hdu2962 Trucking_hdu2962 数据-优快云博客

本文链接：https://blog.youkuaiyun.com/qqchenjunwei/article/details/41050401

本文介绍了一种使用二分查找法解决含有两个变量同时变化的问题的方法，并通过一个具体的最短路径问题来演示该算法的实现过程。文章提供了一个完整的C++程序代码示例，展示了如何在给定节点间距离和高度限制条件下找到可达终点的最大高度及其对应的最短路径长度。

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算是简单题目，遇到有两个变量同时变化时，一般的做法是二分一个变量，求另外一个变量。

#include <iostream>
#include <cstdio>
#include <cstring>

using namespace std;

const int M = 1005;
const int inf = 9999999;

int dist[M][M];
int hight[M][M];
int s, e, maxn, minn, len;
int n, m, ans, Case= 1, mid;

void init() {

    minn = inf;
    ans = -1;
    len = inf;
    for(int i = 1; i <= n; i++) {

        for(int j = 1; j <= n; j++){

            dist[i][j] = inf;
            hight[i][j] = 0;
        }
    }
}

void input() {

    int x, y, h, d;
     for(int i = 0; i < m; i++) {

            scanf("%d%d%d%d", &x, &y, &h, &d);
                dist[x][y] = dist[y][x] = d;
            if(h == -1){
                hight[x][y] = hight[y][x] = inf;

            }else {
                    hight[x][y] = hight[y][x] = h;
            }
            if(h != -1)
            minn = min(h, minn);
        }
    scanf("%d%d%d", &s,&e, &maxn);
    if(Case > 1)
            printf("\n");
}

int Dijstra(int mid) {

    int dis[M];
    int vist[M];
    int index, mmin;
    for(int i = 1; i <= n; i++) {

       if(hight[s][i] >= mid){

            dis[i] = dist[s][i];
        }else {

           dis[i] = inf;
       }
        vist[i] = 0;
    }
    dis[s] = 0;
    vist[s] = 1;
    for(int k = 0; k <= n; k++) {

        mmin = inf;
        for(int i = 1; i <= n; i++) {

            if(!vist[i] &&dis[i] < mmin) {

                mmin = dis[i];
                index = i;
            }
        }
        if(mmin == inf)
            break;
        vist[index] = 1;
        for(int i = 1; i <= n; i++) {

            if(!vist[i] && dis[i] > dis[index] + dist[index][i] && hight[index][i] >= mid) {

                dis[i] = dis[index] + dist[index][i];
            }
        }
    }

   return dis[e];
}

void work() {

    int temp;
     mid = (maxn + minn)/2;
    while(maxn >= minn) {

        temp = Dijstra(mid);
        if(temp != inf){
            ans = mid;
            len = temp;
            minn = mid + 1;

        }else {

            maxn = mid - 1;
        }
         mid = (maxn + minn)/2;
    }

}

void output() {

     printf("Case %d:\n", Case++);
    if(ans != -1) {

   printf("maximum height = %d\n", ans);
   printf("length of shortest route = %d\n", len);

    }else {

        printf("cannot reach destination\n");
    }
}

int main()
{
    while(scanf("%d%d", &n, &m) != EOF && (n || m)) {
        init();
        input();
        work();
        output();
    }
    return 0;
}