主席树，开坑POJ2104,EOJ3335&hdu6162,hdu5919

一些废话

去年自己一知半解写的blog

blog1

blog2

blog3

还没看的blog

n个树，其实是有n个线段树

每个线段树记录前n个数插入的状态，是把整个序列排序之后插入自己该在的位置（类似于树状数组求逆序对的那种插入姿势）

每次新建一个线段树大部分节点都是从前一棵树上掰下来的，公用的，所以每次增加nlogn个节点

poj2104

拿去年的板子改的，去年的代码好丑，换成舒服的风格

# include <cstdio>
# include <cstring>
# include <iostream>
# include <algorithm>
using namespace std;
const int N = 1e5 + 7;
int arr[N];  //arr[]  原数组的数在rank[]中的位置;
int Rank[N]; //rank[] 原数组离散化

struct ChairTree{
    #define sum(x) tree[x].w
    #define lson tree[rt].lc, tree[rt1].lc, l, m
    #define rson tree[rt].rc, tree[rt1].rc, m+1, r
    struct node{
        int lc, rc, w;
        node(){}
    } tree[N * 20];
    int root[N], cnt;
    void build(){
        root[0] = cnt = 0;
        memset(tree, 0, sizeof(tree));
    }

    void add(int pos, int val, int &rt, int rt1, int l, int r){
        tree[rt = ++cnt] = tree[rt1];
        tree[rt].w += val;
        if (l == r) return;
        int m = (l + r) >> 1;
        if (pos <= m) add(pos, val, lson);
        else add(pos, val, rson);
    }

    int query(int k, int rt, int rt1, int l, int r){
        if (l == r) return l;
        int lsize = sum(tree[rt1].lc) - sum(tree[rt].lc);
        int m = (l + r) >> 1;
        if (lsize >= k) return query(k, lson);
        else return query(k - lsize, rson);
    }
} T;

int main(){
    //freopen("in.txt","r",stdin);
    int _, l, r, k, n, q;
    for (; ~scanf("%d%d", &n, &q);){
        T.build();
        for (int i = 1; i <= n; i++) {
            scanf("%d", &arr[i]);
            Rank[i] = arr[i];
        }
        sort(Rank + 1, Rank + n+1);//Rank存储原值
        int m = unique(Rank + 1, Rank + n +1) - (Rank + 1);
        for (int i = 1; i <= n; i++) {//离散化后的数组，仅仅用来更新
            arr[i] = lower_bound(Rank + 1, Rank + n+1, arr[i]) - Rank;
        }
        for (int i = 1; i <= n; i++){
            T.add(arr[i], 1, T.root[i], T.root[i-1], 1, n);
        }
        for (; q--;){
            scanf("%d%d%d", &l, &r, &k);
            int pos = T.query(k, T.root[l-1], T.root[r], 1, n);
            printf("%d\n", Rank[pos]);
        }
    }
    return 0;
}

EOJ3335&&hdu6162

多校第九场02

本题花式A法可以看这里

树上套个主席树

#include <map>
#include <vector>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
const int N = 1e5 + 7;
typedef long long LL;
LL gift[N], Rank[N];//节点权值和离散化

struct ChairTree{
    #define sum(x) tree[x].sum
    #define lson tree[rt].lc, tree[rt1].lc, l, m
    #define rson tree[rt].rc, tree[rt1].rc, m+1, r
    struct node{
        int lc, rc;
        LL sum;
    } tree[N * 30];
    int n, root[N], cnt;

    inline void build(int _n){
        n = _n; cnt = 0;
    }

    void add(int pos, LL val, int &rt, int rt1, int l, int r){
        tree[rt = ++cnt] = tree[rt1];
        tree[rt].sum += val;
        if (l == r) return;
        int m = (l + r) >> 1;
        if (pos <= m) add(pos, val, lson);
        else add(pos, val, rson);
    }

    LL query(int L, int R, int rt, int rt1, int l, int r){
        if (L <= l && r <= R) return sum(rt1) - sum(rt);
        if (sum(rt1) == 0) return 0;
        if (sum(rt1) == sum(rt)) return 0;
        LL ans = 0;
        int m = (l + r) >> 1;
        if (L <= m) ans += query(L, R, lson);
        if (m <  R) ans += query(L, R, rson);
        return ans;
    }
    #undef sum(x)
    #undef lson
    #undef rson
} T;

struct graph{
    struct Edge{
        int from, to, nxt;
        Edge(){}
        Edge(int u, int v, int n):from(u), to(v), nxt(n){}
    } edges[N * 2];
    static const int LCADEP = 17;
    int n, E, head[N];
    int top, dep[N], fa[N][LCADEP + 1];

    inline void AddEdge(int f, int t){
        edges[++E] = Edge(f, t, head[f]);
        head[f] = E;
    }
    inline void Init(int n){
        this -> n = n ; E = -1; top = 0; dep[0] = 0;
        for (int i = 0; i <= n; i++) head[i] = -1;
        memset(fa, 0, sizeof(fa));
    }

    void dfs(int u, int pre){
        T.add(gift[u], Rank[gift[u]], T.root[u], T.root[pre], 1, T.n);
        fa[u][0] = pre;
        dep[u] = dep[pre] + 1;
        for (int i = 1; i <= LCADEP; i++){
            if (dep[u] < (1<<i)) break;
            fa[u][i] = fa[fa[u][i-1]][i-1];
        }
        for (int i = head[u]; i != -1; i = edges[i].nxt){
            if (edges[i].to != pre) dfs(edges[i].to, u);
        }
    }

    int lca(int x, int y){
        if (dep[x] < dep[y]) swap(x,y);
        int t = dep[x] - dep[y];
        for (int i = 0; i <= LCADEP; i++) if ((1<<i) & t) x = fa[x][i];
        for (int i = LCADEP; i >= 0; i--) if (fa[x][i] != fa[y][i]){
            x = fa[x][i]; y = fa[y][i];
        }
        return x==y ? x : fa[x][0];
    }

    LL query(int u, int v, int L, int R){
        int f = lca(u, v);
        LL ans = 0;
        ans += T.query(L, R, T.root[f], T.root[u], 1, T.n);
        ans += T.query(L, R, T.root[fa[f][0]], T.root[v], 1, T.n);
        return ans;
    }
} g ;

int main () {
    //freopen("in.txt", "r", stdin);
    int n, q, u, v;
    for (LL a, b; ~scanf("%d%d", &n, &q);) {
        for(int i = 1; i <= n; i++) {
            scanf("%lld", &gift[i]);
            Rank[i] = gift[i];
        }
        sort(Rank + 1, Rank + n+1);
        int un = unique(Rank + 1, Rank + n+1) - (Rank+1);
        for (int i = 1; i <= n; i++){
            gift[i] = lower_bound(Rank + 1, Rank + un+1, gift[i]) - Rank;
        }

        g.Init(n);
        for(int i = 0; i < n - 1; i++) {
            scanf("%d%d", &u, &v);
            g.AddEdge(u, v);
            g.AddEdge(v, u);
        }
        T.build(un);
        g.dfs(1, 0);

        for (; q--;){
            scanf("%d%d%lld%lld", &u, &v, &a, &b);
            int aa = lower_bound(Rank+1, Rank + un+1, a) - Rank;
            if (Rank[aa] < a) aa++;
            int bb = lower_bound(Rank+1, Rank + un+1, b) - Rank;
            if (bb > un || Rank[bb] > b) bb--;
            printf("%lld", g.query(u, v, aa, bb));
            putchar(q==0 ? '\n' : ' ');
        }
    }
    return 0;
}

hdu5919

看了这个题解写的

题意

有长度为n的序列，强制在线询问[l,r] 这段区间中所有不同数出现的第一个位置，按照位置从小到大排完序以后的中间（向上取整）的那个位置是多少？

真-语文题

解

没有对原来数据的离散化操作，每棵线段树就是原数组的位置

每个数字只有一次，每次+1，前面有了就吧前面的-1

for的时候最坏要update 2*n次，所以要开40*n的大小

# include <cstdio>
# include <cstring>
# include <iostream>
# include <algorithm>
using namespace std;
const int N = 2e5 + 7;
int n, arr[N], last[N];

struct ChairTree{
    #define lson tree[rt].lc, tree[rt1].lc, l, m
    #define rson tree[rt].rc, tree[rt1].rc, m+1, r
    struct node{
        int lc, rc, w;
        node(){}
    } tree[N * 40];
    int root[N], cnt;

    inline void build(){
        root[0] = root[n+1] = cnt = 0;
        memset(tree, 0, sizeof(tree));
        memset(root, 0, sizeof(root));
    }

    void add(int pos, int val, int &rt, int rt1, int l, int r){
        int tmp = rt;
        tree[rt = ++cnt] = tmp ? tree[tmp] : tree[rt1];
        tree[rt].w += val;
        if (l == r) return;
        int m = (l + r) >> 1;
        if (pos <= m) add(pos, val, lson);
        else add(pos, val, rson);
    }

    //下面两个函数, rt==rt1, 带两个仅仅是为了凑个lson和rson的参数

    int sum(int L, int R, int rt, int rt1, int l, int r){
        if (L <= l && r <= R) return tree[rt].w;
        int ans = 0;
        int m = (l + r) >> 1;
        if (L <= m) ans += sum(L, R, lson);
        if (m <  R) ans += sum(L, R, rson);
        return ans;
    }

    int query(int k, int rt, int rt1, int l, int r){
        if (l == r) return l;
        int lsize = tree[tree[rt].lc].w;
        int m = (l + r) >> 1;
        if (lsize >= k) return query(k, lson);
        else return query(k - lsize, rson);
    }
} T;

int main(){
    //freopen("in.txt","r",stdin);
    int _, __, l, r, q;
    scanf("%d", &__);
    for (int _ = 1; _ <= __; _++){
        printf("Case #%d:", _);
        scanf("%d%d", &n, &q);
        for (int i = 1; i <= n; i++) scanf("%d", &arr[i]);
        T.build();
        memset(last, 0, sizeof(last));
        for (int i = n; i >= 1; i--){
            T.add(i, 1, T.root[i], T.root[i+1], 1, n);
            if (last[arr[i]]) T.add(last[arr[i]], -1, T.root[i], T.root[i], 1, n);
            last[arr[i]] = i;
        }
        int ans = 0;
        for (; q--;){
            scanf("%d%d", &l, &r);
            l = (l + ans) % n + 1;
            r = (r + ans) % n + 1;
            if (l > r) swap(l, r);
            int sum = T.sum(l, r, T.root[l], T.root[l], 1, n);
            ans = T.query((sum+1)/2, T.root[l], T.root[l], 1, n);
            printf(" %d", ans);
        }
        puts("");
    }
    return 0;
}