Codeforces 1076D Edge Deletion (最短路 + dfs)

先用Dijkstra计算出1到i的最短路d[i]。再dfs时如果 d[u] + w == d[v] 时就一直继续向下搜索。这些边都可以保留

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<map>
#include<queue>
#include<vector>
#include<string>
#include<fstream>
using namespace std;
#define rep(i, a, n) for(int i = a; i <= n; ++ i);
#define per(i, a, n) for(int i = n; i >= a; -- i);
typedef long long ll;
typedef pair<ll, int> PII;
const int N = 300100;
const int mod = 998244353;
const double Pi = acos(- 1.0);
const ll INF = 1e18;
const int G = 3, Gi = 332748118;
ll qpow(ll a, ll b) { ll res = 1; while(b){ if(b & 1) res = (res * a) % mod; a = (a * a) % mod; b >>= 1;} return res; }
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return a * b / gcd(a, b);}
bool cmp(int a, int b){ return a > b;}
//

int n, m, k;
int head[N], cnt = 0;
int nxt[N << 1], to[N << 1]; ll c[N << 1];
bool vis[N]; 
ll d[N];
vector<int> res;
map<ll, int> mp;

inline void add(ll u, ll v, ll w){
    to[cnt] = v, c[cnt] = w, nxt[cnt] = head[u], head[u] = cnt ++;
    to[cnt] = u, c[cnt] = w, nxt[cnt] = head[v], head[v] = cnt ++;
}

void Dijkstra(int st){
    priority_queue<PII, vector<PII>, greater<PII> > q;
    for(int i = 0; i <= n + 1; ++ i) d[i] = INF;
    d[st] = 0;
    q.push(PII(0, st));
    while(q.size()){
        int u = q.top().second; ll w1 = q.top().first ; q.pop();
        if(w1 != d[u]) continue;
        for(int i = head[u]; i != -1; i = nxt[i]){
            int v = to[i]; ll w2 = c[i];
            if(d[v] > d[u] + w2){
                d[v] = d[u] + w2;
                q.push(PII(d[v], v));
            }
        }
    }
}


void dfs(ll u){
    for(int i =  head[u]; i != -1; i = nxt[i]){
        ll v = to[i]; ll w = c[i];
        if(vis[v]) continue;
        if(d[u] + w == d[v]){
            vis[v] = true;
            res.push_back(mp[u * N + v]);
            dfs(v);
        }
    }
}


int main()
{
    scanf("%d%d%d",&n,&m,&k);
    cnt = 0;
    for(int i = 0; i <= n; ++ i) vis[i] = false, head[i] = -1;
    for(int i = 1; i <= m; ++ i){
        ll x, y, z; scanf("%lld%lld%lld",&x,&y,&z);
        add(x, y, z);
        mp[x * N + y] = mp[y * N + x] = i;
    }
    Dijkstra(1);
    vis[1] = true;
    dfs(1);
    int tt = res.size();
    printf("%d\n",min(tt, k));
    if(tt < k){
        for(int i = 0; i < tt; ++ i) printf("%d ",res[i]);
        int num = k - tt;
        for(int i = 1; i <= n; ++ i){
            if(num <= 0) break;
            if(!vis[i]){
                if(num == 1) printf("%d\n",i);
                else printf("%d ",i);
                num --;
                vis[i] = true;
            }
        }
    }
    else{
        for(int i = 0; i < k; ++ i){
            printf("%d",res[i]);
            if(i == k - 1) printf("\n");
            else printf(" ");
        }
    }
    return 0;
}