3种方法解决PAT_1003_最短路径

原题链接：http://www.patest.cn/contests/pat-a-practise/1003

典型的最短路径，也稍微变了下。

Dijkstra算法，麻烦，容易出错。

#include <iostream>

#include <fstream>

#include <algorithm>

#define INT_MAX 2147483647

#define INT_MIN (-2147483647 - 1)

using namespace std;

int path[500][500];

int d[500];

int exist[500];

int s, e;

int n, m;

int rescue[500];

int cnt[500];

int r[500];

void in()

{

ifstream cin("in.txt");

cin >> n >> m >> s >> e;

for (int i = 0; i < n; i++)

{

for (int j = 0; j < n; j++)

{

path[i][j] = INT_MAX;

}

}

for (int i = 0; i < n; i++)

{

cin >> rescue[i];

}

for (int i = 0; i < m; i++)

{

int a, b;

cin >> a >> b;

cin >> path[a];

path[b][a] = path[a][b];

}

}

int nearest()

{

int max = INT_MAX;

int index;

for (int i = 0; i < n; i++)

{

if (!exist[i] && d[i] < max)

{

max = d[i];

index = i;

}

}

return index;

}

void shortest()

{

exist[s] = 1;

for (int i = 0; i < n; i++)

{

d[i] = path[s][i];

cnt[i] = (d[i] == INT_MAX) ? 0 : 1;

r[i] = (d[i] == INT_MAX) ? INT_MIN : rescue[i] + rescue[s];

}

r[s] = rescue[s];

d[s] = 0;

cnt[s] = 1;

for (int i = 0; i < n - 1; i++)

{

int index = nearest();

exist[index] = 1;

for (int j = 0; j < n; j++)

{

if (exist[j] || path[index][j] == INT_MAX)

{

continue;

}

if (d[index] + path[index][j] < d[j])

{

d[j] = d[index] + path[index][j];

cnt[j] = cnt[index];

r[j] = r[index] + rescue[j];

}

else if (d[index] + path[index][j] == d[j])

{

cnt[j] += cnt[index];

r[j] = max(r[index] + rescue[j], r[j]);

}

}

}

cout << cnt[e] << ' ' << r[e] << endl;

}

int main(int argc, char **argv)

{

in();

shortest();

return 0;

}

[b]dfs深搜，最好的算法，简洁，复杂度高。

#include <iostream>

#include <fstream>

int d[500][500];

int visited[500];

int teams[500];

int n, m;

int s, e;

#define INF 0x7fffffff

int min_dist=INF;

int max_amount;

int cnt;

using namespace std;

void dfs(int start, int dist, int amount)

{

//下面的continue是剪枝

if (start == e)

{

if (dist < min_dist)

{

cnt = 1;

min_dist = dist;

max_amount = amount;

}

else if (dist == min_dist)

{

cnt++;

if (amount>max_amount)

{

max_amount = amount;

}

}

return;

}

for (int i = 0; i < n; i++)

{

if (d[start][i] != 0 && !visited[i])

{

visited[i] = 1;

dfs(i, dist+d[start][i], amount+teams[i]);

visited[i] = 0;

}

}



}

int main(int argc, char **argv)

{

ifstream cin("in.txt");

cin >> n >> m >> s >> e;

for (int i = 0; i < n; i++)

{

cin >> teams[i];

}

for (int i = 0; i < m; i++)

{

int a, b, c;

cin >> a >> b >> c;

d[a] = d[b][a] = c;

}

visited[s] = 1;

dfs(s, 0, teams[s]);

cout << cnt << ' ' << max_amount << endl;

return 0;

}

[b]bfs广搜，还行。不算麻烦。



#include <iostream>

#include <fstream>

#include <vector>

#include <cstring>

#define INF 0x7fffffff

using namespace std;

int teams[500];

int dist[500][500];

int n, m;

int s, e;

vector<vector<int> > ve;

int d[500];

int cnt = 0;

int max_amount = 0;

int min_dist = INF;

void bfs(int s, int e)

{

vector<int> data;

data.push_back(s);

data.push_back(0);

data.push_back(teams[s]);

ve.push_back(data);

int i = 0;

while (i<ve.size())

{

data = ve[i++];

int start, pathdist, amount;

start = data[0];

pathdist = data[1];

amount = data[2];

//下面两处continue是剪枝

if (start == e)

{

if (pathdist < min_dist)

{

min_dist = pathdist;

max_amount = amount;

cnt = 1;

}

else if (pathdist == min_dist)

{

cnt++;

if (amount>max_amount)

{

max_amount = amount;

}

}

continue;

}

else if (d[start] > 0 && pathdist > d[start])

{

continue;

}

d[start] = pathdist;

for (int i = 0; i < n; i++)

{

if (dist[start][i] != 0)

{

data.clear();

data.push_back(i);

data.push_back(d[start] + dist[start][i]);

data.push_back(amount + teams[i]);

ve.push_back(data);

}

}

}

cout << cnt << ' ' << max_amount << endl;

}

int main(int argc, char **argv)

{

ifstream cin("in.txt");

cin >> n >> m >> s >> e;

for (int i = 0; i < n; i++)

{

cin >> teams[i];

}

for (int i = 0; i < m; i++)

{

int a, b, c;

cin >> a >> b >> c;

dist[a][b] = dist[b][a] = c;

}

bfs(s, e);

return 0;

}