2020/8/26

英语四级

学习了kruskal重构树+dfs板的lca

mad dfs的lca竟然会快一点 

#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;
#pragma GCC optimize(2)

inline int read() {
    int x = 0;
    bool f = 1;
    char c = getchar();
    for (; !isdigit(c); c = getchar())
        if (c == '-')
            f = 0;
    for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
    if (f)
        return x;
    return 0 - x;
}

const int N = 300100;
const int mod = 1e9 + 7;
typedef struct Node{
    int x,y,w;
}Node;
Node node[N];
int head[N],ver[N << 1],Next[N << 1],Edge[N << 1],tot;
int n,m,top;
int far[N],w[N];
int A,B,C,P;

int k,t;
int id[N],d[N];
int f[N][20];
int lg[N];

inline int rnd(){return A=(A*B+C)%P;}

inline void add(int x,int y){
    ver[++ tot] = y; Next[tot] = head[x]; head[x] = tot;
}

bool cmp(Node a,Node b){
    return a.w < b.w;
}

inline int Find(int x){
    if(!far[x]) return x;
    return far[x] = Find(far[x]);
}
/*
inline void bfs(int x){
    queue<int> Q;Q.push(x);
    d[x] = 1;
    while(!Q.empty()){
        int x = Q.front(); Q.pop();
        for(int i = head[x]; i; i = Next[i]){
            int y = ver[i];
            if(d[y]) continue;
            d[y] = d[x] + 1;
            f[y][0] = x;
            for(int j = 1; j <= t; j ++)
                f[y][j] = f[f[y][j - 1]][j - 1];
            Q.push(y);
        }
    }
}
inline int lca(int x,int y){
    if(d[x] > d[y]) x ^= y ^= x ^= y;
    for(int i = t; i >= 0; i --)
        if(d[f[y][i]] >= d[x]) y = f[y][i];
    if(x == y) return x;
    for(int i = t; i >= 0; i --)
        if(f[x][i] != f[y][i]) x = f[x][i],y = f[y][i];
    return f[x][0];
}*/
void dfs(int cur, int fath) {
        f[cur][0] = fath; d[cur] = d[fath] + 1;
        for (int i = 1; i <= lg[d[cur]]; ++i)
                f[cur][i] = f[f[cur][i - 1]][i - 1];

        for (int i = head[cur]; i ; i = Next[i])
                if (ver[i] != fath)
                        dfs(ver[i], cur);
}
int lca(int x, int y) {
        if (d[x] < d[y]) swap(x, y);
        while (d[x] > d[y])
                x = f[x][lg[d[x] - d[y]] - 1];
        if (x == y)
                return x;

        for (int i = lg[d[x]] - 1; i >= 0; --i)
                if (f[x][i] != f[y][i])
                        x = f[x][i], y = f[y][i];
        return f[x][0];
}
int main(){
    n = read(); m = read();
    for(int i = 1; i <= m; i ++){
        node[i].x = read(); node[i].y = read();node[i].w = read();
    }
    sort(node + 1,node + m + 1,cmp);
    top = n;
    for(int i = 1; i <= m; i ++){
        int x = node[i].x,y = node[i].y;
        int fx = Find(x),fy = Find(y);
        if(fx == fy) continue;
        w[++ top] = node[i].w;
        add(top,fx); //add(fx,top);
        add(top,fy); //add(fy,top);
        far[fx] = top;
        far[fy] = top;
        if(top  == 2 * n - 1) break;
    }
    for (int i = 1; i < N; ++i)
                lg[i] = lg[i - 1] + (1 << lg[i - 1] == i);
    dfs(top, 0);
    int q = read();
    A = read(); B = read(); C = read(); P = read();
    int s = 0;
    while(q --){
        int u=rnd()%n+1,v=rnd()%n+1;
        int fa = lca(u,v);
        if(u != v)
        s += w[fa];
        if(s >= mod) s -= mod;
    }
    printf("%d
",s);
}
/*
3
1 2 3
2
2 6
*/

#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;

typedef pair<int,int> PII;

inline int read(){
    int s = 0, w = 1; char ch = getchar();
    while(ch < '0' || ch > '9')   { if(ch == '-') w = -1; ch = getchar(); }
    while(ch >= '0' && ch <= '9') { s = (s << 3) + (s << 1) + (ch ^ 48); ch = getchar(); }
    return s * w;
}

const int N = 300100;
int head[N],ver[N << 1],Next[N << 1],Edge[N << 1],tot;
int n,m;
int visit[N],match[N];


void add(int x,int y){
    ver[++ tot] = y; Next[tot] = head[x]; head[x] = tot;
}

bool dfs(int x){
    for(int i = head[x]; i; i = Next[i]){
       int y = ver[i];
       if(visit[y]) continue;
       visit[y] = 1;
       if(!match[y] || dfs(match[y])){
        match[y] = x; return true;
       }
    }
    return false;
}
int main(){
    int T = read();
    while(T --){
        n = read(); m = read();
        tot = 0;
        memset(head,0,sizeof(head));
        memset(match,0,sizeof(match));
        for(int i = 1; i <= m; i ++){
            int x = read(),y = read();
            add(x,y + n);
        }
        int ans = 0;
        for(int i = 1; i <= n + n; i ++){
            memset(visit,0,sizeof(visit));
            if(dfs(i)) ans ++;
        }
        //ans /= 2;
        printf("%d
",n - ans);
    }
}
/*
3
1 2 3
2
2 6
*/


#include"stdio.h"
#include"string.h"
#include"stack"
#include"map"
#include"math.h"
#include"iostream"
#include"vector"
#include"queue"
#include"algorithm"
using namespace std;
#pragma GCC optimize(2)

inline int read() {
    int x = 0;
    bool f = 1;
    char c = getchar();
    for (; !isdigit(c); c = getchar())
        if (c == '-')
            f = 0;
    for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
    if (f)
        return x;
    return 0 - x;
}

const int N = 300100;
const int mod = 1e9 + 7;
typedef struct Node{
    int x,y,w;
}Node;
Node node[N * 3];
int head[N],ver[N << 1],Next[N << 1],Edge[N << 1],tot;
int n,m,top;
int far[N],w[N];
int high[N],b[N],len;
int k,t;
int id[N],d[N];
int f[N][20];
int lg[N];
int root[N << 5],sum[N << 5],lc[N << 5],rc[N << 5],tot1;
int son[N][2],num,h[N],tt;

inline void add(int x,int y){
    ver[++ tot] = y; Next[tot] = head[x]; head[x] = tot;
}

bool cmp(Node a,Node b){
    return a.w < b.w;
}

inline int Find(int x){
    if(!far[x]) return x;
    return far[x] = Find(far[x]);
}
void dfs(int cur, int fath) {
        f[cur][0] = fath; d[cur] = d[fath] + 1;
        for (int i = 1; i <= lg[d[cur]]; ++i)
                f[cur][i] = f[f[cur][i - 1]][i - 1];

        for (int i = head[cur]; i ; i = Next[i])
                if (ver[i] != fath)
                        dfs(ver[i], cur);
}

void Build_Tree(int &rt,int l,int r){
    rt = ++ tot1; sum[rt] = 0;
    if(l == r) return ;
    int mid = (l + r) >> 1;
    Build_Tree(lc[rt],l,mid);
    Build_Tree(rc[rt],mid + 1,r);
}
void Update(int pre,int &rt,int l,int r,int v){
    rt = ++ tot1;
    lc[rt] = lc[pre]; rc[rt] = rc[pre]; sum[rt] = sum[pre] + 1;
    if(l == r) return ;
    int mid = (l + r) >> 1;
    if(mid >= v) Update(lc[pre],lc[rt],l,mid,v);
    else Update(rc[pre],rc[rt],mid + 1,r,v);
}
int query(int u,int v,int l,int r,int k){

    int mid = (l + r) >> 1;
    int x = sum[rc[v]] - sum[rc[u]];
   // printf("v = %d u = %d l = %d r = %d k = %d x = %d
",v,u,l,r,k,x);
    if(l == r) {
        if(k - (sum[v] - sum[u]) == 0)
            return l;
    return 0;
    }
    if(x >= k) return query(rc[u],rc[v],mid + 1,r,k);
    else return query(lc[u],lc[v],l,mid,k - x);
}
void dfs1(int x,int far){
    son[x][0] = num;
    if(head[x] == 0){
        son[x][0] = ++ num;
        int id = lower_bound(b + 1,b + len + 1,high[x]) - b;
        h[++ tt] = id;
        return ;
    }
    for(int i = head[x]; i; i = Next[i]){
        int y = ver[i];
        if(far == y) continue;
        dfs1(y,x);
    }
    son[x][1] = num;
}
int main(){
    n = read(); m = read(); int q = read();
    for(int i = 1; i <= n; i ++) b[i] = high[i] = read();
    sort(b + 1,b + n + 1);
    len = unique(b + 1,b + n + 1) - b - 1;
    for(int i = 1; i <= m; i ++){
        node[i].x = read(); node[i].y = read();node[i].w = read();
    }
    sort(node + 1,node + m + 1,cmp);
    top = n;
    for(int i = 1; i <= m; i ++){
        int x = node[i].x,y = node[i].y;
        int fx = Find(x),fy = Find(y);
        if(fx == fy) continue;
        w[++ top] = node[i].w;
        add(top,fx); //add(fx,top);
        add(top,fy); //add(fy,top);
        far[fx] = top;
        far[fy] = top;
        if(top  == 2 * n - 1) break;
    }
    for (int i = 1; i < N; ++i)
        lg[i] = lg[i - 1] + (1 << lg[i - 1] == i);
    t = (int)(log(top) / log(2)) + 1;
    dfs(top, 0);
    dfs1(top,1);
    Build_Tree(root[0],1,len);
   // printf("tot1 = %d
",tot1);
    for(int i = 1; i <= n; i ++){
      //  printf("h = %d
",h[i]);
        Update(root[i - 1],root[i],1,len,h[i]);
    }
 //   printf("tot1 = %d
",tot1);
    b[0] = -1;
    while(q --){
        int u = read(),x = read(),k = read();
        for(int i = 20; i >= 0; i --){
            if(f[u][i] && w[f[u][i]] <= x) u = f[u][i];
        }
        if(w[u] == 0){
            if(k == 1) printf("%d
",high[u]);
            else printf("-1
"); continue;
        }
      //  printf("u = %d
",u);
       // printf("l = %d r = %d root[l] = %d root[r] = %d
",son[u][0],son[u][1],root[son[u][0]],root[son[u][1]]);
        if(son[u][1] - son[u][0] < k) printf("-1
");
        else{
          int s = query(root[son[u][0]],root[son[u][1]],1,len,k);
          printf("%d
",b[s]);
        }
    }
}
/*
3
1 2 3
2
2 6
*/