下列Dijkstra算法,假设图graph中顶点数v、边数e,则程序的时间复杂度为( )。
typedef struct Edge {
int in, out; // 从下标in顶点到下标out顶点的边
int len; // 边长度
struct Edge * next;
} Edge;
// v: 顶点个数,graph: 出边邻接表,start: 起点下标,dis: 输出每个顶点的最短距离
void dijkstra(int v, Edge * graph[], int start, int * dis) {
const int MAX_DIS = 0x7ffffff;
for (int i = 0; i < v; i++)
dis[i] = MAX_DIS;
dis[start] = 0;
int * visited = new int[v];
for (int i = 0; i < v; i++)
visited[i] = 0;
visited[start] = 1;
for (int t = 0; ; t++) {
int min = MAX_DIS, minv = -1;
for (int i = 0; i < v; i++) {
if (visited[i] == 0 && min > dis[i]) {
min = dis[i];
minv = i;
}
}
if (minv < 0)
break;
visited[minv] = 1;
for (Edge * e = graph[minv]; e != NULL; e = e->next)
if (dis[e->out] > e->len)
dis[e->out] = e->len;
}
delete[] visited;
}
( O(v^2) )
( O(v \log v + e) )
( O((v + e) \log v) )
( O(v + e) )