【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 = 1; x = 0;
        char c = getchar();
        for (; !isdigit(c); c = getchar()) { if (c == '-') f = -f; }
        for (; isdigit(c); c = getchar()) x = (x << 3) + (x << 1) + c - '0';
        x *= f;
}

template <typename T> inline void write(T x) {
    if (x < 0) { putchar('-'); x = -x; }
    if (x > 9) write(x/10);
    putchar(x%10+'0');
}

template <typename T> inline void writeln(T x) {
    write(x);
    puts("");
}

struct Splay {
        int root,total;
        struct Node {
                int fa,size,val,son[2],cnt;
        } Tree[MAXN+10];
        inline bool get(int x) {
                return Tree[Tree[x].fa].son[1] == x;
        }
         inline void new_node(int index,int f,int x) {
                Tree[index].val = x;
                Tree[index].size = Tree[index].cnt = 1;
                Tree[index].fa = f;
                Tree[index].son[0] = Tree[index].son[1] = 0; 
        }
        inline void update(int index) {
                Tree[index].size = Tree[index].cnt;
                Tree[index].size += Tree[Tree[index].son[0]].size;
                Tree[index].size += Tree[Tree[index].son[1]].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^1];
                if (Tree[x].son[tmpx^1]) Tree[Tree[x].son[tmpx^1]].fa = f;
                Tree[x].son[tmpx^1] = 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,0,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[0]) return Tree[index].val;
                        else index = Tree[index].son[0];
                }    
        }
        inline int query_max(int index) {
                while (true) {
                        if (!Tree[index].son[1]) return Tree[index].val;
                        else index = Tree[index].son[1];
                }
        }
        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 > 1) return x;
                else if (Tree[index].son[0]) return query_max(Tree[index].son[0]);
                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 > 1) return x;
                else if (Tree[index].son[1]) return query_min(Tree[index].son[1]);
                else return INF;
        }
} T;

int main() {
        
        read(N);
        for (i = 1; i <= N; i++) {
                minn = INF;
                read(x);
                if (i == 1) { 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 0;
    
}