2021牛客寒假6H - 区间最小生成树

传送门：2021牛客寒假6H

思路分析

线段树每个节点维护一个n-1大小的数组，存的是该区间在最小生成树里的边

AC代码

#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define mp make_pair
#define fun function
#define sz(x) (int)(x).size()
#define lowbit(x) (x)&(-x)
#define all(x) (x).begin(),(x).end()
#define mem(a,b) memset(a,b,sizeof(a))

namespace FastIO {
#define BUF_SIZE 100000
#define OUT_SIZE 100000
    bool IOerror=0;
    inline char nc() {
        static char buf[BUF_SIZE],*p1=buf+BUF_SIZE,*pend=buf+BUF_SIZE;
        if(p1==pend) {
            p1=buf;
            pend=buf+fread(buf,1,BUF_SIZE,stdin);
            if(pend==p1) {
                IOerror=1;
                return -1;
            }
        }
        return *p1++;
    }
    inline bool blank(char ch) {
        return ch==' '||ch=='\n'||ch=='\r'||ch=='\t';
    }
    template<class T> inline bool read(T &x) {
        bool sign=0;
        char ch=nc();
        x=0;
        for(; blank(ch); ch=nc());
        if(IOerror)return false;
        if(ch=='-')sign=1,ch=nc();
        for(; ch>='0'&&ch<='9'; ch=nc())x=x*10+ch-'0';
        if(sign)x=-x;
        return true;
    }
    template<class T,class... U>bool read(T& h,U&... t) {
        return read(h)&&read(t...);
    }
#undef OUT_SIZE
#undef BUF_SIZE
};
using namespace std;
using namespace FastIO;

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

typedef long long ll;
typedef pair<int,int> pii;
typedef unsigned long long ull;

const int INF = 0x3f3f3f3f;
const int N = 3e5+10;

struct edge{
    int u,v,w;
} e[N];

struct node {
    int l,r,mid,idx,sum;
    int g[222];
    void clear(){
        idx = 0;
        sum = 0;
        mem(g,0);
    }
} tree[N*4];

int n,m,q;
int f[N];

int find(int x) {
    return f[x] == x?x:f[x] = find(f[x]);
}

node merge(node x,node y) {
    node ans;
    ans.clear();
    ans.l = x.l;
    ans.r = y.r;
    if(ans.l && ans.r) ans.mid = (ans.l+ans.r)/2;
    int l = 1, r = 1;
    for(int i=1; i<=n; i++) f[i] = i;
    while(l<=x.idx || r<=y.idx) {
        if(ans.idx == n-1) break;
        int lp = x.g[l];
        int rp = y.g[r];
        if((e[lp].w<=e[rp].w && l<=x.idx) || r>y.idx) {
            l++;
            int u = e[lp].u;
            int v = e[lp].v;
            int w = e[lp].w;
            u = find(u);
            v = find(v);
            if(u == v) continue;
            f[u] = v;
            ans.sum+=w;
            ans.g[++ans.idx] = lp;
        } else {
            r++;
            lp = rp;
            int u = e[lp].u;
            int v = e[lp].v;
            int w = e[lp].w;
            u = find(u);
            v = find(v);
            if(u == v) continue;
            f[u] = v;
            ans.sum+=w;
            ans.g[++ans.idx] = lp;
        }
    }
    return ans;
}
#define ls x*2
#define rs x*2+1
void build(int x,int l,int r) {
    tree[x].l = l;
    tree[x].r = r;
    tree[x].sum = tree[x].idx = 0;
    tree[x].mid = (l+r)/2;
    if(l==r) {
        if(e[l].u == e[l].v) {
            tree[x].sum = tree[x].idx = 0;
            return;
        }
        tree[x].idx = 1;
        tree[x].sum = e[l].w;
        tree[x].g[1] = l;
        return ;
    }
    int mid = tree[x].mid;
    build(ls,l,mid);
    build(rs,mid+1,r);
    tree[x] = merge(tree[ls],tree[rs]);
}

void modify(int x,int pos) {
    if(tree[x].l == tree[x].r) {
        if(e[pos].u == e[pos].v) {
            tree[x].sum = tree[x].idx = 0;
            return;
        }
        tree[x].idx = 1;
        tree[x].sum = e[pos].w;
        tree[x].g[1] = pos;
        return ;
    }
    int mid = tree[x].mid;
    if(pos<=mid) modify(ls,pos);
    else modify(rs,pos);
    tree[x] = merge(tree[ls],tree[rs]);
}

node query(int x,int l,int r) {
    if(l == tree[x].l && tree[x].r == r) {
        return tree[x];
    }
    int mid = tree[x].mid;
    if(r<=mid) return query(ls,l,r);
    else if(l>mid) return query(rs,l,r);
    else return merge(query(ls,l,mid),query(rs,mid+1,r));
}


signed main() {

#ifdef xiaofan
    freopen("1.in","r",stdin);
    freopen("1.out","w",stdout);
#endif

    e[0] = {1,1,100};
    cin>>n>>m>>q;
    for(int i=1; i<=m; i++) cin>>e[i].u>>e[i].v>>e[i].w;
    build(1,1,m);
    while(q--) {
        int op;
        cin>>op;
        if(op == 1) {
            int x,y,z,t;
            cin>>x>>y>>z>>t;
            e[x] = {y,z,t};
            modify(1,x);
        } else {
            int l,r;
            cin>>l>>r;
            node ans = query(1,l,r);
            if(ans.idx == n-1) cout<<ans.sum<<endl;
            else cout<<"Impossible"<<endl;
        }
    }




    return 0;
}