algorithm/Graph/shortest_path_bellman_ford.cpp at master · drken1215/algorithm · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
//
// 単一始点最短路 (Bellman-Ford 法, 負辺あり, O(VE))
//
// verified:
//   AOJ Course - Single Source Shortest Path (Negative Edges)
//     https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_1_B&lang=ja
//
//   AtCoder ABC 061 D - Score Attack
//     https://atcoder.jp/contests/abc061/tasks/abc061_d
//


#include <bits/stdc++.h>
using namespace std;


// Edge
template<class T> struct Edge {
    int to;
    T weight;
    Edge(int t, T w) : to(t), weight(w) {}
};

// Graph
template<class T> struct Graph : vector<vector<Edge<T>>> {
    Graph() {}
    Graph(int N) : vector<vector<Edge<T>>>(N) {}
};

// Bellman-Ford
template<class T> struct BellmanFord {
    // input
    Graph<T> G;

    // results
    // unbounded[v] := whether the length of s-v path is unbounded
    // dp[v] := length of the shortest s-v path
    // prev[v] := previous node of node v on the shortest path
    bool exist_negative = false;
    vector<bool> unbounded;
    vector<T> dp;
    vector<int> prev;

    // constructor
    BellmanFord() {}
    BellmanFord(const Graph<T> &graph, int S) { init(graph, S); }
    void init(const Graph<T> &graph, int S) {
        G = graph;
        solve(S);
    }

    // find the shortest path from node S
    void solve(int S) {
        // init
        exist_negative = false;
        unbounded.assign(G.size(), false);
        dp.assign(G.size(), numeric_limits<T>::max());
        prev.assign(G.size(), -1);

        // bellman-Ford
        dp[S] = 0;
        for (int iter = 0; iter <= G.size()*2; ++iter) {
            for (int v = 0; v < G.size(); ++v) {
                if (dp[v] == numeric_limits<T>::max()) continue;
                for (const auto &e : G[v]) {
                    if (dp[e.to] > dp[v] + e.weight) {
                        dp[e.to] = dp[v] + e.weight;
                        prev[e.to] = v;
                        if (iter == G.size()*2) {
                            exist_negative = true;
                            unbounded[e.to] = true;
                        }
                    }
                }
            }
        }
    }

    // reconstruct the shortest path by using prev
    vector<int> reconstruct(int s, int t) {
        vector<int> res;
        int v = t;
        do {
            res.push_back(v);
            v = prev[v];
        } while (v != s && v != -1);
        res.push_back(s);
        reverse(res.begin(), res.end());
        return res;
    }
};


/*/////////////////////////////*/
// Examples
/*/////////////////////////////*/

void AOJ_Single_Source_Shortest_Path_Negative() {
    const long long INF = 1LL<<60;
    int N, M, s;
    cin >> N >> M >> s;
    Graph<long long> G(N);
    for (int i = 0; i < M; ++i) {
        int a, b, c;
        cin >> a >> b >> c;
        G[a].emplace_back(b, c);
    }

    BellmanFord<long long> bf(G, s);

    if (bf.exist_negative) cout << "NEGATIVE CYCLE" << endl;
    else {
        for (int v = 0; v < N; ++v) {
            if (bf.dp[v] < INF) cout << bf.dp[v] << endl;
            else cout << "INF" << endl;
        }
    }
}

void ABC_061_D() {
    int N, M;
    cin >> N >> M;
    Graph<long long> G(N);
    for (int i = 0; i < M; ++i) {
        int a, b, c;
        cin >> a >> b >> c;
        --a, --b;
        G[a].emplace_back(b, -c);
    }

    BellmanFord<long long> bf(G, 0);

    // ある負閉路 C が存在して、頂点 0 から C へ到達可能、かつ、C から頂点 N-1 へ到達可能
    if (bf.unbounded[N-1]) cout << "inf" << endl;
    else cout << -bf.dp[N-1] << endl;
}


int main() {
    //AOJ_Single_Source_Shortest_Path_Negative();
    ABC_061_D();
}