res2 += 2ll*(bridge2-str[i].se);
			}
			res1 += str[i].se-str[i].fi;
			res2 += str[i].se-str[i].fi;
		}
		ans += min(res1,res2);
	}else{
		//k=2 
		sort(all(str),cmp);
		multiset<ll>sm,bg;
		ll sum_sm=0ll,sum_bg=0ll;
		for(int i=0; i<n-1; i++){ //bridge 1, pref
			sm.insert(str[i].fi);
			bg.insert(str[i].se);
			sum_sm += str[i].fi;
			sum_bg += str[i].se;
			while(*sm.rbegin()>*bg.begin()){ // swap em, so the median is still at sm(last),bg(first)
				ll dif = *sm.rbegin()-*bg.begin();
				sum_sm -= dif;
				sum_bg += dif;
				sm.insert(*bg.begin());
				bg.insert(*sm.rbegin());
				sm.erase(--sm.end());
				bg.erase(bg.begin());
			}
			pref[i] = sum_bg-sum_sm;
		}
		sm=bg=multiset<ll>();
		sum_sm=sum_bg=0ll;
		for(int i=n-1; i>0; i--){ //bridge 2, suff
			sm.insert(str[i].fi);
			bg.insert(str[i].se);
			sum_sm += str[i].fi;
			sum_bg += str[i].se;
			while(*sm.rbegin()>*bg.begin()){ // swap em
				ll dif = *sm.rbegin()-*bg.begin();
				sum_sm -= dif;
				sum_bg += dif;
				sm.insert(*bg.begin());
				bg.insert(*sm.rbegin());
				sm.erase(--sm.end());
				bg.erase(bg.begin());
			}
			//always throw to bg group, so easier to calc the dif between groups
			suff[i] = sum_bg-sum_sm;
		}
		// combining pref_i+suff_(i+1) as pref and suff go to bridge 1 and 2 respectively
		ll res = 1e18;
		for(int i=0; i<n-1; i++){
			res = min(res,pref[i]+suff[i+1]);
		}
		ans += res;
	}
	cout << ans << '\n';
	return 0;
}

Subtask #1

8.0 / 8.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	0 ms	384 KB	Output is correct
4	Correct	1 ms	384 KB	Output is correct
5	Correct	1 ms	384 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	384 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	1 ms	384 KB	Output is correct
10	Correct	1 ms	384 KB	Output is correct
11	Correct	1 ms	384 KB	Output is correct

Subtask #2

14.0 / 14.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	0 ms	384 KB	Output is correct
4	Correct	1 ms	384 KB	Output is correct
5	Correct	1 ms	384 KB	Output is correct
6	Correct	1 ms	384 KB	Output is correct
7	Correct	1 ms	384 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	1 ms	384 KB	Output is correct
10	Correct	2 ms	360 KB	Output is correct
11	Correct	1 ms	384 KB	Output is correct
12	Correct	24 ms	5748 KB	Output is correct
13	Correct	52 ms	6632 KB	Output is correct
14	Correct	36 ms	5996 KB	Output is correct
15	Correct	30 ms	4208 KB	Output is correct
16	Correct	32 ms	6644 KB	Output is correct
17	Correct	38 ms	6636 KB	Output is correct
18	Correct	42 ms	6636 KB	Output is correct
19	Correct	49 ms	6644 KB	Output is correct
20	Correct	37 ms	6636 KB	Output is correct
21	Correct	48 ms	6636 KB	Output is correct

Subtask #3

9.0 / 9.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	0 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	0 ms	384 KB	Output is correct
6	Correct	0 ms	384 KB	Output is correct
7	Correct	0 ms	384 KB	Output is correct
8	Correct	0 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	0 ms	384 KB	Output is correct
11	Correct	1 ms	384 KB	Output is correct
12	Correct	0 ms	384 KB	Output is correct

Subtask #4

32.0 / 32.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	1 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	0 ms	384 KB	Output is correct
6	Correct	0 ms	384 KB	Output is correct
7	Correct	0 ms	384 KB	Output is correct
8	Correct	0 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	1 ms	384 KB	Output is correct
11	Correct	1 ms	384 KB	Output is correct
12	Correct	0 ms	384 KB	Output is correct
13	Correct	1 ms	512 KB	Output is correct
14	Correct	2 ms	512 KB	Output is correct
15	Correct	2 ms	512 KB	Output is correct
16	Correct	0 ms	384 KB	Output is correct
17	Correct	1 ms	384 KB	Output is correct
18	Correct	1 ms	384 KB	Output is correct
19	Correct	1 ms	512 KB	Output is correct
20	Correct	2 ms	512 KB	Output is correct
21	Correct	1 ms	512 KB	Output is correct
22	Correct	1 ms	512 KB	Output is correct
23	Correct	1 ms	512 KB	Output is correct
24	Correct	2 ms	512 KB	Output is correct

Subtask #5

37.0 / 37.0

#	Verdict	Execution time	Memory	Grader output
1	Correct	0 ms	384 KB	Output is correct
2	Correct	0 ms	384 KB	Output is correct
3	Correct	0 ms	384 KB	Output is correct
4	Correct	0 ms	384 KB	Output is correct
5	Correct	1 ms	384 KB	Output is correct
6	Correct	0 ms	384 KB	Output is correct
7	Correct	0 ms	384 KB	Output is correct
8	Correct	1 ms	384 KB	Output is correct
9	Correct	0 ms	384 KB	Output is correct
10	Correct	0 ms	384 KB	Output is correct
11	Correct	1 ms	384 KB	Output is correct
12	Correct	0 ms	384 KB	Output is correct
13	Correct	1 ms	512 KB	Output is correct
14	Correct	2 ms	512 KB	Output is correct
15	Correct	2 ms	512 KB	Output is correct
16	Correct	1 ms	384 KB	Output is correct
17	Correct	1 ms	384 KB	Output is correct
18	Correct	1 ms	384 KB	Output is correct
19	Correct	1 ms	512 KB	Output is correct
20	Correct	1 ms	512 KB	Output is correct
21	Correct	1 ms	512 KB	Output is correct
22	Correct	2 ms	512 KB	Output is correct
23	Correct	2 ms	512 KB	Output is correct
24	Correct	1 ms	512 KB	Output is correct
25	Correct	118 ms	12904 KB	Output is correct
26	Correct	149 ms	12904 KB	Output is correct
27	Correct	289 ms	12904 KB	Output is correct
28	Correct	278 ms	12900 KB	Output is correct
29	Correct	288 ms	12904 KB	Output is correct
30	Correct	132 ms	7024 KB	Output is correct
31	Correct	117 ms	12908 KB	Output is correct
32	Correct	188 ms	12904 KB	Output is correct
33	Correct	124 ms	12904 KB	Output is correct
34	Correct	183 ms	12904 KB	Output is correct
35	Correct	155 ms	12904 KB	Output is correct
36	Correct	191 ms	12904 KB	Output is correct
37	Correct	107 ms	12904 KB	Output is correct