yukicoder No.160 - 最短経路のうち辞書順最小

問題

http://yukicoder.me/problems/no/160

日.

解法

Warshall-Floyd法で解きました.
最短経路を更新するさいになるべく小さい数字のノードを選んで, それを保存するようにすればOKです.

ソースコード

#include <iostream>
#include <vector>
using namespace std;

const int kINF = 1 << 28;
const int kMAX_N = 210;
const int kMAX_M = kMAX_N * (kMAX_N - 1) / 2;

int N, M, S, G;
int cost[kMAX_N][kMAX_N];
int next_node[kMAX_N][kMAX_N];

int a[kMAX_M], b[kMAX_M], c[kMAX_M];

void WarshallFloyd() {
    for (int k = 0; k < N; k++) {
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                if (cost[i][j] > cost[i][k] + cost[k][j]) {
                    cost[i][j] = cost[i][k] + cost[k][j];
                    next_node[i][j] = next_node[i][k];
                } else if (cost[i][j] == cost[i][k] + cost[k][j] && next_node[i][j] > next_node[i][k]) {
                    next_node[i][j] = next_node[i][k];
                }
            }
        }
    }
}

vector<int> RestoreRoute(int node, int goal) {
    vector<int> route;
    route.push_back(node);
    do {
        node = next_node[node][goal];
        route.push_back(node);
    } while (node != goal);
    return route;
}


void Solve() {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            if (i == j) {
                cost[i][j] = 0;
                next_node[i][j] = kINF;
            } else {
                cost[i][j] = kINF;
                next_node[i][j] = j;
            }
        }
    }

    for (int i = 0; i < M; i++) {
        cost[a[i]][b[i]] = cost[b[i]][a[i]] = c[i];
    }

    WarshallFloyd();

    vector<int> route = RestoreRoute(S, G);

    for (int i = 0; i < route.size(); i++) {
        cout << (i == 0 ? "" : " ") << route[i] << (i == route.size() - 1 ? "\n" : "");
    }
}

int main() {
    cin >> N >> M >> S >> G;

    for (int i = 0; i < M; i++) {
        cin >> a[i] >> b[i] >> c[i];
    }

    Solve();

    return 0;
}

感想

経路復元自体は典型問題ですけど, Warshall-Floyd法の経路復元に慣れてなかったので時間をかけてしまいました...