Submission #732726

#TimeUsernameProblemLanguageResultExecution timeMemory
732726senthetaAliens (IOI16_aliens)C++17
100 / 100
232 ms10272 KiB
#include "aliens.h" // author : sentheta aka vanwij #include<iostream> #include<iomanip> #include<algorithm> #include<cassert> #include<random> #include<chrono> #include<cmath> #include<string> #include<vector> #include<bitset> #include<queue> #include<stack> #include<map> #include<set> using namespace std; #define Int long long #define V vector #define pii pair<int,int> #define ff first #define ss second mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); #define pow2(x) (1LL<<(x)) #define msb(x) (63-__builtin_clzll(x)) #define bitcnt(x) (__builtin_popcountll(x)) #define nl '\n' #define _ << ' ' << #define all(x) (x).begin(), (x).end() #define rep(i,a,b) for(int i = (int)(a); i < (int)(b); i++) #define dbg(x) if(1) cout << "?" << #x << " : " << (x) << endl << flush; #define cerr if(1) cerr const Int INF = 1e18; const Int N = 1e5+5; // const Int K = 505; const Int M = 1e6+5; struct line { Int m, c; int idx; Int eval(Int x) { return m * x + c; } Int cut(line l) { return (c - l.c) / (l.m - m); } }; struct Cht { line s[N]; int st = 1, ed = 0; void upd(line cur) { while(ed-st+1>=2 && cur.cut(s[ed])<=s[ed].cut(s[ed-1])) --ed; s[++ed] = cur; } line qry(Int x) { while(ed-st+1>=2 && s[st].eval(x) > s[st+1].eval(x)) st++; return s[st]; } }; Int n, m, k; V<Int> l, r; Int dp[N], cnt[N]; inline Int sqr(Int x){return x*x;} void solve(Int cost){ Cht cht; dp[0] = sqr(r[0]-l[0]+1) +cost; cnt[0] = 1; rep(i,1,n){ // dp[i] = sqr(r[i]-l[0]+1) +cost; // cnt[i] = 1; // rep(j,1,i+1){ // Int x = dp[j-1] +sqr(r[i]-l[j]+1) -(l[j]<=r[j-1] ? sqr(r[j-1]-l[j]+1):0) + cost; // if(x < dp[i]){ // dp[i] = x; // cnt[i] = cnt[j-1]+1; // } // if(x==dp[i]){ // cnt[i] = min(cnt[i], cnt[j-1]+1); // } // } Int m = -2*l[i]; Int c = l[i]*l[i]-2*l[i] +dp[i-1] -(l[i]<=r[i-1] ? sqr(r[i-1]-l[i]+1):0); line cur = {m, c, i}; cht.upd(cur); Int from0 = sqr(r[i]-l[0]+1) +cost; Int not0 = r[i]*r[i] +2*r[i] +1 +cht.qry(r[i]).eval(r[i]) +cost; if(from0 <= not0){ dp[i] = from0; cnt[i] = 1; } else{ dp[i] = not0; cnt[i] = cnt[cht.qry(r[i]).idx-1] + 1; // cnt[i] = mpcnt[{bm,bc}] + 1; } // dbg(dp[i]); // dbg(cnt[i]); } } Int take_photos(int _n,int _m,int _k,V<int> _l,V<int> _r){ n = _n; m = _m; k = _k; l = V<Int>(all(_l)); r = V<Int>(all(_r)); // remove subsegments V<int> ord; rep(i,0,n){ if(l[i] > r[i]) swap(l[i], r[i]); ord.push_back(i); } sort(all(ord),[&](int i,int j){ if(l[i]==l[j]) return r[i] < r[j]; return l[i] > l[j]; }); V<int> stak; for(int i : ord){ while(!stak.empty() && r[stak.back()]<=r[i]) stak.pop_back(); stak.push_back(i); } reverse(all(stak)); ord.swap(stak); // result is ordered from l // reorder l[] and r[] { V<Int> vl, vr; for(int i : ord){ // cerr << l[i] _ r[i] << nl; vl.push_back(l[i]); vr.push_back(r[i]); } l.swap(vl); r.swap(vr); } n = ord.size(); // find minimum cost to make <= k merging Int cost = -1; for(Int J=1LL<<42; J; J/=2){ // for(Int J=m*m; J; J/=2) rep(loop,0,2){ // { // check cost+J solve(cost+J); if(cnt[n-1] > k) cost+=J; else ; } cost++; // dbg(k); solve(cost-1); Int a = dp[n-1], b = cnt[n-1]; Int ans1 = a - b*(cost-1); // dbg(cnt[n-1]); solve(cost); Int c = dp[n-1], d = cnt[n-1]; Int ans2 = c - d*cost; // dbg(cnt[n-1]); if(k>=n) return ans2; // linear progression from ans1 to ans2 Int ans = ans1 + (k-b)*(ans2-ans1)/(d-b); // dbg(k); // dbg(cnt[n-1]); // assert(cnt[n-1] <= k); // Int ans = dp[n-1] - cnt[n-1]*cost; return ans; }
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