5.8 每日一题题解

一个顶俩

• 题目链接：https://cometoj.com/contest/81/problem/F?problem_id=4270

涉及知识点：

• bfs/最短路

solution：

• (做法较多，这里提两种容易理解的做法：)
• (做法1，直接bfs，想象成一个图)
• (将每一个字符串的首位和末位相连，比如bcde，就可以理解成b到e连一条线)
• (那么题目就变成了求a到b最短需要走几条路，直接bfs即可)
• (那显然做法2也出来了，直接求a到所有点的最短路，如果a到b的距离是inf，则输出-1)

BFSstd:

#include<bits/stdc++.h>
using namespace std;
#define ll long long 
const int maxn = 105;
struct node{
   int x,w;
};
vector<int> v[maxn];
int flag[maxn];
map<char,int> mp;
int ans = -1;
void bfs(int x){
    queue<node> q;
    q.push(node{x,0});
    flag[1] = 1;
    while(!q.empty()){
        node now = q.front();
        q.pop();
        if(now.x == 2){
            ans = now.w;
            break ;
        }
        int siz = v[now.x].size();
        for(int i=0;i<siz;i++){
            if(flag[v[now.x][i]] == 0){
                flag[v[now.x][i]] = 1;
                q.push(node{v[now.x][i] , now.w + 1});
            }
        }
    }
    return ;
}
int main()
{
    int n,cnt = 2;
    string s;
	char a,b;
	cin>>a>>b;
	mp[a] = 1,mp[b] = 2;
	cin>>n;
	for(int i=1;i<=n;i++){
	    cin>>s;
	    if(mp[s[0]] == 0){
	        mp[s[0]] = ++cnt;
	    }
	    if(mp[s[3]] == 0){
	        mp[s[3]] = ++cnt;
	    }
	    int x = mp[s[0]] , y = mp[s[3]];
	    v[x].push_back(y);
	}
	bfs(1);
	cout<<ans<<endl;
	return 0;
}

最短路std:

#include<bits/stdc++.h>
using namespace std;
#define ll long long 
const int maxn = 105;
const int inf = 1e9;
struct node{
  int to;
  int w;
  friend bool operator <(node p1,node p2){
      return p1.w > p2.w;
  }
};

vector<node> v[maxn];
priority_queue<node> q;
int dis[maxn] , cnt = 2 ,n;
void spfa(int s){
    fill(dis+1,dis+1+cnt,inf);
    dis[s] = 0;
    while(!q.empty()) q.pop();
    q.push(node{s,0});
    while(!q.empty())
    {
        node x = q.top();q.pop();
        int k = x.to;
        int w = x.w;
        if(w > dis[k])
            continue;
        int siz = v[k].size();
        for(int i=0;i<siz;i++){
            if(dis[v[k][i].to] > w + v[k][i].w){
                dis[v[k][i].to] = w + v[k][i].w;
                q.push(node{v[k][i].to,dis[v[k][i].to]});
            }
        } 
    }
}
map<char,int> mp;
int main()
{
        string s;
	char a,b;
	cin>>a>>b;
	mp[a] = 1,mp[b] = 2;
	cin>>n;
	for(int i=1;i<=n;i++){
	    cin>>s;
	    if(mp[s[0]] == 0){
	        mp[s[0]] = ++cnt;
	    }
	    if(mp[s[3]] == 0){
	        mp[s[3]] = ++cnt;
	    }
	    int x = mp[s[0]] , y = mp[s[3]];
	    v[x].push_back(node{y,1});
	}
	spfa(1);
	int ans = dis[2];
	if(dis[2] == inf)
	    ans = -1;
	cout<<ans<<endl;
	return 0;
}