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Submission #873516

# Submission time Handle Problem Language Result Execution time Memory
873516 2023-11-15T08:41:17 Z dsyz Relay Marathon (NOI20_relaymarathon) C++17
100 / 100
 1663 ms 285320 KB 
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define MAXN (100005)
ll dist[MAXN], distA[MAXN], distB[MAXN];
ll source[MAXN];
vector<pair<ll,ll> > v[MAXN];
int main() {
	ios_base::sync_with_stdio(false);cin.tie(0);
	ll N,M,K;
	cin>>N>>M>>K;
	vector<pair<ll,pair<ll,ll> > > edges;
	for(ll i = 0;i < M;i++){
		ll a,b,c;
		cin>>a>>b>>c;
		a--;
		b--;
		v[a].push_back({c,b});
		v[b].push_back({c,a});
		edges.push_back({c,{a,b}});
	}
	priority_queue<pair<ll,pair<ll,ll> >,vector<pair<ll,pair<ll,ll> > >,greater<pair<ll,pair<ll,ll> > > > pq;
	ll special[K];
	memset(dist,-1,sizeof(dist));
	memset(source,-1,sizeof(source));
	for(ll i = 0;i < K;i++){
		cin>>special[i];
		special[i]--;
		pq.push({0,{special[i],special[i]}}); //d, cur node, source
		dist[special[i]] = 0;
		source[special[i]] = special[i];
	}
	while(!pq.empty()){
		ll d = pq.top().first;
		ll x = pq.top().second.first;
		ll Source = pq.top().second.second;
		pq.pop();
		if(d != dist[x]){
			continue;
		}
		for(auto u : v[x]){
			if(dist[u.second] == -1 || d + u.first < dist[u.second]){
				pq.push({d + u.first,{u.second,Source}});
				dist[u.second] = d + u.first;
				source[u.second] = Source;
			}
		}
	}
	ll A = -1, B = -1, minimum = 1e18;
	for(auto u : edges){
		ll a = u.second.first;
		ll b = u.second.second;
		ll c = u.first;
		if(dist[a] == -1 || dist[b] == -1 || source[a] == source[b]){
			continue;
		}
		if(dist[a] + c + dist[b] <= minimum){
			minimum = dist[a] + c + dist[b];
			A = source[a];
			B = source[b];
		}
	}
	
	ll sum = 1e18;
	//Case 1: First Pair (A, B) fixed, Second pair (C, D) unknown
	memset(dist,-1,sizeof(dist));
	memset(source,-1,sizeof(source));
	for(ll i = 0;i < K;i++){
		if(special[i] != A && special[i] != B){
			//cout<<"SOURCE: "<<special[i]<<'\n';
			pq.push({0,{special[i],special[i]}}); //d, cur node, source
			dist[special[i]] = 0;
			source[special[i]] = special[i];
		}
	}
	while(!pq.empty()){
		ll d = pq.top().first;
		ll x = pq.top().second.first;
		ll Source = pq.top().second.second;
		pq.pop();
		if(x == A || x == B) continue;
		if(d != dist[x]){
			continue;
		}
		for(auto u : v[x]){
			if(u.second == A || u.second == B) continue;
			if(dist[u.second] == -1 || d + u.first < dist[u.second]){
				pq.push({d + u.first,{u.second,Source}});
				dist[u.second] = d + u.first;
				source[u.second] = Source;
			}
		}
	}
	ll C = -1, D = -1, minimum2 = 1e18;
	for(auto u : edges){
		ll a = u.second.first;
		ll b = u.second.second;
		ll c = u.first;
		if(dist[a] == -1 || dist[b] == -1 || source[a] == source[b]){
			continue;
		}
		if(dist[a] + c + dist[b] <= minimum2){
			minimum2 = dist[a] + c + dist[b];
			C = source[a];
			D = source[b];
		}
	}
	sum = min(sum,minimum + minimum2);
	//cout<<"Case 1 SUM: "<<minimum + minimum2<<" "<<A<<" with "<<B<<" ,  "<<C<<" with "<<D<<'\n';
	
	//Case 2: Half of both pairs are known (A, C) and (B, D)
	memset(distA,-1,sizeof(distA));
	pq.push({0,{A,A}}); //d, cur node, source
	distA[A] = 0;
	source[A] = A;
	while(!pq.empty()){ //dikjstra from A
		ll d = pq.top().first;
		ll x = pq.top().second.first;
		ll Source = pq.top().second.second;
		pq.pop();
		if(d != distA[x]){
			continue;
		}
		for(auto u : v[x]){
			if(distA[u.second] == -1 || d + u.first < distA[u.second]){
				pq.push({d + u.first,{u.second,Source}});
				distA[u.second] = d + u.first;
				source[u.second] = Source;
			}
		}
	}
	pair<ll,ll> C1 = {-1,1e18}, C2 = {-1,1e18}; //first-best choice for C, second-best choice for C
	for(ll i = 0;i < K;i++){
		ll x = special[i];
		if(distA[x] == -1 || x == A || x == B) continue;
		if(distA[x] <= C1.second){
			C2 = C1;
			C1 = {x,distA[x]};
		}else if(distA[x] <= C2.second){
			C2 = {x,distA[x]};
		}
	}
	
	memset(distB,-1,sizeof(distB));
	pq.push({0,{B,B}}); //d, cur node, source
	distB[B] = 0;
	source[B] = B;
	while(!pq.empty()){ //dikjstra from B
		ll d = pq.top().first;
		ll x = pq.top().second.first;
		ll Source = pq.top().second.second;
		pq.pop();
		if(d != distB[x]){
			continue;
		}
		for(auto u : v[x]){
			if(distB[u.second] == -1 || d + u.first < distB[u.second]){
				pq.push({d + u.first,{u.second,Source}});
				distB[u.second] = d + u.first;
				source[u.second] = Source;
			}
		}
	}
	
	for(ll i = 0;i < K;i++){
		ll D = special[i];
		if(D == A || D == B || C1.first == -1 || distB[D] == -1) continue;
		if(D == C1.first){
			if(C2.first == -1) continue;
			sum = min(sum,C2.second + distB[D]);
			//cout<<"Case 2 SUM: "<<C2.second + distB[D]<<" "<<A<<" with "<<C2.first<<" ,  "<<B<<" with "<<D<<'\n';
		}else{
			sum = min(sum,C1.second + distB[D]);
			//cout<<"Case 2 SUM: "<<C1.second + distB[D]<<" "<<A<<" with "<<C1.first<<" ,  "<<B<<" with "<<D<<'\n';
		}
	}
	cout<<sum<<'\n';
}

Compilation message

RelayMarathon.cpp: In function 'int main()':
RelayMarathon.cpp:94:5: warning: variable 'C' set but not used [-Wunused-but-set-variable]
   94 |  ll C = -1, D = -1, minimum2 = 1e18;
      |     ^
RelayMarathon.cpp:94:13: warning: variable 'D' set but not used [-Wunused-but-set-variable]
   94 |  ll C = -1, D = -1, minimum2 = 1e18;
      |             ^

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5724 KB Output is correct
2 Correct 2 ms 5980 KB Output is correct
3 Correct 2 ms 5724 KB Output is correct
4 Correct 2 ms 5724 KB Output is correct
5 Correct 1 ms 5724 KB Output is correct
6 Correct 2 ms 5784 KB Output is correct
7 Correct 2 ms 5976 KB Output is correct
8 Correct 2 ms 6232 KB Output is correct
9 Correct 1 ms 5764 KB Output is correct
10 Correct 1 ms 5720 KB Output is correct
11 Correct 2 ms 5724 KB Output is correct
12 Correct 2 ms 5720 KB Output is correct
13 Correct 2 ms 5980 KB Output is correct
14 Correct 2 ms 5980 KB Output is correct
15 Correct 2 ms 6232 KB Output is correct
16 Correct 1 ms 5724 KB Output is correct
17 Correct 2 ms 5976 KB Output is correct
18 Correct 2 ms 5724 KB Output is correct
19 Correct 2 ms 6028 KB Output is correct
20 Correct 2 ms 5764 KB Output is correct
21 Correct 2 ms 5980 KB Output is correct
22 Correct 1 ms 5728 KB Output is correct
23 Correct 2 ms 5980 KB Output is correct
24 Correct 1 ms 5724 KB Output is correct
25 Correct 1 ms 5724 KB Output is correct
26 Correct 2 ms 5724 KB Output is correct
27 Correct 2 ms 5764 KB Output is correct
28 Correct 2 ms 5980 KB Output is correct
29 Correct 2 ms 5980 KB Output is correct
30 Correct 2 ms 5980 KB Output is correct

Subtask #2
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5724 KB Output is correct
2 Correct 2 ms 5980 KB Output is correct
3 Correct 2 ms 5724 KB Output is correct
4 Correct 2 ms 5724 KB Output is correct
5 Correct 1 ms 5724 KB Output is correct
6 Correct 2 ms 5784 KB Output is correct
7 Correct 2 ms 5976 KB Output is correct
8 Correct 2 ms 6232 KB Output is correct
9 Correct 1 ms 5764 KB Output is correct
10 Correct 1 ms 5720 KB Output is correct
11 Correct 2 ms 5724 KB Output is correct
12 Correct 2 ms 5720 KB Output is correct
13 Correct 2 ms 5980 KB Output is correct
14 Correct 2 ms 5980 KB Output is correct
15 Correct 2 ms 6232 KB Output is correct
16 Correct 1 ms 5724 KB Output is correct
17 Correct 2 ms 5976 KB Output is correct
18 Correct 2 ms 5724 KB Output is correct
19 Correct 2 ms 6028 KB Output is correct
20 Correct 2 ms 5764 KB Output is correct
21 Correct 2 ms 5980 KB Output is correct
22 Correct 1 ms 5728 KB Output is correct
23 Correct 2 ms 5980 KB Output is correct
24 Correct 1 ms 5724 KB Output is correct
25 Correct 1 ms 5724 KB Output is correct
26 Correct 2 ms 5724 KB Output is correct
27 Correct 2 ms 5764 KB Output is correct
28 Correct 2 ms 5980 KB Output is correct
29 Correct 2 ms 5980 KB Output is correct
30 Correct 2 ms 5980 KB Output is correct
31 Correct 2 ms 5724 KB Output is correct
32 Correct 2 ms 5980 KB Output is correct
33 Correct 2 ms 5980 KB Output is correct
34 Correct 1 ms 5724 KB Output is correct
35 Correct 1 ms 5724 KB Output is correct
36 Correct 3 ms 6260 KB Output is correct
37 Correct 5 ms 6492 KB Output is correct
38 Correct 2 ms 5976 KB Output is correct
39 Correct 21 ms 13340 KB Output is correct
40 Correct 7 ms 7444 KB Output is correct
41 Correct 2 ms 5980 KB Output is correct
42 Correct 6 ms 7700 KB Output is correct
43 Correct 3 ms 6232 KB Output is correct
44 Correct 2 ms 5980 KB Output is correct
45 Correct 2 ms 5724 KB Output is correct
46 Correct 25 ms 14192 KB Output is correct
47 Correct 5 ms 7064 KB Output is correct
48 Correct 20 ms 13236 KB Output is correct
49 Correct 22 ms 13340 KB Output is correct
50 Correct 2 ms 5976 KB Output is correct
51 Correct 2 ms 5976 KB Output is correct
52 Correct 2 ms 5980 KB Output is correct
53 Correct 13 ms 9796 KB Output is correct
54 Correct 23 ms 13572 KB Output is correct
55 Correct 2 ms 5980 KB Output is correct
56 Correct 2 ms 5724 KB Output is correct
57 Correct 2 ms 5980 KB Output is correct
58 Correct 29 ms 14632 KB Output is correct
59 Correct 2 ms 5724 KB Output is correct
60 Correct 2 ms 5980 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 41 ms 13056 KB Output is correct
2 Correct 4 ms 6488 KB Output is correct
3 Correct 1388 ms 245748 KB Output is correct
4 Correct 701 ms 105140 KB Output is correct
5 Correct 127 ms 25588 KB Output is correct
6 Correct 95 ms 19708 KB Output is correct
7 Correct 190 ms 26204 KB Output is correct
8 Correct 45 ms 12732 KB Output is correct
9 Correct 98 ms 18092 KB Output is correct
10 Correct 61 ms 14532 KB Output is correct
11 Correct 1474 ms 244908 KB Output is correct
12 Correct 88 ms 15616 KB Output is correct
13 Correct 482 ms 70104 KB Output is correct
14 Correct 140 ms 27976 KB Output is correct
15 Correct 1460 ms 244976 KB Output is correct
16 Correct 31 ms 11528 KB Output is correct
17 Correct 1086 ms 164276 KB Output is correct
18 Correct 4 ms 6808 KB Output is correct
19 Correct 1617 ms 249380 KB Output is correct
20 Correct 191 ms 26604 KB Output is correct
21 Correct 118 ms 24492 KB Output is correct
22 Correct 53 ms 15104 KB Output is correct
23 Correct 16 ms 9728 KB Output is correct
24 Correct 1070 ms 183564 KB Output is correct
25 Correct 85 ms 18276 KB Output is correct
26 Correct 44 ms 13324 KB Output is correct
27 Correct 67 ms 16376 KB Output is correct
28 Correct 11 ms 8208 KB Output is correct
29 Correct 134 ms 26868 KB Output is correct
30 Correct 279 ms 50164 KB Output is correct

Subtask #4
58.0 / 58.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 5724 KB Output is correct
2 Correct 2 ms 5980 KB Output is correct
3 Correct 2 ms 5724 KB Output is correct
4 Correct 2 ms 5724 KB Output is correct
5 Correct 1 ms 5724 KB Output is correct
6 Correct 2 ms 5784 KB Output is correct
7 Correct 2 ms 5976 KB Output is correct
8 Correct 2 ms 6232 KB Output is correct
9 Correct 1 ms 5764 KB Output is correct
10 Correct 1 ms 5720 KB Output is correct
11 Correct 2 ms 5724 KB Output is correct
12 Correct 2 ms 5720 KB Output is correct
13 Correct 2 ms 5980 KB Output is correct
14 Correct 2 ms 5980 KB Output is correct
15 Correct 2 ms 6232 KB Output is correct
16 Correct 1 ms 5724 KB Output is correct
17 Correct 2 ms 5976 KB Output is correct
18 Correct 2 ms 5724 KB Output is correct
19 Correct 2 ms 6028 KB Output is correct
20 Correct 2 ms 5764 KB Output is correct
21 Correct 2 ms 5980 KB Output is correct
22 Correct 1 ms 5728 KB Output is correct
23 Correct 2 ms 5980 KB Output is correct
24 Correct 1 ms 5724 KB Output is correct
25 Correct 1 ms 5724 KB Output is correct
26 Correct 2 ms 5724 KB Output is correct
27 Correct 2 ms 5764 KB Output is correct
28 Correct 2 ms 5980 KB Output is correct
29 Correct 2 ms 5980 KB Output is correct
30 Correct 2 ms 5980 KB Output is correct
31 Correct 2 ms 5724 KB Output is correct
32 Correct 2 ms 5980 KB Output is correct
33 Correct 2 ms 5980 KB Output is correct
34 Correct 1 ms 5724 KB Output is correct
35 Correct 1 ms 5724 KB Output is correct
36 Correct 3 ms 6260 KB Output is correct
37 Correct 5 ms 6492 KB Output is correct
38 Correct 2 ms 5976 KB Output is correct
39 Correct 21 ms 13340 KB Output is correct
40 Correct 7 ms 7444 KB Output is correct
41 Correct 2 ms 5980 KB Output is correct
42 Correct 6 ms 7700 KB Output is correct
43 Correct 3 ms 6232 KB Output is correct
44 Correct 2 ms 5980 KB Output is correct
45 Correct 2 ms 5724 KB Output is correct
46 Correct 25 ms 14192 KB Output is correct
47 Correct 5 ms 7064 KB Output is correct
48 Correct 20 ms 13236 KB Output is correct
49 Correct 22 ms 13340 KB Output is correct
50 Correct 2 ms 5976 KB Output is correct
51 Correct 2 ms 5976 KB Output is correct
52 Correct 2 ms 5980 KB Output is correct
53 Correct 13 ms 9796 KB Output is correct
54 Correct 23 ms 13572 KB Output is correct
55 Correct 2 ms 5980 KB Output is correct
56 Correct 2 ms 5724 KB Output is correct
57 Correct 2 ms 5980 KB Output is correct
58 Correct 29 ms 14632 KB Output is correct
59 Correct 2 ms 5724 KB Output is correct
60 Correct 2 ms 5980 KB Output is correct
61 Correct 41 ms 13056 KB Output is correct
62 Correct 4 ms 6488 KB Output is correct
63 Correct 1388 ms 245748 KB Output is correct
64 Correct 701 ms 105140 KB Output is correct
65 Correct 127 ms 25588 KB Output is correct
66 Correct 95 ms 19708 KB Output is correct
67 Correct 190 ms 26204 KB Output is correct
68 Correct 45 ms 12732 KB Output is correct
69 Correct 98 ms 18092 KB Output is correct
70 Correct 61 ms 14532 KB Output is correct
71 Correct 1474 ms 244908 KB Output is correct
72 Correct 88 ms 15616 KB Output is correct
73 Correct 482 ms 70104 KB Output is correct
74 Correct 140 ms 27976 KB Output is correct
75 Correct 1460 ms 244976 KB Output is correct
76 Correct 31 ms 11528 KB Output is correct
77 Correct 1086 ms 164276 KB Output is correct
78 Correct 4 ms 6808 KB Output is correct
79 Correct 1617 ms 249380 KB Output is correct
80 Correct 191 ms 26604 KB Output is correct
81 Correct 118 ms 24492 KB Output is correct
82 Correct 53 ms 15104 KB Output is correct
83 Correct 16 ms 9728 KB Output is correct
84 Correct 1070 ms 183564 KB Output is correct
85 Correct 85 ms 18276 KB Output is correct
86 Correct 44 ms 13324 KB Output is correct
87 Correct 67 ms 16376 KB Output is correct
88 Correct 11 ms 8208 KB Output is correct
89 Correct 134 ms 26868 KB Output is correct
90 Correct 279 ms 50164 KB Output is correct
91 Correct 137 ms 17452 KB Output is correct
92 Correct 1569 ms 265008 KB Output is correct
93 Correct 208 ms 27992 KB Output is correct
94 Correct 976 ms 152616 KB Output is correct
95 Correct 5 ms 6808 KB Output is correct
96 Correct 5 ms 6856 KB Output is correct
97 Correct 306 ms 36724 KB Output is correct
98 Correct 108 ms 17148 KB Output is correct
99 Correct 100 ms 18996 KB Output is correct
100 Correct 1663 ms 282592 KB Output is correct
101 Correct 726 ms 106036 KB Output is correct
102 Correct 703 ms 103904 KB Output is correct
103 Correct 1087 ms 189520 KB Output is correct
104 Correct 1343 ms 244660 KB Output is correct
105 Correct 62 ms 13564 KB Output is correct
106 Correct 1121 ms 191224 KB Output is correct
107 Correct 400 ms 53892 KB Output is correct
108 Correct 180 ms 24720 KB Output is correct
109 Correct 11 ms 8976 KB Output is correct
110 Correct 53 ms 13328 KB Output is correct
111 Correct 198 ms 25336 KB Output is correct
112 Correct 1646 ms 281912 KB Output is correct
113 Correct 1620 ms 285320 KB Output is correct
114 Correct 180 ms 24692 KB Output is correct
115 Correct 585 ms 99580 KB Output is correct
116 Correct 1460 ms 260064 KB Output is correct
117 Correct 1075 ms 184776 KB Output is correct
118 Correct 964 ms 166536 KB Output is correct
119 Correct 1497 ms 244676 KB Output is correct
120 Correct 884 ms 136408 KB Output is correct