oj.uz

답안 #51747

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
51747 2018-06-20T23:21:37 Z hugo_pm Evacuation plan (IZhO18_plan) C++14
100 / 100
 1718 ms 49628 KB 
#include <bits/stdc++.h>
#define ford(i,n) for (int i = n-1; i >= 0; i--)
#pragma GCC diagnostic ignored "-Wunused-result"
using namespace std;

typedef pair<int, int> pii;
typedef pair<int, pii> Lien;
typedef priority_queue<pii, vector<pii>, greater<pii>> MinHeap;
const int INF = (INT_MAX - 3) / 2;
const int borneMax = (int)(1e5) + 5;

int nbNod, nbArc, nbCen, nbReq;
vector<pii> adj[borneMax];
vector<pii> mst[borneMax];
vector<int> cen;
vector<int> valeur(borneMax, INF);
bool exemple = false;
int pere[borneMax];
int depth[borneMax];
int ancetre[borneMax][18];
int minpoids[borneMax][18];

void lireEntree()
{
    scanf("%d%d", &nbNod, &nbArc);
    for (int ind = 0; ind < nbArc; ++ind)
    {
        int nod1, nod2, poids;
        scanf("%d%d%d", &nod1, &nod2, &poids);
        adj[nod1].push_back({nod2, poids});
        adj[nod2].push_back({nod1, poids});
    }

    scanf("%d", &nbCen);
    cen.resize(nbCen);
    for (int ind = 0; ind < nbCen; ++ind)
    {
        scanf("%d", &cen[ind]);
    }
}

void preparer()
{
    MinHeap dij;
    for (int nod : cen)
    {
        dij.push({nod, 0});
        valeur[nod] = 0;
    }
    while (! dij.empty())
    {
        auto e = dij.top();
        int nod = e.first, dis = e.second;
        dij.pop();
        if (dis > valeur[nod]) continue;
        for (pii obj : adj[nod])
        {
            int voisin = obj.first, poids = obj.second;
            if (dis + poids < valeur[voisin])
            {
                valeur[voisin] = dis + poids;
                dij.push({voisin, dis + poids});
            }
        }
    }
}

// Structure union-find optimisée en temps
// Complexité des opérations : O(log N)
class UnionFind
{
    public:
        UnionFind(int sz);
        int findRepr(int elem);
        bool unir(int a, int b);

    private:
        int taille;
        vector<int> repr, couverts;
};

UnionFind::UnionFind(int sz) : taille(sz), repr(sz+1), couverts(sz+1)
{
    for (int ind = 0; ind <= taille; ++ind)
    {
        repr[ind] = ind;
        couverts[ind] = 1;
    }
}

int UnionFind::findRepr(int elem)
{
    stack<int> vus; // (!) Consommation mémoire pour optimisation temporelle
    while (elem != repr[elem])
    {
        vus.push(elem);
        elem = repr[elem];
    }

    // Compression de chemin
    while (! vus.empty())
    {
        repr[vus.top()] = elem;
        vus.pop();
    }

    return elem;
}

// Retourne vrai si les deux élements ont été unis (n'étaient pas dans la même composante)
bool UnionFind::unir(int a, int b)
{
    a = findRepr(a);
    b = findRepr(b);
    if (a == b)
        return false;

    // Equilibrage : on insère le petit arbre dans le grand
    if (couverts[a] > couverts[b])
        swap(a, b);
    repr[a] = b;
    couverts[b] += couverts[a];

    return true;
}

void kruskal()
{
    vector<Lien> arcs;
    for (int ind = 1; ind <= nbNod; ++ind)
    {
        for (auto voiraw : adj[ind])
        {
            int voisin = voiraw.first;
            if (ind < voisin) arcs.push_back({-min(valeur[ind], valeur[voisin]), {ind, voisin}});
        }
    }
    sort(arcs.begin(), arcs.end());
    UnionFind uf(nbNod + 1);
    for (auto arc : arcs)
    {
        int poids = -arc.first, nod1 = arc.second.first, nod2 = arc.second.second;
        if (uf.unir(nod1, nod2))
        {
            mst[nod1].push_back({nod2, poids});
            mst[nod2].push_back({nod1, poids});
        }
    }
}

void genInfos()
{
    fill_n(&minpoids[0][0], borneMax * 18, INF);
    pere[1] = depth[1] = 0;
    stack<int> dfs;
    dfs.push(1);
    while (! dfs.empty())
    {
        int nod = dfs.top(); dfs.pop();
        for (pii vo : mst[nod]) if (vo.first != pere[nod])
        {
            pere[vo.first] = ancetre[vo.first][0] = nod;
            minpoids[vo.first][0] = vo.second;
            depth[vo.first] = depth[nod] + 1;
            dfs.push(vo.first);
        }
    }
    dfs.push(1);
    while (! dfs.empty())
    {
        int nod = dfs.top(); dfs.pop();
        for (int k = 1; (1 << k) <= depth[nod]; ++k)
        {
            ancetre[nod][k] = ancetre[ancetre[nod][k-1]][k-1];
            minpoids[nod][k] = min(minpoids[nod][k-1], minpoids[ancetre[nod][k-1]][k-1]);
        }
        for (pii vo : mst[nod]) if (vo.first != pere[nod])
        {
            dfs.push(vo.first);
        }
    }
}

int LCA(int u, int v)
{
    if (depth[u] > depth[v]) swap(u, v); // v plus bas que u
    ford(k, 18)
    {
        if (depth[v] - depth[u] >= (1 << k)) v = ancetre[v][k];
    }
    if (u == v) return u;
    ford(k, 18)
    {
        if (depth[u] < (1 << k)) continue;
        if (ancetre[u][k] != ancetre[v][k])
        {
            u = ancetre[u][k];
            v = ancetre[v][k];
        }
    }
    return pere[u];
}

int minTo(int nod, int par)
{
    int m = INF;
    ford(k, 18) if (depth[nod] - depth[par] >= (1 << k))
    {
        m = min(m, minpoids[nod][k]);
        nod = ancetre[nod][k];
    }
    return m;
}

int main()
{
    lireEntree();
    preparer();
    kruskal();
    genInfos();
    scanf("%d", &nbReq);
    for (int ind = 0; ind < nbReq; ++ind)
    {
        int nod1, nod2;
        scanf("%d%d", &nod1, &nod2);
        int lc = LCA(nod1, nod2);
        int m = min(minTo(nod1, lc), minTo(nod2, lc));
        printf("%d\n", m);
    }
}

Subtask #1
10.0 / 10.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 12408 KB Output is correct
2 Correct 14 ms 12664 KB Output is correct
3 Correct 14 ms 12664 KB Output is correct
4 Correct 12 ms 12408 KB Output is correct
5 Correct 14 ms 12664 KB Output is correct
6 Correct 14 ms 12664 KB Output is correct
7 Correct 13 ms 12536 KB Output is correct
8 Correct 15 ms 12536 KB Output is correct
9 Correct 15 ms 12664 KB Output is correct
10 Correct 14 ms 12664 KB Output is correct
11 Correct 14 ms 12664 KB Output is correct
12 Correct 14 ms 12664 KB Output is correct
13 Correct 15 ms 12664 KB Output is correct
14 Correct 14 ms 12664 KB Output is correct
15 Correct 14 ms 12664 KB Output is correct

Subtask #2
13.0 / 13.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 12408 KB Output is correct
2 Correct 14 ms 12664 KB Output is correct
3 Correct 14 ms 12664 KB Output is correct
4 Correct 12 ms 12408 KB Output is correct
5 Correct 14 ms 12664 KB Output is correct
6 Correct 14 ms 12664 KB Output is correct
7 Correct 13 ms 12536 KB Output is correct
8 Correct 15 ms 12536 KB Output is correct
9 Correct 15 ms 12664 KB Output is correct
10 Correct 14 ms 12664 KB Output is correct
11 Correct 14 ms 12664 KB Output is correct
12 Correct 14 ms 12664 KB Output is correct
13 Correct 15 ms 12664 KB Output is correct
14 Correct 14 ms 12664 KB Output is correct
15 Correct 14 ms 12664 KB Output is correct
16 Correct 354 ms 25936 KB Output is correct
17 Correct 1654 ms 46764 KB Output is correct
18 Correct 101 ms 15428 KB Output is correct
19 Correct 351 ms 30600 KB Output is correct
20 Correct 1624 ms 46848 KB Output is correct
21 Correct 482 ms 31072 KB Output is correct
22 Correct 291 ms 28200 KB Output is correct
23 Correct 1481 ms 46748 KB Output is correct
24 Correct 1333 ms 40892 KB Output is correct
25 Correct 1052 ms 37892 KB Output is correct
26 Correct 239 ms 29124 KB Output is correct
27 Correct 237 ms 29252 KB Output is correct
28 Correct 249 ms 30324 KB Output is correct
29 Correct 256 ms 30496 KB Output is correct
30 Correct 219 ms 29248 KB Output is correct

Subtask #3
12.0 / 12.0

# 결과 실행 시간 메모리 Grader output
1 Correct 13 ms 12408 KB Output is correct
2 Correct 13 ms 12536 KB Output is correct
3 Correct 16 ms 12408 KB Output is correct
4 Correct 15 ms 12408 KB Output is correct
5 Correct 13 ms 12536 KB Output is correct
6 Correct 13 ms 12412 KB Output is correct
7 Correct 13 ms 12536 KB Output is correct
8 Correct 13 ms 12408 KB Output is correct
9 Correct 13 ms 12408 KB Output is correct
10 Correct 13 ms 12408 KB Output is correct

Subtask #4
19.0 / 19.0

# 결과 실행 시간 메모리 Grader output
1 Correct 691 ms 32980 KB Output is correct
2 Correct 1487 ms 46408 KB Output is correct
3 Correct 1432 ms 46308 KB Output is correct
4 Correct 217 ms 27344 KB Output is correct
5 Correct 1234 ms 40400 KB Output is correct
6 Correct 1217 ms 40552 KB Output is correct
7 Correct 1180 ms 40528 KB Output is correct
8 Correct 1371 ms 46384 KB Output is correct
9 Correct 1478 ms 46352 KB Output is correct
10 Correct 1451 ms 46396 KB Output is correct
11 Correct 1353 ms 46376 KB Output is correct
12 Correct 1120 ms 40496 KB Output is correct
13 Correct 1089 ms 40480 KB Output is correct
14 Correct 1002 ms 37584 KB Output is correct
15 Correct 903 ms 37628 KB Output is correct
16 Correct 1020 ms 40592 KB Output is correct
17 Correct 1133 ms 40604 KB Output is correct
18 Correct 1444 ms 46392 KB Output is correct
19 Correct 207 ms 27348 KB Output is correct
20 Correct 1250 ms 40516 KB Output is correct
21 Correct 770 ms 38036 KB Output is correct
22 Correct 183 ms 28836 KB Output is correct
23 Correct 231 ms 28400 KB Output is correct
24 Correct 155 ms 28888 KB Output is correct
25 Correct 179 ms 28936 KB Output is correct
26 Correct 252 ms 28272 KB Output is correct
27 Correct 218 ms 27344 KB Output is correct
28 Correct 154 ms 28872 KB Output is correct
29 Correct 220 ms 27396 KB Output is correct
30 Correct 157 ms 28868 KB Output is correct
31 Correct 218 ms 27348 KB Output is correct

Subtask #5
46.0 / 46.0

# 결과 실행 시간 메모리 Grader output
1 Correct 12 ms 12408 KB Output is correct
2 Correct 14 ms 12664 KB Output is correct
3 Correct 14 ms 12664 KB Output is correct
4 Correct 12 ms 12408 KB Output is correct
5 Correct 14 ms 12664 KB Output is correct
6 Correct 14 ms 12664 KB Output is correct
7 Correct 13 ms 12536 KB Output is correct
8 Correct 15 ms 12536 KB Output is correct
9 Correct 15 ms 12664 KB Output is correct
10 Correct 14 ms 12664 KB Output is correct
11 Correct 14 ms 12664 KB Output is correct
12 Correct 14 ms 12664 KB Output is correct
13 Correct 15 ms 12664 KB Output is correct
14 Correct 14 ms 12664 KB Output is correct
15 Correct 14 ms 12664 KB Output is correct
16 Correct 354 ms 25936 KB Output is correct
17 Correct 1654 ms 46764 KB Output is correct
18 Correct 101 ms 15428 KB Output is correct
19 Correct 351 ms 30600 KB Output is correct
20 Correct 1624 ms 46848 KB Output is correct
21 Correct 482 ms 31072 KB Output is correct
22 Correct 291 ms 28200 KB Output is correct
23 Correct 1481 ms 46748 KB Output is correct
24 Correct 1333 ms 40892 KB Output is correct
25 Correct 1052 ms 37892 KB Output is correct
26 Correct 239 ms 29124 KB Output is correct
27 Correct 237 ms 29252 KB Output is correct
28 Correct 249 ms 30324 KB Output is correct
29 Correct 256 ms 30496 KB Output is correct
30 Correct 219 ms 29248 KB Output is correct
31 Correct 13 ms 12408 KB Output is correct
32 Correct 13 ms 12536 KB Output is correct
33 Correct 16 ms 12408 KB Output is correct
34 Correct 15 ms 12408 KB Output is correct
35 Correct 13 ms 12536 KB Output is correct
36 Correct 13 ms 12412 KB Output is correct
37 Correct 13 ms 12536 KB Output is correct
38 Correct 13 ms 12408 KB Output is correct
39 Correct 13 ms 12408 KB Output is correct
40 Correct 13 ms 12408 KB Output is correct
41 Correct 691 ms 32980 KB Output is correct
42 Correct 1487 ms 46408 KB Output is correct
43 Correct 1432 ms 46308 KB Output is correct
44 Correct 217 ms 27344 KB Output is correct
45 Correct 1234 ms 40400 KB Output is correct
46 Correct 1217 ms 40552 KB Output is correct
47 Correct 1180 ms 40528 KB Output is correct
48 Correct 1371 ms 46384 KB Output is correct
49 Correct 1478 ms 46352 KB Output is correct
50 Correct 1451 ms 46396 KB Output is correct
51 Correct 1353 ms 46376 KB Output is correct
52 Correct 1120 ms 40496 KB Output is correct
53 Correct 1089 ms 40480 KB Output is correct
54 Correct 1002 ms 37584 KB Output is correct
55 Correct 903 ms 37628 KB Output is correct
56 Correct 1020 ms 40592 KB Output is correct
57 Correct 1133 ms 40604 KB Output is correct
58 Correct 1444 ms 46392 KB Output is correct
59 Correct 207 ms 27348 KB Output is correct
60 Correct 1250 ms 40516 KB Output is correct
61 Correct 770 ms 38036 KB Output is correct
62 Correct 183 ms 28836 KB Output is correct
63 Correct 231 ms 28400 KB Output is correct
64 Correct 155 ms 28888 KB Output is correct
65 Correct 179 ms 28936 KB Output is correct
66 Correct 252 ms 28272 KB Output is correct
67 Correct 218 ms 27344 KB Output is correct
68 Correct 154 ms 28872 KB Output is correct
69 Correct 220 ms 27396 KB Output is correct
70 Correct 157 ms 28868 KB Output is correct
71 Correct 218 ms 27348 KB Output is correct
72 Correct 720 ms 31964 KB Output is correct
73 Correct 1418 ms 43776 KB Output is correct
74 Correct 1348 ms 44092 KB Output is correct
75 Correct 1718 ms 48828 KB Output is correct
76 Correct 1345 ms 43812 KB Output is correct
77 Correct 1300 ms 43400 KB Output is correct
78 Correct 1533 ms 49628 KB Output is correct
79 Correct 1508 ms 48792 KB Output is correct
80 Correct 1528 ms 47652 KB Output is correct
81 Correct 1527 ms 48356 KB Output is correct
82 Correct 1226 ms 41984 KB Output is correct
83 Correct 1201 ms 41700 KB Output is correct
84 Correct 1086 ms 38960 KB Output is correct
85 Correct 1016 ms 39584 KB Output is correct
86 Correct 1171 ms 42584 KB Output is correct
87 Correct 1360 ms 41700 KB Output is correct
88 Correct 1546 ms 47836 KB Output is correct
89 Correct 374 ms 28808 KB Output is correct
90 Correct 1473 ms 48172 KB Output is correct
91 Correct 893 ms 39892 KB Output is correct
92 Correct 242 ms 29980 KB Output is correct
93 Correct 347 ms 29784 KB Output is correct
94 Correct 239 ms 29740 KB Output is correct
95 Correct 236 ms 29868 KB Output is correct
96 Correct 352 ms 29264 KB Output is correct
97 Correct 382 ms 28468 KB Output is correct
98 Correct 239 ms 29640 KB Output is correct
99 Correct 375 ms 28368 KB Output is correct
100 Correct 237 ms 29924 KB Output is correct