USACO 2.4 Bessie Come Home (comehome)

//Main idea
//Calculate the shortest path from 'Z' to ohter pastures by  Dijkstra algorithm;
//And then choose shortest path among 'A' to 'Y';

/*
ID: haolink1
PROG: comehome
LANG: C++
*/

//#include <iostream>
#include <fstream>

const int INF = 52 * 1000 + 1;
int min_path[52];
bool is_remove[52];
int dist[52][52];
using namespace std;

bool IsCapital(char x){
if(x >= 'A' && x <= 'Z')
return true;
else return false;
}

int ExtractMin(){
int min_index = -1;
int min = INF;
for(int i = 0; i < 52; i++){
if(min > min_path[i] && is_remove[i] == 0){
min = min_path[i];
min_index = i;
}
}
if(min_index >= 0)
is_remove[min_index] =1;
return min_index;
}

void Relax(int x,int y){
if(min_path[y] > min_path[x] + dist[x][y])
min_path[y] = min_path[x] + dist[x][y];
}

void Dijkstra(){
for(short i = 0; i < 52; i++){
min_path[i] = INF;
}
min_path[25] = 0;
while(1){
int index = ExtractMin();
if(index < 0)
break;
for(int i = 0; i < 52; i++){
if(dist[index][i] < INF ){
Relax(index,i);
}
}
}
}

int main(){
for(short i = 0; i < 52; i++ ){
for(short j = 0; j < 52; j++){
dist[i][j] = INF;//Note dist[i][i] is also INF and it will be used in Dijkstra;
}
}
int num = 0;
ifstream fin("comehome.in");
fin >> num;
for(int i = 0; i < num; i++){
int x, y;
char x_char,y_char;
int dis;
fin >> x_char >> y_char >> dis;
if(IsCapital(x_char)){
x = x_char-'A';
}else
x = x_char - 'a' + 26;
if(IsCapital(y_char))
y = y_char-'A';
else
y = y_char- 'a' + 26;
if(dis < dist[x][y] && x != y)//For each path between two pastures, we only take the shortest;
dist[x][y] = dist[y][x] = dis;
}
Dijkstra();
int min = INF;
int index = -1;
for(int i = 0; i < 25; i++){
if(min_path[i] < min){
min = min_path[i];
index = i;
}
}
char cow = 'A' + index;
ofstream fout("comehome.out");
fout << cow <<" "<< min << endl;
return 0;
}