#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
#define scan(x) do{while((x=getchar())<'0'); for(x-='0'; '0'<=(_=getchar()); x=(x<<3)+(x<<1)+_-'0');}while(0)
char _;
#define complete_unique(a) a.erase(unique(a.begin(),a.end()),a.end())
#define all(a) a.begin(),a.end()
#define println printf("\n");
#define readln(x) getline(cin,x);
#define pb push_back
#define endl "\n"
#define INT_INF 0x3f3f3f3f
#define LL_INF 0x3f3f3f3f3f3f3f3f
#define MOD 1000000007
#define MOD2 1190492669
#define SEED 131
#define mp make_pair
#define fastio cin.tie(0); cin.sync_with_stdio(0);
#define MAXN 100005
#define MAXV 100005
typedef unsigned long long ull;
typedef long long ll;
typedef long double ld;
typedef unordered_map<int,int> umii;
typedef pair<int,int> pii;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef pair<int,pii> triple;
typedef int8_t byte;
mt19937 g1(time(0));
int randint(int a, int b){return uniform_int_distribution<int>(a, b)(g1);}
ll randlong(ll a,ll b){return uniform_int_distribution<long long>(a, b)(g1);}
ll gcd(ll a, ll b){return b == 0 ? a : gcd(b, a % b);}
ll lcm(ll a, ll b){return a*b/gcd(a,b);}
ll fpow(ll b, ll exp, ll mod){if(exp == 0) return 1;ll t = fpow(b,exp/2,mod);if(exp&1) return t*t%mod*b%mod;return t*t%mod;}
ll divmod(ll i, ll j, ll mod){i%=mod,j%=mod;return i*fpow(j,mod-2,mod)%mod;}
struct node{
int l,r;
pair<int,pair<ld,ld>> bst;
};
struct MaxLiChaoTree{
node seg[4*MAXV];
inline ld calc(int rt, int m){return seg[rt].bst.second.first*m+seg[rt].bst.second.second;}
inline ld calc(pair<ld,ld> bst, int m){return bst.first*m+bst.second;}
inline ld inter(pair<ld,ld> f, pair<ld,ld> s){return (s.second-f.second)/(f.first-s.first);}
void build(int l, int r, int rt){
seg[rt].l = l, seg[rt].r = r, seg[rt].bst = mp(-1,mp(0,-LL_INF));
if(l == r) return;
int mid = (l+r)/2;
build(l,mid,rt<<1);
build(mid+1,r,rt<<1|1);
}
void add_line(int rt, pair<int,pair<ld,ld>> line){
if(seg[rt].l == seg[rt].r){
if(calc(line.second,seg[rt].l) >= calc(rt,seg[rt].l)) seg[rt].bst = line;
return;
}
int mid = (seg[rt].l+seg[rt].r)/2;
bool f = calc(rt,seg[rt].l) <= calc(line.second,seg[rt].l);
bool s = calc(rt,seg[rt].r) <= calc(line.second,seg[rt].r);
if(f && s){
seg[rt].bst = line;
return;
}else if(!f && !s) return;
ld x = inter(line.second,seg[rt].bst.second);
if(x <= mid){
if(calc(line.second,mid) >= calc(rt,mid)) swap(line,seg[rt].bst);
add_line(rt<<1,line);
}else{
if(calc(line.second,mid) >= calc(rt,mid)) swap(line,seg[rt].bst);
add_line(rt<<1|1,line);
}
}
pair<ld,int> get(int rt, int pos){
if(seg[rt].l == seg[rt].r) return mp(calc(rt,pos),seg[rt].bst.first);
int mid = (seg[rt].l+seg[rt].r)/2;
if(pos <= mid) return max(mp(calc(rt,pos),seg[rt].bst.first),get(rt<<1,pos));
return max(mp(calc(rt,pos),seg[rt].bst.first),get(rt<<1|1,pos));
}
};
int N,K;
double dp2[MAXN][MAXN];
pair<ld,int> dp[MAXN];
MaxLiChaoTree t;
inline double inter(int j, int k){
double m1 = dp[j].first, b1 = -j;
double m2 = dp[k].first, b2 = -k;
return (b2-b1)/(m1-m2);
}
inline int getGroups(double C){
// deque<int> dq; dq.pb(0);
t.build(1,N,1); t.add_line(1,mp(0,mp(0,0)));
for(int i=1; i<=N; i++){
// while(dq.size() >= 2 && dp[dq[0]].first*i-dq[0] <= dp[dq[1]].first*i-dq[1]) dq.pop_front();
pair<ld,int> p = t.get(1,i);
dp[i].first = p.first/i+1-C;
dp[i].second = dp[p.second].second+1;
// while(dq.size() >= 2 && inter(dq[dq.size()-2],i) <= inter(dq[dq.size()-2],dq.back())) dq.pop_back();
// dq.pb(i);
t.add_line(1,mp(i,mp(dp[i].first,-i)));
}
return dp[N].second;
}
//inline double solve(){
// for(int k=1; k<=K; k++){
// deque<int> dq; dq.pb(0);
// for(int i=1; i<=N; i++){
// while(dq.size() >= 2 && dp2[k-1][dq[0]]*i-dq[0] <= dp2[k-1][dq[1]]*i-dq[1]) dq.pop_front();
// dp2[k][i] = (dp2[k-1][dq[0]]*i-dq[0])/i+1;
// while(dq.size() >= 2 && inter(k,dq[dq.size()-2],i) <= inter(k,dq[dq.size()-2],dq.back())) dq.pop_back();
// dq.pb(i);
// }
// }
// return dp2[K][N];
//}
int main(){
scanf("%d %d",&N,&K);
double low = 0, high = 20, ans = 0;
while(high-low >= 1e-15){
double mid = (low+high)/2;
int g = getGroups(mid);
if(g <= K){
ans = mid;
high = mid-1e-15;
}else low = mid+1e-15;
}
getGroups(ans);
ld res = dp[N].first+ans*K;
printf("%.8Lf\n",res);
}
/*
2 1
ans=1.5
*/
Compilation message
akvizna.cpp: In function 'int main()':
akvizna.cpp:134:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
scanf("%d %d",&N,&K);
~~~~~^~~~~~~~~~~~~~~
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::(anonymous namespace)::__destroy_string<wchar_t>(void*)':
(.text._ZNSt13__facet_shims12_GLOBAL__N_116__destroy_stringIwEEvPv+0x1e): relocation truncated to fit: R_X86_64_32S against symbol `std::basic_string<wchar_t, std::char_traits<wchar_t>, std::allocator<wchar_t> >::_Rep::_S_empty_rep_storage' defined in .bss._ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE[_ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-wstring-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::(anonymous namespace)::__destroy_string<char>(void*)':
(.text._ZNSt13__facet_shims12_GLOBAL__N_116__destroy_stringIcEEvPv+0x1e): relocation truncated to fit: R_X86_64_32S against symbol `std::string::_Rep::_S_empty_rep_storage' defined in .bss._ZNSs4_Rep20_S_empty_rep_storageE[_ZNSs4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-string-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `std::__facet_shims::(anonymous namespace)::money_get_shim<wchar_t>::do_get(std::istreambuf_iterator<wchar_t, std::char_traits<wchar_t> >, std::istreambuf_iterator<wchar_t, std::char_traits<wchar_t> >, bool, std::ios_base&, std::_Ios_Iostate&, std::basic_string<wchar_t, std::char_traits<wchar_t>, std::allocator<wchar_t> >&) const':
(.text._ZNKSt13__facet_shims12_GLOBAL__N_114money_get_shimIwE6do_getESt19istreambuf_iteratorIwSt11char_traitsIwEES6_bRSt8ios_baseRSt12_Ios_IostateRSbIwS5_SaIwEE+0xfe): relocation truncated to fit: R_X86_64_32S against symbol `std::basic_string<wchar_t, std::char_traits<wchar_t>, std::allocator<wchar_t> >::_Rep::_S_empty_rep_storage' defined in .bss._ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE[_ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-wstring-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `std::__facet_shims::(anonymous namespace)::money_get_shim<wchar_t>::do_get(std::istreambuf_iterator<wchar_t, std::char_traits<wchar_t> >, std::istreambuf_iterator<wchar_t, std::char_traits<wchar_t> >, bool, std::ios_base&, std::_Ios_Iostate&, std::basic_string<wchar_t, std::char_traits<wchar_t>, std::allocator<wchar_t> >&) const':
(.text._ZNKSt13__facet_shims12_GLOBAL__N_114money_get_shimIwE6do_getESt19istreambuf_iteratorIwSt11char_traitsIwEES6_bRSt8ios_baseRSt12_Ios_IostateRSbIwS5_SaIwEE+0x17b): relocation truncated to fit: R_X86_64_32S against symbol `std::basic_string<wchar_t, std::char_traits<wchar_t>, std::allocator<wchar_t> >::_Rep::_S_empty_rep_storage' defined in .bss._ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE[_ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-wstring-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `std::__facet_shims::(anonymous namespace)::money_get_shim<char>::do_get(std::istreambuf_iterator<char, std::char_traits<char> >, std::istreambuf_iterator<char, std::char_traits<char> >, bool, std::ios_base&, std::_Ios_Iostate&, std::string&) const':
(.text._ZNKSt13__facet_shims12_GLOBAL__N_114money_get_shimIcE6do_getESt19istreambuf_iteratorIcSt11char_traitsIcEES6_bRSt8ios_baseRSt12_Ios_IostateRSs+0xfe): relocation truncated to fit: R_X86_64_32S against symbol `std::string::_Rep::_S_empty_rep_storage' defined in .bss._ZNSs4_Rep20_S_empty_rep_storageE[_ZNSs4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-string-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `std::__facet_shims::(anonymous namespace)::money_get_shim<char>::do_get(std::istreambuf_iterator<char, std::char_traits<char> >, std::istreambuf_iterator<char, std::char_traits<char> >, bool, std::ios_base&, std::_Ios_Iostate&, std::string&) const':
(.text._ZNKSt13__facet_shims12_GLOBAL__N_114money_get_shimIcE6do_getESt19istreambuf_iteratorIcSt11char_traitsIcEES6_bRSt8ios_baseRSt12_Ios_IostateRSs+0x17b): relocation truncated to fit: R_X86_64_32S against symbol `std::string::_Rep::_S_empty_rep_storage' defined in .bss._ZNSs4_Rep20_S_empty_rep_storageE[_ZNSs4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-string-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::__numpunct_fill_cache<char>(std::integral_constant<bool, false>, std::locale::facet const*, std::__numpunct_cache<char>*)':
(.text._ZNSt13__facet_shims21__numpunct_fill_cacheIcEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E[_ZNSt13__facet_shims21__numpunct_fill_cacheIcEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E]+0xa1): relocation truncated to fit: R_X86_64_32S against symbol `std::string::_Rep::_S_empty_rep_storage' defined in .bss._ZNSs4_Rep20_S_empty_rep_storageE[_ZNSs4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-string-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::__numpunct_fill_cache<char>(std::integral_constant<bool, false>, std::locale::facet const*, std::__numpunct_cache<char>*)':
(.text._ZNSt13__facet_shims21__numpunct_fill_cacheIcEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E[_ZNSt13__facet_shims21__numpunct_fill_cacheIcEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E]+0x24f): relocation truncated to fit: R_X86_64_32S against symbol `std::string::_Rep::_S_empty_rep_storage' defined in .bss._ZNSs4_Rep20_S_empty_rep_storageE[_ZNSs4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-string-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::__numpunct_fill_cache<wchar_t>(std::integral_constant<bool, false>, std::locale::facet const*, std::__numpunct_cache<wchar_t>*)':
(.text._ZNSt13__facet_shims21__numpunct_fill_cacheIwEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E[_ZNSt13__facet_shims21__numpunct_fill_cacheIwEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E]+0xa9): relocation truncated to fit: R_X86_64_32S against symbol `std::string::_Rep::_S_empty_rep_storage' defined in .bss._ZNSs4_Rep20_S_empty_rep_storageE[_ZNSs4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-string-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::__numpunct_fill_cache<wchar_t>(std::integral_constant<bool, false>, std::locale::facet const*, std::__numpunct_cache<wchar_t>*)':
(.text._ZNSt13__facet_shims21__numpunct_fill_cacheIwEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E[_ZNSt13__facet_shims21__numpunct_fill_cacheIwEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E]+0x114): relocation truncated to fit: R_X86_64_32S against symbol `std::basic_string<wchar_t, std::char_traits<wchar_t>, std::allocator<wchar_t> >::_Rep::_S_empty_rep_storage' defined in .bss._ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE[_ZNSbIwSt11char_traitsIwESaIwEE4_Rep20_S_empty_rep_storageE] section in /usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-wstring-inst.o)
/usr/lib/gcc/x86_64-linux-gnu/7/libstdc++.a(cow-shim_facets.o): In function `void std::__facet_shims::__numpunct_fill_cache<wchar_t>(std::integral_constant<bool, false>, std::locale::facet const*, std::__numpunct_cache<wchar_t>*)':
(.text._ZNSt13__facet_shims21__numpunct_fill_cacheIwEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E[_ZNSt13__facet_shims21__numpunct_fill_cacheIwEEvSt17integral_constantIbLb0EEPKNSt6locale5facetEPSt16__numpunct_cacheIT_E]+0x294): additional relocation overflows omitted from the output
collect2: error: ld returned 1 exit status
