【HNOI 2002】 营业额统计

【题目链接】

点击打开链接

【算法】

观察式子 ： 最小波动值 = min{|该天营业额 - 之前某天的营业额|}

= min{该天营业额 - 该天营业额的前驱，该天营业额的后继 - 该天营业额}

用Splay维护前驱和后继即可

【代码】

#include<bits/stdc++.h>

using namespace std;

#define MAXN 32767

const int INF = 2e9;

int i,N,minn,x,ans;

template <typename T> inline void read(T &x) {

        int f = ; x = ;

        char c = getchar();

        for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }

        for (; isdigit(c); c = getchar()) x = (x << ) + (x << ) + c - '';

        x *= f;

}

template <typename T> inline void write(T x) {

    if (x < ) { putchar('-'); x = -x; }

    if (x > ) write(x/);

    putchar(x%+'');

}

template <typename T> inline void writeln(T x) {

    write(x);

    puts("");

}

struct Splay {

        int root,total;

        struct Node {

                int fa,size,val,son[],cnt;

        } Tree[MAXN+];

        inline bool get(int x) {

                return Tree[Tree[x].fa].son[] == x;

        }

         inline void new_node(int index,int f,int x) {

                Tree[index].val = x;

                Tree[index].size = Tree[index].cnt = ;

                Tree[index].fa = f;

                Tree[index].son[] = Tree[index].son[] = ;

        }

        inline void update(int index) {

                Tree[index].size = Tree[index].cnt;

                Tree[index].size += Tree[Tree[index].son[]].size;

                Tree[index].size += Tree[Tree[index].son[]].size;

        }

        inline void rotate(int x) {

                int f = Tree[x].fa,g = Tree[f].fa,

                        tmpx = get(x),tmpf = get(f);

                if (!f) return;

                Tree[f].son[tmpx] = Tree[x].son[tmpx^];

                if (Tree[x].son[tmpx^]) Tree[Tree[x].son[tmpx^]].fa = f;

                Tree[x].son[tmpx^] = f;

                Tree[f].fa = x;

                Tree[x].fa = g;

                if (g) Tree[g].son[tmpf] = x;

                update(f);

                update(x);

        }

        inline void splay(int x) {

                int f;

                for (f = Tree[x].fa; (f = Tree[x].fa); rotate(x))

                        rotate((get(x) == get(f)) ? (f) : (x));

                root = x;

        }

        inline void Insert(int x) {

                int index = root;

                bool tmp;

                if (!total) {

                        new_node(++total,,x);

                        root = total;

                        return;

                }

                while (true) {

                        if (Tree[index].val == x) {

                                ++Tree[index].cnt;

                                splay(index);

                                return;

                        }

                        tmp = Tree[index].val < x;

                        if (!Tree[index].son[tmp]) {

                                new_node(++total,index,x);

                                Tree[index].son[tmp] = total;

                                splay(total);

                                return;

                        } else

                                index = Tree[index].son[tmp];

                }

        }

        inline int query_min(int index) {

                while (true) {

                        if (!Tree[index].son[]) return Tree[index].val;

                        else index = Tree[index].son[];

                }

        }

        inline int query_max(int index) {

                while (true) {

                        if (!Tree[index].son[]) return Tree[index].val;

                        else index = Tree[index].son[];

                }

        }

        inline int pred(int x) {

                int index = root;

                bool tmp;

                while (true) {

                        if (Tree[index].val == x) break;

                        tmp = Tree[index].val < x;

                        index = Tree[index].son[tmp];

                }

                splay(index);

                if (Tree[index].cnt > ) return x;

                else if (Tree[index].son[]) return query_max(Tree[index].son[]);

                else return -INF;

        }

        inline int succ(int x) {

                int index = root;

                bool tmp;

                while (true) {

                        if (Tree[index].val == x) break;

                        tmp = Tree[index].val < x;

                        index = Tree[index].son[tmp];

                }

                splay(index);

                if (Tree[index].cnt > ) return x;

                else if (Tree[index].son[]) return query_min(Tree[index].son[]);

                else return INF;

        }

} T;

int main() {

        read(N);

        for (i = ; i <= N; i++) {

                minn = INF;

                read(x);

                if (i == ) { ans += x; T.Insert(x); continue; }

                T.Insert(x);

                if (x - T.pred(x) < minn) minn = x - T.pred(x);

                if (T.succ(x) - x < minn) minn = T.succ(x) - x;

                ans += minn;

        }

        writeln(ans);

        return ;

}