【题解】ZJOI2007报表统计

洛谷传送门

主要思路大概也是差不多的，对于两种询问分别用线段树与平衡树来维护。

1.MIN_SORT_GAP：显然平衡树简单操作，来一发前驱、后继即可。

2.MIN_GAP：这一个我用的是线段树：可以注意到插入元素的操作，如果是在一个元素之后反复插入，这些元素之间更新出来的最小值是不会发生改变的。只有元素与元素之间会有不断的插入而导致最小值变大。所以用线段树单点修改+维护区间min值，相邻插入值（中间不会再出现新的数字）之间可以直接暴力维护。

代码如下：

#include <bits/stdc++.h>
using namespace std;
#define INF 99999999999LL
#define maxn 2000000 
#define int long long
int n, m, tot, M1 = INF, M2 = INF, a[maxn];
int b[maxn], root;
struct tree
{
    int l, r, num;  
}T[maxn];

struct node
{
    int v, ch[2], fa;
}P[maxn];

int read()
{
    int x = 0, k = 1;
    char c;
    c = getchar();
    while(c < '0' || c > '9') { if(c == '-') k = -1; c = getchar();}
    while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
    return x * k;
}

struct Splay_Balanced_Tree
{
    void rotate(int x)
    {
        int f = P[x].fa, gf = P[f].fa;
        int k = x == P[f].ch[1];
        P[x].fa = gf;
        if(gf) P[gf].ch[f == P[gf].ch[1]] = x;
        P[f].ch[k] = P[x].ch[k ^ 1], P[P[x].ch[k ^ 1]].fa = f;
        P[f].fa = x, P[x].ch[k ^ 1] = f;
    }

    void Splay(int x, int goal)
    {
        while(P[x].fa != goal)
        {
            int f = P[x].fa, gf = P[f].fa;
            if(gf != goal) (P[f].ch[1] == x) ^ (P[gf].ch[1] == f) ? rotate(x) : rotate(f);
            rotate(x);
        }
        if(goal == 0) root = x; 
    }

    void ins(int x)
    {
        int u = root, ff = 0;
        while(u && P[u].v != x)
        {
            ff = u;
            u = P[u].ch[P[u].v < x];
        }
        if(!u)
        {
            u = ++ tot;
            P[u].fa = ff;
            if(ff) P[ff].ch[P[ff].v < x] = u;
            P[u].v = x;
            Splay(u, 0);
        } 
    }

    void Find(int x)
    {
        int u = root;
        if(!u) return;
        while(P[u].v != x && P[u].ch[P[u].v < x]) u = P[u].ch[P[u].v < x];
        Splay(u, 0);
    }

    int next(int x, int k)
    {
        Find(x);
        int u = root;
        if(P[u].v == x) return P[u].v;
        if((P[u].v < x && !k) || (P[u].v > x && k)) return P[u].v;
        u = P[u].ch[k];
        while(P[u].ch[k ^ 1]) u = P[u].ch[k ^ 1];
        return P[u].v;
    }
}SBT;

struct Segament_Tree
{
    void build(int p, int l, int r)
    {
        T[p].l = l, T[p].r = r;
        if(l == r) 
        {
            T[p].num = abs(a[l] - a[l - 1]);
            return;
        }
        int mid = (l + r) >> 1;
        build(p << 1, l, mid), build(p << 1 | 1, mid + 1, r);
        T[p].num = min(T[p << 1].num, T[p << 1 | 1].num);
    }

    void update(int p, int x, int num)
    {
        int mid = (T[p].l + T[p].r) >> 1;
        if(T[p].l == T[p].r)
        {
            T[p].num = num;
            return;
        }
        if(x <= mid) update(p << 1, x, num);
        else update(p << 1 | 1, x, num);
        T[p].num = min(T[p << 1].num, T[p << 1 | 1].num);
    }
}SGT;

signed main()
{
    n = read(), m = read();
    SBT.ins(INF), SBT.ins(- INF);
    a[0] = a[n + 1] = INF;
    for(int i = 1; i <= n; i ++)
    {
        a[i] = read();
        if(i != 1) 
        {
            int l = SBT.next(a[i], 0), r = SBT.next(a[i], 1);
            M2 = min(M2, min(abs(l - a[i]), abs(r - a[i])));
        }
        SBT.ins(a[i]);
        b[i] = a[i];
    }
    SGT.build(1, 1, n);
    for(int i = 1; i <= m; i ++)
    {
        string s;
        cin >> s;
        if(s[0] == 'I')
        {
            int x = read(), y = read();
            int l = SBT.next(y, 0), r = SBT.next(y, 1);
            M2 = min(M2, min(abs(l - y), abs(r - y)));
            SBT.ins(y);
            M1 = min(M1, abs(b[x] - y));
            SGT.update(1, x + 1, abs(a[x + 1] - y));
            b[x] = y;
        }
        else if(s[4] == 'G') printf("%lld
", min(M1, T[1].num));
        else printf("%lld
", M2);
    }
    return 0;
}