This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include "bits/stdc++.h"
using namespace std;
//#define int long long
const int MAXN = 3e5 + 10;
const int MOD = 998244353;
#define ll __int128
mt19937_64 rng((int)std::chrono::steady_clock::now().time_since_epoch().count());
int rnd(int x, int y) {
int u = uniform_int_distribution<int>(x, y)(rng); return u;
}
ll read() { int x; cin >> x; return (ll)x; }
long long bm(long long b, long long p) {
if(p==0) return 1 % MOD;
long long r = bm(b, p >> 1);
if(p&1) return (((r*r) % MOD) * b) % MOD;
return (r*r) % MOD;
}
long long inv(long long b) {
return bm(b, MOD-2);
}
long long f[MAXN];
long long nCr(int n, int r) {
long long ans = f[n]; ans *= inv(f[r]); ans %= MOD;
ans *= inv(f[n-r]); ans %= MOD; return ans;
}
long long fib[MAXN], lucas[MAXN];
void precomp() {
for(int i=0; i<MAXN; i++) f[i] = (i == 0 ? 1 % MOD : (f[i-1] * i) % MOD);
lucas[0] = 2;
lucas[1] = 1;
for(int i=2; i<MAXN; i++) lucas[i] = (lucas[i-2] + lucas[i-1]) % MOD;
fib[0] = 0;
fib[1] = 1;
for(int i=2; i<MAXN; i++) fib[i] = (fib[i-2] + fib[i-1]) % MOD;
}
int fastlog(int x) {
return (x == 0 ? -1 : 64 - __builtin_clzll(x) - 1);
}
void google(int i) { cout << "Case #" << i << ": "; }
int csb(int l, int r, int k) { // count number of [l, r] such that i & 2^k > 0
if(l > r) return 0;
if(l == 0) {
int s = r / (1ll << (k+1)); // number of complete cycles
int t = r % (1ll << (k+1));
int ans = s * (1ll << k);
ans += (t >= (1ll << k) ? t - (1ll << k) + 1 : 0);
return ans;
}
else return csb(0, r, k) - csb(0, l - 1, k);
}
int lis(vector<int> a) {
int n = a.size();
int bucket[n+1];
for(int i=1; i<=n; i++) bucket[i] = 1e18;
int ans = 1;
for(int x: a) {
auto it = lower_bound(bucket + 1, bucket +n +1, x);
int d = distance(bucket, it);
ans = max(ans, d);
bucket[d] = min(bucket[d], x);
}
return ans;
}
bool cmp(pair<int, int> x, pair<int, int> y) {
return x.second < y.second;
}
int n, k, a[MAXN], b[MAXN];
double fun(int bcnt) {
double dp[k - bcnt + 1][bcnt + 1][n + 1]; // type A, type B, prefix
for(int i=0; i<=k-bcnt; i++) {
for(int j=0; j<=bcnt; j++) {
for(int l=0; l<=n; l++) {
dp[i][j][l] = 1e9;
}
}
}
for(int i=0; i<=n; i++) dp[0][0][i] = 0;
for(int i=0; i<=k-bcnt; i++) {
for(int j=0; j<=bcnt; j++) {
if(i == 0 && j == 0) continue;
for(int l=1; l<=n; l++) {
// register as type A
if(i > 0) dp[i][j][l] = dp[i-1][j][l-1] + a[l] * 1.0 / (bcnt + 1);
// register as type B
if(j > 0 && b[l] != 1226) dp[i][j][l] = min(dp[i][j][l], dp[i][j-1][l-1] + b[l] * 1.0 / j);
// register as neither
dp[i][j][l] = min(dp[i][j][l], dp[i][j][l-1]);
}
}
}
return dp[k-bcnt][bcnt][n];
}
void solve(int tc) {
cin >> n >> k;
pair<int, int> p[n+1];
for(int i=1; i<=n; i++) {
cin >> p[i].first >> p[i].second;
if(p[i].second == -1) p[i].second = 1226;
}
sort(p+1, p+n+1, cmp);
for(int i=1; i<=n; i++) {
a[i] = p[i].first, b[i] = p[i].second;
}
int lb = 0, rb = k;
while(lb < rb) {
int mid = (lb + rb) >> 1;
if(fun(mid) > fun(mid+1)) lb = mid+1;
else rb = mid;
}
cout << fixed << setprecision(10) << fun(lb) << "\n";
}
int32_t main() {
precomp();
ios::sync_with_stdio(0); cin.tie(0);
int t = 1; //cin >> t;
for(int i=1; i<=t; i++) solve(i);
}
// I don't know geometry.
// Teaming is unfair.
/*
8
7
3 15
19 40
11 62
7 72
16 27
33 53
14 50
17 24
*/
Compilation message (stderr)
Main.cpp: In function 'int lis(std::vector<int>)':
Main.cpp:54:39: warning: overflow in conversion from 'double' to 'int' changes value from '1.0e+18' to '2147483647' [-Woverflow]
54 | for(int i=1; i<=n; i++) bucket[i] = 1e18;
| ^~~~
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