链接:https://oj.ahstu.cc/JudgeOnline/problem.php?id=2037
题意:
安科的夏天真是不一般的热,避免炎热,伍学长因此想为自己规划一个校园出行方案,使得从宿舍出发到校园的各个地方距离花费时间最短。我们已知校园一共有N个路口,标号为1的路口是宿舍所在地,2..N这N-1这几个标号分别是学校的N-1个地方,
M则表示安科共有M条路,N=M=0表示输入结束,接下来M行,每行有3个整数A,B,C(1<=A,B<=N,1<=C<=1000),表示在路口A与B之间有一条路,伍学长从A走到B花费时间C,伍学长来回用时相等,他现在想知道他分别到这N-1个路口的最小花费时间及步行方案
思路:
Dijkstra算法。
路径由Father数组记录每个位置最短路上的上一个结点。
每次成功松弛时,被松弛点的上一个结点便是用来松弛的点。
打印的时候用栈记录即可。
代码:
#include <iostream>
#include <memory.h>
#include <string>
#include <istream>
#include <sstream>
#include <vector>
#include <stack>
using namespace std;
const int MAXN = 110;
int n,m;
int Map[MAXN][MAXN];
int Dis[MAXN];
int Vis[MAXN];
int Father[MAXN];void init()
{for (int i = 1;i<=n;i++){Dis[i] = Map[1][i];Vis[i] = 0;Father[i] = 1;}Vis[1] = 1;
}void Dijkstra()
{init();for (int i = 1;i<=n;i++){int w = -1,small = 999999;for (int j = 1;j<=n;j++){if (Vis[j] == 0&&Dis[j] < small){small = Dis[w = j];}}Vis[w] = 1;for (int j = 1;j<=n;j++){if (Vis[j] == 0&&Dis[j] > Dis[w] + Map[w][j]){Father[j] = w;Dis[j] = Dis[w] + Map[w][j];}}}
}void Print_Path(int x)
{stack<int> Path;while (1){Path.push(x);if (Father[x] == 1)break;x = Father[x];}while (Path.size()){cout << "->" << Path.top();Path.pop();}cout << endl;
}int main()
{while (cin >> n >> m&&m){int l, r, v;for (int i = 1;i<=n;i++)for (int j = 1;j<=n;j++)if (i == j)Map[i][j] = 0;elseMap[i][j] = 999999;for (int i = 1; i <= m; i++){cin >> l >> r >>v;Map[l][r] = Map[r][l] = v;}Dijkstra();for (int i = 2;i<=n;i++){cout << Dis[i] << ' ';cout << 1;Print_Path(i);}}return 0;
}