[hdoj5192] 树状数组

枚举所有的区间。对于确定的区间，假设最终的高度为h，
代价是max(∑(Hi−h),∑(h−Hj))（Hi＞h,Hj≤h)
等价于max(∑Hi−cnt(i)∗h,cnt(j)∗h−∑Hj)
(cnt(i)表示满足Hi＞h的堆数, cnt(j)表示满足Hj≤h 的堆数)。∑Hi−cnt(i)∗h关于h呈递减，cnt(j)∗h−∑Hj关于h呈递增。一个递减到0，一个从0开始递增，所以代价与h的函数图像是V字形的，交点处代价最小。此时 ∑Hi−cnt(i)∗h=cnt(j)∗h−∑Hj，h=∑Hi+∑Hjcnt(i)+cnt(j)，分母是总堆数W，分子是这个区间积木的总个数。h实际上就是这个区间的平均高度aver。考虑到四舍五入，答案是aver或者aver+1，当然还需要与题目给定的H做下比较，最终的方案是这3个数之一。确定高度之后，把高的变矮需要知道比当前高度大的个数以及高度总和，把矮的变高类似。因此添加一堆和删除一堆时，需要维护个数和总和。可以通过树状数组维护，整个问题的复杂度O((n+W)logn).
代码如下：

 #include <iostream>
 #include <cstdio>
 #include <algorithm>
 #include <cstring>
 #include <map>
 #include <queue>
 #include <cmath>
 #include <vector>
 #include <ctime>
 #include <cctype>
 
 using namespace std;
 
 #define mem0(a) memset(a, 0, sizeof(a))
 #define lson l, m, rt << 1
 #define rson m + 1, r, rt << 1 | 1
 #define define_m int m = (l + r) >> 1
 #define Rep(a, b) for(int a = 0; a < b; a++)
 #define lowbit(x) ((x) & (-(x)))
 #define constructInt3(name, a, b, c) name(int a = 0, int b = 0, int c = 0): a(a), b(b), c(c) {}
 #define constructInt2(name, a, b) name(int a = 0, int b = 0): a(a), b(b) {}
 
 typedef double db;
 typedef long long LL;
 
 const int dx[] = {, , -, };
 const int dy[] = {, -, , };
 const int maxn = 1e4 + ;
 const int maxm = 1e5 + ;
 const int MD = 1e9 +;
 
 struct Point {
     int x, y;
     bool operator < (const Point &opt) const {
         return x < opt.x || x == opt.x && y < opt.y;
     }
     Point operator - (const Point &opt) const {
         return Point(x - opt.x, y - opt.y);
     }
     constructInt2(Point, x, y);
     void inp() {
         scanf("%d %d", &x, &y);
     }
     void outp() {
         printf("(%d, %d), ", x, y);
     }
 };
 
 struct Trie {
         const static int char_size = ;
         int cc;
         int cht[][char_size];
         int mark[];
         Trie() { cc = ; mem0(mark); mem0(cht); }
         int Idex(char ch) { return ch - ''; }
         void Insert(char s[], int v) {
                 int pos = ;
                 for(int i = ; s[i]; i++) {
                         int id = Idex(s[i]);
                         if(!cht[pos][id]) cht[pos][id] = ++cc;
                         pos = cht[pos][id];
                 }
                 mark[pos] = v;
         }
         bool Find(char s[]) {
                 int pos = ;
                 for(int i = ; s[i]; i++) {
                         int id = Idex(s[i]);
                         if(!cht[pos][id]) return ;
                         pos = cht[pos][id];
                 }
                 return mark[pos];
         }
 };
 
 struct KMP {
         int next[];
         void GetNext(char s[]) {
                 mem0(next);
                 next[] = next[] = ;
                 for(int i = ; s[i]; i++) {
                         int j = next[i];
                         while(j && s[i] != s[j]) j = next[j];
                         next[i + ] = s[j] == s[i]? j +  : ;
                 }
         }
         void Match(char s[], char t[]) {
                 int j = , len = strlen(t);
                 for(int i = ; s[i]; i++) {
                         while(j && s[i] != t[j]) j = next[j];
                         if(s[i] == t[j]) j++;
                         if(j == len) printf("%d\n", i - len + );
                 }
         }
 };
 
 struct Matrix {
         int a[][];
         Matrix operator * (const Matrix &_A) const {
                 Matrix tmp;
                 mem0(tmp.a);
                 for(int i = ; i < ; i++) {
                         for(int j = ; j < ; j++) {
                                 for(int k = ; k < ; k++) {
                                         tmp.a[i][j] = ((LL)a[i][k] * _A.a[k][j] + tmp.a[i][j]) % MD;
                                 }
                         }
                 }
                 return tmp;
         }
 };
 
 struct Edge {
     int u, v;
     constructInt2(Edge, u, v);
 };
 
 struct Segment {
         Point a, b;
         void inp() {
                 scanf("%d%d%d%d", &a.x, &a.y, &b.x, &b.y);
                 if(a.x > b.x) {
                         swap(a.x, b.x);
                         swap(a.y, b.y);
                 }
         }
 };
 
 Matrix CalcMatrix(Matrix a, int n) {
         if(n == ) return a;
         Matrix tmp = CalcMatrix(a, n >> );
         tmp = tmp * tmp;
         if(n & ) tmp = tmp * a;
         return tmp;
 }
 
 inline int ReadInt() {
     char c = getchar();
     while(!isdigit(c)) c = getchar();
 
     int x = ;
     while(isdigit(c)) {
         x = x *  + c - '';
         c = getchar();
     }
     return x;
 }
 
 inline void WriteInt(int i) {
     int p = ;
     static int buf[];
     if(i == ) p++;
     else while(i) {
         buf[p++] = i % ;
         i /= ;
     }
     for(int j = p - ; j; j--) putchar('' + buf[j]);
 }
 
 int Cross(Point a, Point b) {
     return a.x * b.y - a.y * b.x;
 }
 
 int Dist2(Point a, Point b) {
     int x = a.x - b.x, y = a.y - b.y;
     return x * x + y * y;
 }
 int ConvexHull(Point *p, int n, Point *ch) {
     sort(p, p + n);
     int m = ;
     for (int i = ; i < n; i++) {
         while (m >  && Cross(ch[m - ] - ch[m - ], p[i] - ch[m - ]) <= ) m--;
         ch[m++] = p[i];
     }
     int k = m;
     for (int i = n - ; i >= ; i--) {
         while (m > k && Cross(ch[m - ] - ch[m - ], p[i] - ch[m - ]) <= ) m--;
         ch[m++] = p[i];
     }
     if (n > ) m--;
     return m;
 }
 
 template<class edge> struct Graph {
     vector<vector<edge> > adj;
     Graph(int n) { adj.clear(); adj.resize(n + ); }
     Graph() { adj.clear(); }
     void resize(int n) { adj.resize(n + ); }
     void add(int s, edge e){ adj[s].push_back(e); }
     void del(int s, edge e) { adj[s].erase(find(iter(adj[s]), e)); }
     void clear() { adj.clear(); }
     vector<edge>& operator [](int t) { return adj[t]; }
 };
 
 template<class T> struct TreeArray {
     vector<T> c;
     int maxn;
     TreeArray(int n) { c.resize(n + ); maxn = n; }
     TreeArray() { c.clear(); maxn = ; }
     void clear() { memset(&c[], , sizeof(T) * maxn); }
     void resize(int n) { c.resize(n + ); maxn = n; }
     void add(int p, T x) { while (p < maxn) { c[p] += x; p += lowbit(p); } }
     T get(int p) { T res = ; while (p) { res += c[p]; p -= lowbit(p); } return res; }
     T range(int a, int b) { return get(b) - get(a - ); }
 };
 
 int n, W, H, a[];
 LL sum[], step, maxh;
 TreeArray<LL> ta(), ta0();
 void Check(int h, int r) {
     if (sum[n +  * W - ] < (LL)h * W) return ;
     LL sum1 = ta0.get(h + ), sumall = sum[r] - sum[r - W], c = ta.get(h + );
     LL newsum1 = h * c - sum1, newsum2 = sumall - h * W + newsum1;
     LL res = max(newsum1, newsum2);
     if (res < step || res == step && h > maxh) {
         step = res;
         maxh = h;
     }
 }
 int main() {
     //freopen("in.txt", "r", stdin);
     while (cin >> n >> W >> H) {
         mem0(a);
         for (int i = ; i < n; i++) {
             scanf("%d", a + i + W);
         }
         int total = n +  * W;
         for (int i = ; i < total; i++) sum[i] = sum[i - ] + a[i];
 
         if (sum[total - ] < (LL)H * W) {
             puts("-1");
             continue;
         }
 
         ta.clear();
         ta0.clear();
         step = H * W;
         maxh = H;
         ta.add(, W );
         ta0.add(, );
 
         for (int i = W; i < total; i++) {
             int num = sum[i] - sum[i - W], ave = num / W;
             if (ave < H) ave = H;
             ta.add(a[i - W] + , -);
             ta0.add(a[i - W] + , -a[i - W]);
             ta.add(a[i] + , );
             ta0.add(a[i] + , a[i]);
             Check(ave, i);
             Check(ave + , i);
         }
         cout << maxh << " " << step << endl;
     }
     return ;
 }