poj 3266 Cow School (splay 斜率优化)

#include<iostream>#include<cstring>#include<string>#include<cstdio>#include<stdio.h>#include<algorithm>#include<cmath>#include<map>#include<queue>#include<bitset>#include<stack>#include<set>using namespace std;#pragma comment(linker, "/STACK:1024000000,1024000000")#define inf 1e11#define eps 1e-9#define pii pair<int,int>#define MP make_pair#define LL  long long#define ULL unsigned long long #define N ( 300000 + 10 )#define M ( 200000 + 10)#define mod  1000000007double mi[N], ma[N], g[N];struct node {LL t, p;bool operator < ( const node &ot) const {return (LL)t * ot.p < (LL)p * ot.t;}}a[N];int x[N], y[N];int ch[N][2];double lk[N], rk[N];int par[N];int root, sz;int n;bool e;int newnode() {if(e) return ++sz;else return sz--;}int dcmp(double x) {if(fabs(x) < eps) return 0;return x < 0 ? -1 : 1;}void rot(int x) {int y = par[x], d = ch[y][1] == x;ch[y][d] = ch[x][!d];if(ch[x][!d]) par[ch[x][!d]] = y;ch[x][!d] = y;par[x] = par[y];par[y] = x;if(par[x]) ch[par[x]][ch[par[x]][1] == y] = x;}void splay(int x, int goal) {while(par[x] != goal) {int f = par[x], ff = par[f];if(ff == goal)rot(x);else if((ch[ff][1] == f) == (ch[f][1] == x))rot(f), rot(x);else rot(x), rot(x);}if(!goal) root = x;}int find(double x) {if(!root) {if(e) return 0;else return n + 1;}int u = root;while(u) {if(dcmp(x-lk[u]) > 0) u = ch[u][0];else if(dcmp(rk[u] - x) > 0) u = ch[u][1];else if(dcmp(lk[u]-x)>=0 && dcmp(x-rk[u])>=0) return u;}return u;}void insert(int i) {if(root == 0) {root = newnode();lk[root] = inf;rk[root] = -inf;return ;}int u = root;while(u) {if(x[i] <= x[u]) {if(!ch[u][0]) {ch[u][0] = newnode(), par[ch[u][0]] = u, splay(ch[u][0], 0);return ;}else u = ch[u][0];}else {if(!ch[u][1]) {ch[u][1] = newnode(), par[ch[u][1]] = u, splay(ch[u][1], 0);return ;}else u = ch[u][1];}}}double get(int i, int j) {if(x[i] == x[j]) {if(y[j] > y[i]) return inf;else return -inf;}return (1.0*y[i] - y[j]) / (1.0*x[i] - x[j]);}int getl(int x) {int t = ch[x][0];int ans = t;while(t) { if(dcmp(lk[t] - get(t,x)) >= 0) ans = t, t = ch[t][1];else t = ch[t][0];}return ans;}int getr(int x) {int t = ch[x][1], ans = t;while(t) {if(dcmp(rk[t] - get(x,t))<= 0) ans = t, t = ch[t][0];else t = ch[t][1];}return ans;}void maintain(int x) {splay(x, 0);if(ch[x][0]) {int ls = getl(x);splay(ls, root);par[ch[ls][1]] = 0, ch[ls][1] = 0;rk[ls] = lk[x] = get(ls, x);}else lk[x] = inf;if(ch[x][1]) {int rs = getr(x);splay(rs, root);par[ch[rs][0]] = 0, ch[rs][0] = 0;lk[rs] = rk[x] = get(x, rs);}else rk[x] = -inf;if(lk[x] <= rk[x]) {splay(x, 0);int ls = ch[x][0], rs = ch[x][1];if(!ls && !rs) {root = 0;return;}if(!ls) {root = rs;par[rs] = 0;lk[rs] = inf;return ;}if(!rs) {root = ls;par[ls] = 0;rk[ls] = -inf;return ;}par[ch[x][0]] = 0, ch[x][0] = 0;splay(ls, 0);ch[ls][1] = ch[x][1], par[ch[x][1]] = ls;rk[ls] = lk[rs] = get(ls, rs);}}void init(){root = 0;for(int i = 0; i <= n; ++i) ch[i][0] = ch[i][1] = 0, par[i] = 0;}void debug() {for(int i = 1; i <= n; ++i) {double mma = -inf, mmi = inf;for(int j = 1; j < i; ++j)mma = max(a[j].t - g[i] * a[j].p, mma);for(int j = i; j <= n; ++j)mmi = min(a[j].t - g[i] * a[j].p, mmi);printf("i %d mi %.5lf %.5lf ma %.5lf %.5lf\n", i, mi[i], mmi, ma[i], mma);}}int main() {//freopen("in.in", "r", stdin);//freopen("out.out", "w", stdout);while(~scanf("%d", &n)) {LL sumt = 0, sump = 0;for(int i = 1; i <= n; ++i)scanf("%lld%lld", &a[i].t, &a[i].p);sort(a+1, a+n+1);int cnt = 1;for(int i = n; i >= 1; --i) {sumt += a[i].t;sump += a[i].p;g[i] = (double)sumt / sump;}e = 1;init();sz = 0;for(int i = 1; i <= n; ++i) {int j = find(g[i]);if(j == 0) ma[i] = -inf;else ma[i] = a[j].t - g[i] * a[j].p;x[i] = a[i].p;y[i] = a[i].t;insert(i);maintain(i);}e = 0;init();sz = n;for(int i = n; i >= 1; --i) {x[i] = a[i].p;y[i] = -a[i].t;insert(i);maintain(i);int j = find(-g[i]);if(j == n+1) mi[i] = inf;else mi[i] = a[j].t - g[i] * a[j].p;}int ans = 0;for(int i = 1; i <= n; ++i) {if(dcmp(ma[i] - mi[i]) > 0) ++ans;}printf("%d\n", ans);for(int i = 1; i <= n; ++i) {if(dcmp(ma[i]- mi[i]) > 0) printf("%d\n", i-1);}}}