華爲機試 地鐵換乘問題（最短路徑算法）

1.題目描述

      描述: 已知2條地鐵線路，其中A爲環線，B爲東西向線路，線路都是雙向的。經過的站點名分別如下，兩條線交叉的換乘點用T1、T2表示。編寫程序，任意輸入兩個站點名稱，輸出乘坐地鐵最少需要經過的車站數量（含輸入的起點和終點，換乘站點只計算一次）。

       地鐵線A（環線）經過車站：A1 A2 A3 A4 A5 A6 A7 A8 A9 T1 A10 A11 A12 A13 T2 A14 A15 A16 A17 A18

       地鐵線B（直線）經過車站：B1 B2 B3 B4 B5 T1 B6 B7 B8 B9 B10 T2 B11 B12 B13 B14 B15

 

       輸入: 輸入兩個不同的站名

       輸出: 輸出最少經過的站數,含輸入的起點和終點，換乘站點只計算一次

2.解法（floyd最短路徑）

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#define MAX 35
using namespace std;


int D[MAX][MAX] =
{
/* A1 */ 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A2 */ 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A3 */    65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A4 */    65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A5 */    65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A6 */    65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A7 */    65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A8 */    65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A9 */    65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 65535,
/* A10*/    65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 65535,
/* A11*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A12*/    65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A13*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1,
/* A14*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1,
/* A15*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A16*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A17*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* A18*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B1 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B2 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B3 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B4 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B5 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 65535,
/* B6 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 65535,
/* B7 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B8 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B9 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535,
/* B10*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 65535, 65535, 65535, 65535, 65535, 65535, 1,
/* B11*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 1, 65535, 65535, 65535, 65535, 1,
/* B12*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535, 65535,
/* B13*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535, 65535,
/* B14*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 1, 65535, 65535,
/* B15*/ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 0, 65535, 65535,
/* T1 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 0, 65535,
/* T2 */ 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 1, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 65535, 1, 1, 65535, 65535, 65535, 65535, 65535, 0
};


int P[MAX][MAX];
string PATH[MAX] = {
"A1", "A2", "A3", "A4", "A5", "A6", "A7", "A8", "A9", "A10", "A11", "A12", "A13", "A14" ,"A15", "A16",
"A17", "A18", "B1", "B2", "B3", "B4", "B5", "B6", "B7", "B8", "B9", "B10", "B11", "B12", "B13", "B14", "B15", "T1", "T2" };
int main()
{
for (int i = 0; i < 35; ++i)
{
for (int j = 0; j < 35; ++j)
P[i][j] = j;          //最小路徑前驅矩陣初始化
}
for (int i = 0; i < 35; ++i)//Floyd最短距離算法
{
for (int j = 0; j < 35; ++j)
{
for (int k = 0; k < 35; ++k)
{
if (D[j][k] > D[j][i] + D[k][i])
{
D[j][k] = D[j][i] + D[k][i];
P[j][k] = P[j][i];
}
}
}
}

int m = 0, n = 0;
string begin, end;
cin >> begin >> end;
for (int i = 0; i < 35; ++i)
{
if (begin == PATH[i])
m = i;
if (end == PATH[i])
n = i;
}

while (m != n)
{
cout << PATH[m] << "->";
m = P[m][n];
}
cout << PATH[n] << endl;

return 0;
}