1018 Public Bike Management (30 分)

• PAT原题
• 牛课网上的题目

牛课网的所有测试案例可以通过，但是可能会卡在PAT的第7个测试点。因为Note that if such a path is not unique, output the one that requires minimum number of bikes that we must take back to PBMC.即相同路径长度排序应该是先比较send较小的情况，其次在比较back较小的情况。

思路

• Dijkstra+dfs
• 使用Dijkstra搜得所有最短路径
• 遍历最短路径，选择send较小的，如果send相同，则选择back较小的

#include
#include
#include
using namespace std;

const int INF = 1000000000;
const int maxn = 501;
const int maxc = 100;

int G[maxn][maxn];

int bikes[maxn];
bool vis[maxn] = {0};
vector pre[maxn];
int d[maxn];

int c, n, s, m, perfect;

void dijkstra() {
    fill(d, d+maxn, INF);
    d[0] = 0;
    for (int i = 0; i <= n; ++i)
    {
        int u = -1;
        int MIN = INF;
        for (int j = 0; j <= n; ++j)
        {
            if(MIN > d[j] && !vis[j]) {
                u = j;
                MIN = d[j];
            }
        }

        if(u == -1) return; // the graph is not connected!
        vis[u] = true;

        for (int v = 0; v <= n; ++v)
        {
            if(G[u][v] != INF && !vis[v]) {
                //printf("d[%d]:%d ,d[%d]:%d + G[%d][%d]:%d\n", v, d[v], u, d[u], u, v, G[u][v]);
                if(d[v] > d[u]+G[u][v]) {
                    d[v] = d[u]+G[u][v];
                    pre[v].clear();
                    pre[v].push_back(u);
                }
                else if(d[v] == d[u]+G[u][v]) {
                    pre[v].push_back(u);
                }
            }
        }
    }
}

vector temp;
int optVal = INF;
int returnBike = 0;
vector bestPath;
void dfs(int s) {   
    if(s == 0) {
        int move = 0;
        int remain = 0;
        for (int i = temp.size()-1; i >= 0; --i)
        {
            if(temp[i] > 50) {
                remain += bikes[temp[i]] - perfect;
            }
            else {
                if(remain >= perfect - bikes[temp[i]]) {
                    remain -= (perfect - bikes[temp[i]]);
                }
                else {
                    move += perfect - bikes[temp[i]] - remain;
                    remain = 0;
                }
            }

        }
        if(move < optVal) {
            optVal = move;
            returnBike = remain;
            temp.push_back(0);
            bestPath = temp;
            temp.pop_back();
        }
        else if(move == optVal) {
            if(returnBike > remain) {
                optVal = move;
                returnBike = remain;
                temp.push_back(0);
                bestPath = temp;
                temp.pop_back();
            }
        }
        //temp.pop_back();
        return;
    }

    temp.push_back(s);
    for (int i = 0; i < pre[s].size(); ++i)
    {
        dfs(pre[s][i]);
    }
    temp.pop_back();
}

int main() {
    scanf("%d %d %d %d", &c, &n, &s, &m);
    perfect = c / 2;
    fill(G[0], G[0]+maxn*maxn, INF);
    for (int i = 1; i <= n; ++i)
    {
        scanf("%d", &bikes[i]);
    }

    for (int i = 0; i < m; ++i)
    {
        int start, end, edge;
        scanf("%d %d %d", &start, &end, &edge);
        G[start][end] = edge;
        G[end][start] = edge;
    }

    dijkstra();
    
    dfs(s);
    printf("%d ", optVal>0?optVal:0);
    for (int i = bestPath.size()-1; i >= 0; --i)
    {
        printf("%d", bestPath[i]);
        if(i != 0) printf("->");
    }
    printf(" %d\n", returnBike);
}