#4864. [BeiJing 2017 Wc]神秘物质 [FHQ Treap]

Posted 2021-03-15 isaunoya

这题其实挺简单的，有个东西可能稍微难维护了一点点。。

(merge x e) 当前第 (x) 个原子和第 (x+1) 个原子合并，得到能量为 (e) 的新原子；
(insert x e) 在当前第 (x) 个原子和第 (x+1) 个原子之间插入一个能量为 (e) 的新原子。
(max x y) 当前第 (x) 到第 (y) 个原子之间的任意子区间中区间极差的最大值；
(min x y) 当前第 (x) 到第 (y) 个原子之间的任意子区间中区间极差的最小值。

极差最大值其实很显然是个区间 (max - min)
极差最小的区间呢，长度至少为 (2) 也必须为 (2)
至于证明的话
考虑 (x,y,z)

如果 (x) 和 (z) 的差的绝对值是解，那么 (|x-y|) 或者 (|y-z|) 一定更优

因为 (x leq y leq z) 才符合这种情况。

所以随便写写，把相邻两个的差变成后一个点的值，随便写写就可以了。

// by Isaunoya
#include <bits/stdc++.h>
using namespace std;
#define rep(i, x, y) for (register int i = (x); i <= (y); ++i)
#define Rep(i, x, y) for (register int i = (x); i >= (y); --i)

const int _ = 1 << 21;
struct I {
    char fin[_], *p1 = fin, *p2 = fin;
    inline char gc() {
        return (p1 == p2) && (p2 = (p1 = fin) + fread(fin, 1, _, stdin), p1 == p2) ? EOF : *p1++;
    }
    inline I& operator>>(int& x) {
        bool sign = 1;
        char c = 0;
        while (c < 48) ((c = gc()) == 45) && (sign = 0);
        x = (c & 15);
        while ((c = gc()) > 47) x = (x << 1) + (x << 3) + (c & 15);
        x = sign ? x : -x;
        return *this;
    }
    inline I& operator>>(double& x) {
        bool sign = 1;
        char c = 0;
        while (c < 48) ((c = gc()) == 45) && (sign = 0);
        x = (c - 48);
        while ((c = gc()) > 47) x = x * 10 + (c - 48);
        if (c == '.') {
            double d = 1.0;
            while ((c = gc()) > 47) d = d * 0.1, x = x + (d * (c - 48));
        }
        x = sign ? x : -x;
        return *this;
    }
    inline I& operator>>(char& x) {
        do
            x = gc();
        while (isspace(x));
        return *this;
    }
    inline I& operator>>(string& s) {
        s = "";
        char c = gc();
        while (isspace(c)) c = gc();
        while (!isspace(c) && c != EOF) s += c, c = gc();
        return *this;
    }
} in;
struct O {
    char st[100], fout[_];
    signed stk = 0, top = 0;
    inline void flush() {
        fwrite(fout, 1, top, stdout), fflush(stdout), top = 0;
    }
    inline O& operator<<(int x) {
        if (top > (1 << 20)) flush();
        if (x < 0) fout[top++] = 45, x = -x;
        do
            st[++stk] = x % 10 ^ 48, x /= 10;
        while (x);
        while (stk) fout[top++] = st[stk--];
        return *this;
    }
    inline O& operator<<(char x) {
        fout[top++] = x;
        return *this;
    }
    inline O& operator<<(string s) {
        if (top > (1 << 20)) flush();
        for (char x : s) fout[top++] = x;
        return *this;
    }
} out;
#define pb emplace_back
#define fir first
#define sec second

template < class T > inline void cmax(T & x , const T & y) {
    (x < y) && (x = y) ;
}
template < class T > inline void cmin(T & x , const T & y) {
    (x > y) && (x = y) ;
}


int n , m , rt = 0 ;
const int N = 2e5 + 10 ;
int a[N] ;
const int inf = 0x7fffffff ;
int rnd[N] , val[N] , mx[N] , mn[N] , ch[N][2] , sz[N] ;
int cnt = 0 ;
#define ls(x) ch[x][0]
#define rs(x) ch[x][1]
int newnode(int v) {
    ++ cnt ;
    val[cnt] = mx[cnt] = mn[cnt] = v ;
    rnd[cnt] = rand() ;
    sz[cnt] = 1 ;
    return cnt ;
}
int t[N] , s[N] ;
void pushup(int rt) {
    mx[rt] = mn[rt] = val[rt] ;
    if(ls(rt)) cmin(mn[rt] , mn[ls(rt)]) , cmax(mx[rt] , mx[ls(rt)]) ;
    if(rs(rt)) cmin(mn[rt] , mn[rs(rt)]) , cmax(mx[rt] , mx[rs(rt)]) ;
    sz[rt] = sz[ls(rt)] + sz[rs(rt)] + 1 ;
    t[rt] = min(t[ls(rt)] , t[rs(rt)]) , cmin(t[rt] , s[rt]) ;
}
int merge(int u , int v) {
    if(! u || ! v) return u | v ;
    if(rnd[u] < rnd[v]) {
        rs(u) = merge(rs(u) , v) ;
        pushup(u) ;
        return u ;
    } else {
        ls(v) = merge(u , ls(v)) ;
        pushup(v) ;
        return v ;
    }
}
void split(int cur , int k , int & u , int & v) {
    if(! cur) {
        u = v = 0 ;
        return ;
    }
    if(k <= sz[ls(cur)]) {
        v = cur ;
        split(ls(v) , k , u , ls(v)) ;
    } else {
        u = cur ;
        split(rs(u) , k - sz[ls(u)] - 1 , rs(u) , v) ;
    }
    pushup(cur) ;
}
void ins(int k , int v) {
    int x , y , z , xx ;
    split(rt , k - 1 , x , y) ;
    split(y , 1 , y , z) ;
    split(z , 1 , z , xx) ;
    int now = newnode(v) ;
    t[now] = s[now] = abs(val[now] - val[y]) ;
    if(! y) {
        t[now] = s[now] = inf ;
    }
    t[z] = s[z] = abs(val[z] - val[now]) ;
    if(! z) {
        t[z] = s[z] = inf ;
    }
    rt = merge(merge(merge(merge(x , y) , now) , z) , xx) ;
}
void _merge(int k , int v) {
    int x , y , z , xx ;
    split(rt , k - 1 , x , y) ;
    split(y , 1 , y , z) ;
    split(z , 1 , z , xx) ;
    rt = merge(x , xx) ;
    ins(k - 1 , v) ;
}
int qrymax(int l , int r) {
    int x , y , z ;
    split(rt , r , x , z) ;
    split(x , l - 1 , x , y) ;
    int res = mx[y] - mn[y] ;
    rt = merge(merge(x , y) , z) ;
    return res ;
}
int qrymin(int l , int r) {
    ++ l ;
    int x , y , z ;
    split(rt , r , x , z) ;
    split(x , l - 1 , x , y) ;
    int res = t[y] ;
    rt = merge(merge(x , y) , z) ;
    return res ;
}
void dfs(int u) {
    if(ls(u)) dfs(ls(u)) ;
    out << val[u] << '
' ;
    if(rs(u)) dfs(rs(u)) ;
}
signed main() {
#ifdef _WIN64
    freopen("testdata.in" , "r" , stdin) ;
#endif
    in >> n >> m ;
    rep(i , 1 , n) in >> a[i] ;
    rt = newnode(a[1]) ;
    t[rt] = s[rt] = inf ;
    rep(i , 2 , n) ins(i - 1 , a[i]) ;
    rep(i , 1 , m) {
        string s ;
        in >> s ;
        int x , y ;
        in >> x >> y ;
        if(s == "max") out << qrymax(x , y) << '
' ;
        if(s == "min") out << qrymin(x , y) << '
' ;
        if(s == "merge") _merge(x , y) ;
        if(s == "insert") ins(x , y) ;
    }
    return out.flush(), 0;
}