Data Structures and Algorithms7-25—

我的Data Structures and Algorithms代码仓：https://github.com/617076674/Data-Structures-and-Algorithms

原题链接：https://pintia.cn/problem-sets/16/problems/687

题目描述：

知识点：最短路径、SPFA算法

思路：对每个点为起点做SPFA算法

期望时间复杂度是O(kMN)，其中k是一个常数，在很多情况下k不超过2，M是图中的边数，可见这个算法异常高效，并且经常性地优于堆优化的Dijkstra算法。空间复杂度是O(N + M)。

C++代码：

#include<iostream>
#include<vector>
#include<queue>using namespace std;struct node{int v, len;node(int _v, int _len){v = _v;len = _len;}
};int N, M, v1, v2, len, INF = 1000000000;
vector<node> graph[101];
int d[101], countInq[101];
bool inq[101];
int minIndex, minLen = INF;bool spfa(int s);int main(){scanf("%d %d", &N, &M);for(int i = 0; i < M; i++){scanf("%d %d %d", &v1, &v2, &len);graph[v1].push_back(node(v2, len));graph[v2].push_back(node(v1, len));}for(int i = 1; i <= N; i++){spfa(i);int maxLen = 0;for(int j = 1; j <= N; j++){if(d[j] > maxLen){maxLen = d[j];}}if(maxLen != INF){if(maxLen < minLen){minLen = maxLen;minIndex = i;}}}if(minLen == INF){printf("0\n");return 0;}printf("%d %d\n", minIndex, minLen);return 0;
}bool spfa(int s){fill(d + 1, d + N + 1, INF);fill(countInq + 1, countInq + N + 1, 0);fill(inq + 1, inq + N + 1, false);d[s] = 0;queue<int> q;q.push(s);countInq[s]++;inq[s] = true;while(!q.empty()){int u = q.front();q.pop();inq[u] = false;for(int i = 0; i < graph[u].size(); i++){int v = graph[u][i].v;int len = graph[u][i].len;if(d[u] + len < d[v]){d[v] = d[u] + len;if(!inq[v]){q.push(v);countInq[v]++;inq[v] = true;if(countInq[v] > N - 1){return false;}}}}}return true;
}

C++解题报告：

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Data Structures and Algorithms7-25——Harry Potter's Exam

思路：对每个点为起点做SPFA算法

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