CF1076D Edge Deletion 最短路径树+bfs-CFANZ编程社区

题目描述

You are given an undirected connected weighted graph consisting of CF1076D Edge Deletion 最短路径树+bfs_#include

You have to erase some edges of the graph so that at most CF1076D Edge Deletion 最短路径树+bfs_#define_02

Your goal is to erase the edges in such a way that the number of good vertices is maximized.

输入输出格式

输入格式：

The first line contains three integers CF1076D Edge Deletion 最短路径树+bfs_i++_03

Then CF1076D Edge Deletion 最短路径树+bfs_i++_04

The given graph is connected (any vertex can be reached from any other vertex) and simple (there are no self-loops, and for each unordered pair of vertices there exists at most one edge connecting these vertices).

输出格式：

In the first line print CF1076D Edge Deletion 最短路径树+bfs_#define_05

In the second line print CF1076D Edge Deletion 最短路径树+bfs_#define_06

输入输出样例

输入样例#1：

复制

输出样例#1： 复制

2
1 2

输入样例#2： 复制

输出样例#2： 复制

2
3 2 

n 个点 m条边的连通图，只能最多保留K条边，最后要满足从1出发到其他节点最短距离不变的点最多，问方案（边）
先 dijkstra 一下，保存一下父亲和儿子节点以及边的编号；
最后 bfs一下，每次如果此时的 K>0，那么就选择改边；

#include
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#include
#include
#include
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#include
#include
//#include
//#pragma GCC optimize("O3")
using namespace std;
#define maxn 400005
#define inf 0x3f3f3f3f
#define INF 9999999999
#define rdint(x) scanf("%d",&x)
#define rdllt(x) scanf("%lld",&x)
#define rdult(x) scanf("%lu",&x)
#define rdlf(x) scanf("%lf",&x)
#define rdstr(x) scanf("%s",x)
typedef long long  ll;
typedef unsigned long long ull;
typedef unsigned int U;
#define ms(x) memset((x),0,sizeof(x))
const long long int mod = 1e9 + 7;
#define Mod 1000000000
#define sq(x) (x)*(x)
#define eps 1e-3
typedef pair pii;
#define pi acos(-1.0)
const int N = 1005;
#define REP(i,n) for(int i=0;i<(n);i++)
typedef pair pii;
inline ll rd() {
    ll x = 0;
    char c = getchar();
    bool f = false;
    while (!isdigit(c)) {
        if (c == '-') f = true;
        c = getchar();
    }
    while (isdigit(c)) {
        x = (x << 1) + (x << 3) + (c ^ 48);
        c = getchar();
    }
    return f ? -x : x;
}

ll gcd(ll a, ll b) {
    return b == 0 ? a : gcd(b, a%b);
}
ll sqr(ll x) { return x * x; }

/*ll ans;
ll exgcd(ll a, ll b, ll &x, ll &y) {
    if (!b) {
        x = 1; y = 0; return a;
    }
    ans = exgcd(b, a%b, x, y);
    ll t = x; x = y; y = t - a / b * y;
    return ans;
}
*/



ll qpow(ll a, ll b, ll c) {
    ll ans = 1;
    a = a % c;
    while (b) {
        if (b % 2)ans = ans * a%c;
        b /= 2; a = a * a%c;
    }
    return ans;
}

int n, m, k;
int head[maxn<<1];
struct node {
    int to;
    ll dis;
    node(){}
    node(int to,ll dis):to(to),dis(dis){}

    bool operator < (const node&rhs)const {
        return dis > rhs.dis;
    }
}edge[maxn<<1];

struct Edge {
    int id;
    int v; ll w;
    int nxt;

    Edge(){}
    Edge(int id,int v,int w):id(id),v(v),w(w){}

}EDGE[maxn<<1];

ll dis[maxn];
bool vis[maxn];
int fath[maxn], fathedge[maxn];
vectorG[maxn];

void addedge(int i, int u, int v, int w) {
    G[u].push_back(Edge(i, v, w)); G[v].push_back(Edge(i, u, w));
}

priority_queuepq;

void dijkstra() {
    memset(dis, 0x3f, sizeof(dis)); ms(vis);
    dis[1] = 0; vis[1] = 0;
    fath[1] = 1;
    pq.push(node(1, 0));
    while (!pq.empty()) {
        node tmp = pq.top(); pq.pop();
        int u = tmp.to;
        if (vis[u])continue; vis[u] = 1;
        for (int i = 0; i < G[u].size(); i++) {
            int v = G[u][i].v;
            if (dis[v] > dis[u] + (ll)G[u][i].w) {
                dis[v] = dis[u] + (ll)G[u][i].w;
                fath[v] = u; fathedge[v] = G[u][i].id;
                pq.push(node(v, (ll)dis[v]));
            }
        }
    }
}

vectorson[maxn];
vectorres;
queueq;

void bfs() {
    q.push(1);
    while (!q.empty()) {
        int u = q.front(); q.pop();
        for (int i = 0; i < son[u].size(); i++) {
            int v = son[u][i];
            if (k > 0) {
                res.push_back(fathedge[v]); q.push(v); k--;
            }
            else
                break;
        }
    }
}


int main()
{
    //ios::sync_with_stdio(0);
    rdint(n); rdint(m); rdint(k);
    for (int i = 1; i <= m; i++) {
        int u, v, w; rdint(u); rdint(v); rdint(w);
        addedge(i, u, v, w);
    }
    dijkstra();
    for (int i = 2; i <= n; i++) {
        son[fath[i]].push_back(i);
    }
    bfs();
    cout << res.size() << endl;
    for (int i = 0; i < res.size(); i++) {
        cout << res[i] << ' ';
    }
    cout << endl;
    return 0;
}

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