USACO 2.4 Bessie Come Home (comehome)_usaco2.4 comehome-优快云博客

本文链接：https://blog.youkuaiyun.com/damonhao/article/details/19910873

本文介绍了一个使用迪杰斯特拉算法求解从指定起点到其它各点最短路径的问题实例。通过C++实现，从一个特定点出发找到到达其他牧场的最短路径，并从中选择一条从A到Y的最短路径。

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//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;
}