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Kayaks CodeChef Solution
Problem -Kayaks CodeChef Solution
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Kayaks CodeChef Solution in C++14
#include <iostream>
#include <string>
#include <sstream>
#include <iomanip>
#include <math.h>
#include <stdio.h>
#include <assert.h>
#include <string.h>
#include <queue>
#include <stack>
#include <vector>
#include <map>
#include <set>
#include <functional>
#include <algorithm>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <complex>
using namespace std;
typedef long long LL;
typedef pair<LL, LL> PL;
typedef vector<LL> VL;
typedef vector<PL> VPL;
typedef vector<VL> VVL;
typedef pair<int, int> PI;
typedef vector<int> VI;
typedef vector<PI> VPI;
typedef vector<vector<int>> VVI;
typedef vector<vector<PI>> VVPI;
typedef long double LD;
typedef pair<LD, LD> PLDLD;
typedef complex<double> CD;
typedef vector<CD> VCD;
typedef vector<string> VS;
#define MP make_pair
#define PB push_back
#define F first
#define S second
#define LB lower_bound
#define UB upper_bound
#define SZ(x) ((int)x.size())
#define LEN(x) ((int)x.length())
#define ALL(x) begin(x), end(x)
#define RSZ resize
#define ASS assign
#define REV(x) reverse(x.begin(), x.end());
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
const LL INF = 1E18;
const int MAXX = 300005;
const LD PAI = 4 * atan((LD)1);
template <typename T>
class fenwick_tree {
public:
vector<T> fenw;
int n;
fenwick_tree(int _n) : n(_n) {
fenw.resize(n);
}
void update(int x, T v) {
while (x < n) {
fenw[x] += v;
x |= (x + 1);
//x += (x & (-x));
}
}
T query(int x) {
T v{};
while (x >= 0) {
v += fenw[x];
x = (x & (x + 1)) - 1;
}
return v;
}
T query_full(int a, int b) { // range query
return query(b) - ((a <= 1) ? 0 : query(a - 1));
}
};
template <typename T>
vector<T> serialize(vector<T> a, int startvalue = 0) {
int n = a.size(), i, j, k, ct;
vector<T> ans(n);
map<T, T> id;
for (auto p : a) id[p] = 0;
ct = startvalue;
for (auto p : id) id[p.first] = ct++;
for (i = 0; i < n; i++) ans[i] = id[a[i]];
return ans;
}
template <typename T>
class segment_tree {
vector<T> t;
T VERYBIG;
bool ISMAXRANGE;
int size;
public:
segment_tree(int n, bool range_max = true) {
if (is_same<T, int>::value) VERYBIG = (1 << 30);
else if (is_same<T, LL>::value) VERYBIG = (1LL << 60);
//else if (is_same<T, PII>::value) VERYBIG = PII({ 1E9, 1E9 });
//else if (is_same<T, PLL>::value) VERYBIG = { 1LL << 60, 1LL << 60 };
ISMAXRANGE = range_max;
if (ISMAXRANGE) t.assign(4 * n + 1, 0);
else t.assign(4 * n + 1, VERYBIG);
size = n;
}
void initialize_array(vector<T>& v) {
initialize_with_array(1, 0, size - 1, v);
}
void initialize_with_array(int startpos, int l, int r, vector<T>& v) {
if (l == r) {
t[startpos] = v[l];
}
else {
int m = (l + r) / 2;
initialize_with_array(2 * startpos, l, m, v);
initialize_with_array(2 * startpos + 1, m + 1, r, v);
if (ISMAXRANGE == 1) t[startpos] = max(t[startpos * 2], t[startpos * 2 + 1]);
else t[startpos] = min(t[startpos * 2], t[startpos * 2 + 1]);
}
}
void update(int index, T val) { // insert val into location index
update_full(1, 0, size - 1, index, val);
}
void update_full(int startpos, int l, int r, int index, T val) {
if (l == r) {
t[startpos] = val;
}
else {
int m = (l + r) / 2;
if (index <= m) update_full(2 * startpos, l, m, index, val);
else update_full(2 * startpos + 1, m + 1, r, index, val);
if (ISMAXRANGE) t[startpos] = max(t[startpos * 2], t[startpos * 2 + 1]);
else t[startpos] = min(t[startpos * 2], t[startpos * 2 + 1]);
}
}
T query(int l, int r) { // get range min/max between l and r
if (l > r) {
if (ISMAXRANGE) return 0;
else return VERYBIG;
}
return query_full(1, 0, size - 1, l, r);
}
T query_full(int startpos, int left, int right, int l, int r) { // left/right = current range, l/r = intended query range
if ((left >= l) && (right <= r)) return t[startpos];
int m = (left + right) / 2;
T ans;
if (ISMAXRANGE) ans = -VERYBIG;
else ans = VERYBIG;
if (m >= l) {
if (ISMAXRANGE) ans = max(ans, query_full(startpos * 2, left, m, l, r));
else ans = min(ans, query_full(startpos * 2, left, m, l, r));
}
if (m + 1 <= r) {
if (ISMAXRANGE) ans = max(ans, query_full(startpos * 2 + 1, m + 1, right, l, r));
else ans = min(ans, query_full(startpos * 2 + 1, m + 1, right, l, r));
}
return ans;
}
};
//#define MOD 1000000007
int MOD = 1, root = 2; // 998244353
template<class T> T invGeneral(T a, T b) {
a %= b; if (a == 0) return b == 1 ? 0 : -1;
T x = invGeneral(b, a);
return x == -1 ? -1 : ((1 - (LL)b * x) / a + b) % b;
}
template<class T> struct modular {
T val;
explicit operator T() const { return val; }
modular() { val = 0; }
modular(const LL& v) {
val = (-MOD <= v && v <= MOD) ? v : v % MOD;
if (val < 0) val += MOD;
}
friend ostream& operator<<(ostream& os, const modular& a) { return os << a.val; }
friend bool operator==(const modular& a, const modular& b) { return a.val == b.val; }
friend bool operator!=(const modular& a, const modular& b) { return !(a == b); }
friend bool operator<(const modular& a, const modular& b) { return a.val < b.val; }
modular operator-() const { return modular(-val); }
modular& operator+=(const modular& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
modular& operator-=(const modular& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
modular& operator*=(const modular& m) { val = (LL)val * m.val % MOD; return *this; }
friend modular pow(modular a, LL p) {
modular ans = 1; for (; p; p /= 2, a *= a) if (p & 1) ans *= a;
return ans;
}
friend modular inv(const modular& a) {
auto i = invGeneral(a.val, MOD); assert(i != -1);
return i;
} // equivalent to return exp(b,MOD-2) if MOD is prime
modular& operator/=(const modular& m) { return (*this) *= inv(m); }
friend modular operator+(modular a, const modular& b) { return a += b; }
friend modular operator-(modular a, const modular& b) { return a -= b; }
friend modular operator*(modular a, const modular& b) { return a *= b; }
friend modular operator/(modular a, const modular& b) { return a /= b; }
};
typedef modular<int> mi;
typedef pair<mi, mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
namespace vecOp {
template<class T> vector<T> rev(vector<T> v) { reverse(ALL(v)); return v; }
template<class T> vector<T> shift(vector<T> v, int x) { v.insert(v.begin(), x, 0); return v; }
template<class T> vector<T>& operator+=(vector<T>& l, const vector<T>& r) {
l.rSZ(max(SZ(l), SZ(r))); F0R(i, SZ(r)) l[i] += r[i]; return l;
}
template<class T> vector<T>& operator-=(vector<T>& l, const vector<T>& r) {
l.rSZ(max(SZ(l), SZ(r))); F0R(i, SZ(r)) l[i] -= r[i]; return l;
}
template<class T> vector<T>& operator*=(vector<T>& l, const T& r) { trav(t, l) t *= r; return l; }
template<class T> vector<T>& operator/=(vector<T>& l, const T& r) { trav(t, l) t /= r; return l; }
template<class T> vector<T> operator+(vector<T> l, const vector<T>& r) { return l += r; }
template<class T> vector<T> operator-(vector<T> l, const vector<T>& r) { return l -= r; }
template<class T> vector<T> operator*(vector<T> l, const T& r) { return l *= r; }
template<class T> vector<T> operator*(const T& r, const vector<T>& l) { return l * r; }
template<class T> vector<T> operator/(vector<T> l, const T& r) { return l /= r; }
template<class T> vector<T> operator*(const vector<T>& l, const vector<T>& r) {
if (min(SZ(l), SZ(r)) == 0) return {};
vector<T> x(SZ(l) + SZ(r) - 1); F0R(i, SZ(l)) F0R(j, SZ(r)) x[i + j] += l[i] * r[j];
return x;
}
template<class T> vector<T>& operator*=(vector<T>& l, const vector<T>& r) { return l = l * r; }
template<class T> vector<T> rem(vector<T> a, vector<T> b) {
while (SZ(b) && b.back() == 0) b.pop_back();
assert(SZ(b)); b /= b.back();
while (SZ(a) >= SZ(b)) {
a -= a.back() * shift(b, SZ(a) - SZ(b));
while (SZ(a) && a.back() == 0) a.pop_back();
}
return a;
}
template<class T> vector<T> interpolate(vector<pair<T, T>> v) {
vector<T> ret;
F0R(i, SZ(v)) {
vector<T> prod = { 1 };
T todiv = 1;
F0R(j, SZ(v)) if (i != j) {
todiv *= v[i].f - v[j].f;
vector<T> tmp = { -v[j].f,1 }; prod *= tmp;
}
ret += prod * (v[i].s / todiv);
}
return ret;
}
}
using namespace vecOp;
class factorial {
public:
LL MAXX, MOD;
VL f, ff;
factorial(LL maxx = 200010, LL mod = 998244353) {
MAXX = maxx;
MOD = mod;
f.RSZ(MAXX);
ff.RSZ(MAXX);
f[0] = 1;
for (int i = 1; i < MAXX; i++) f[i] = (f[i - 1] * i) % MOD;
for (int i = 0; i < MAXX; i++) ff[i] = mul_inv(f[i], MOD);
}
long long mul_inv(long long a, long long b)
{
long long b0 = b, t, q;
long long x0 = 0, x1 = 1;
if (b == 1) return 1;
while (a > 1) {
q = a / b;
t = b, b = a % b, a = t;
t = x0, x0 = x1 - q * x0, x1 = t;
}
if (x1 < 0) x1 += b0;
return x1;
}
long long division(long long a, long long b) { // (a / b) mod p = ((a mod p) * (b^(-1) mod p)) mod p
long long ans, inv;
inv = mul_inv(b, MOD);
ans = ((a % MOD) * inv) % MOD;
return ans;
}
LL calcc(LL n, LL a) {
if (n == a) return 1;
if (n == 0) return 0;
if (n < a) return 0;
LL ans = (f[n] * ff[a]) % MOD;
ans = (ans * ff[n - a]) % MOD;
return ans;
}
LL calcp(LL n, LL a) {
LL ans = (f[n] * ff[n - a]) % MOD;
return ans;
}
LL exp(LL base, LL n) {
base %= MOD;
LL ans = 1, x = base, MAXLEVEL = 60, i;
for (i = 0; i < MAXLEVEL; i++) {
if ((1LL << i) > n) break;
if ((1LL << i) & n) ans = (ans * x) % MOD;
x = (x * x) % MOD;
}
return ans;
}
};
#ifdef _MSC_VER
//#include <intrin.h>
#endif
namespace FFT {
#ifdef _MSC_VER
int size(int s) {
if (s == 0) return 0;
unsigned long index;
_BitScanReverse(&index, s);
return index + 1;
}
#else
constexpr int size(int s) { return s > 1 ? 32 - __builtin_clz(s - 1) : 0; }
#endif
template<class T> bool small(const vector<T>& a, const vector<T>& b) {
return (LL)SZ(a) * SZ(b) <= 500000;
}
void genRoots(vmi& roots) { // primitive n-th roots of unity
int n = SZ(roots); mi r = pow(mi(root), (MOD - 1) / n);
roots[0] = 1; FOR(i, 1, n) roots[i] = roots[i - 1] * r;
}
void genRoots(VCD& roots) { // change cd to complex<double> instead?
int n = SZ(roots); LD ang = 2 * PAI / n;
F0R(i, n) roots[i] = CD(cos(ang * i), sin(ang * i)); // is there a way to do this more quickly?
}
template<class T> void fft(vector<T>& a, vector<T>& roots) {
int n = SZ(a);
for (int i = 1, j = 0; i < n; i++) { // sort by reverse bit representation
int bit = n >> 1;
for (; j & bit; bit >>= 1) j ^= bit;
j ^= bit; if (i < j) swap(a[i], a[j]);
}
for (int len = 2; len <= n; len <<= 1)
for (int i = 0; i < n; i += len)
F0R(j, len / 2) {
auto u = a[i + j], v = a[i + j + len / 2] * roots[n / len * j];
a[i + j] = u + v, a[i + j + len / 2] = u - v;
}
}
template<class T> vector<T> conv(vector<T> a, vector<T> b) {
//if (small(a, b)) return a * b;
int s = SZ(a) + SZ(b) - 1, n = 1 << size(s);
vector<T> roots(n); genRoots(roots);
a.RSZ(n), fft(a, roots); b.RSZ(n), fft(b, roots);
F0R(i, n) a[i] *= b[i];
reverse(begin(roots) + 1, end(roots)); fft(a, roots); // inverse FFT
T in = T(1) / T(n); trav(x, a) x *= in;
a.RSZ(s); return a;
}
VL conv(const VL& a, const VL& b) {
//if (small(a, b)) return a * b;
VCD X = conv(VCD(ALL(a)), VCD(ALL(b)));
VL x(SZ(X)); F0R(i, SZ(X)) x[i] = round(X[i].real());
return x;
} // ~0.55s when SZ(a)=SZ(b)=1<<19
VL conv(const VL& a, const VL& b, LL mod) { // http://codeforces.com/contest/960/submission/37085144
//if (small(a, b)) return a * b;
int s = SZ(a) + SZ(b) - 1, n = 1 << size(s);
VCD v1(n), v2(n), r1(n), r2(n);
F0R(i, SZ(a)) v1[i] = CD(a[i] >> 15, a[i] & 32767); // v1(x)=a0(x)+i*a1(x)
F0R(i, SZ(b)) v2[i] = CD(b[i] >> 15, b[i] & 32767); // v2(x)=b0(x)+i*b1(x)
VCD roots(n); genRoots(roots);
fft(v1, roots), fft(v2, roots);
F0R(i, n) {
int j = (i ? (n - i) : i);
CD ans1 = (v1[i] + conj(v1[j])) * CD(0.5, 0); // a0(x)
CD ans2 = (v1[i] - conj(v1[j])) * CD(0, -0.5); // a1(x)
CD ans3 = (v2[i] + conj(v2[j])) * CD(0.5, 0); // b0(x)
CD ans4 = (v2[i] - conj(v2[j])) * CD(0, -0.5); // b1(x)
r1[i] = (ans1 * ans3) + (ans1 * ans4) * CD(0, 1); // a0(x)*v2(x)
r2[i] = (ans2 * ans3) + (ans2 * ans4) * CD(0, 1); // a1(x)*v2(x)
}
reverse(begin(roots) + 1, end(roots));
fft(r1, roots), fft(r2, roots); F0R(i, n) r1[i] /= n, r2[i] /= n;
VL ret(n);
F0R(i, n) {
LL av = (LL)round(r1[i].real()); // a0*b0
LL bv = (LL)round(r1[i].imag()) + (LL)round(r2[i].real()); // a0*b1+a1*b0
LL cv = (LL)round(r2[i].imag()); // a1*b1
av %= mod, bv %= mod, cv %= mod;
ret[i] = (av << 30) + (bv << 15) + cv;
ret[i] = (ret[i] % mod + mod) % mod;
}
ret.resize(s);
return ret;
} // ~0.8s when SZ(a)=SZ(b)=1<<19
}
using namespace FFT;
long long gcd(long long a, long long b)
{
while (b != 0) {
long long t = b;
b = a % b;
a = t;
}
return a;
}
class tree { // implementation of recurvie programming
int ct;
public:
int nn, root; // # of nodes, id of root
vector<int> parent; // parent of each node; -1 if unassigned
vector<int> depth; // depth of each node
vector<int> sz; // subtree size of each node
vector<vector<int>> adj; // adjacency list from each node
vector<vector<int>> sons; // sons list from each node
// for cartesian_decomposition
vector<int> in, out; // starting and ending position of a subtree
vector<int> pos; // inorder of DFS
// for LCA sparse table
vector<vector<int>> pred;
int MAXLEVEL;
tree(int n) {
nn = n;
adj.clear();
adj.resize(n);
}
void add_path(int a, int b) {
adj[a].push_back(b);
adj[b].push_back(a);
}
void add_directed_path(int a, int b) {
adj[a].push_back(b);
}
void dfs_set_root(int id, bool cartesian_decomposition = false) { // internal
if (cartesian_decomposition) {
in[id] = ct;
pos[ct] = id;
ct++;
}
sz[id]++;
for (auto p : adj[id]) {
if (parent[p] == -1) {
parent[p] = id;
depth[p] = depth[id] + 1;
dfs_set_root(p, cartesian_decomposition);
sz[id] += sz[p];
sons[id].push_back(p);
}
}
if (cartesian_decomposition) out[id] = ct - 1;
}
void set_root(int id, bool cartesian_decomposition = true) { // set root of the tree and calculate necessary info
if (cartesian_decomposition) {
in.resize(nn);
out.resize(nn);
pos.resize(nn);
ct = 0;
}
parent.assign(nn, -1);
depth.assign(nn, -1);
sz.assign(nn, 0);
sons.clear();
sons.resize(nn);
// dfs_set_root(id, cartesian_decomposition);
// set root using stack
stack<pair<int, int>> st; // id, # of sons processes
st.push({ id, 0 });
parent[id] = 0;
depth[id] = 0;
int ct = 0;
while (!st.empty()) {
int id = st.top().first, x = st.top().second;
if (x == 0) {
in[id] = ct;
pos[ct] = id;
sz[id] = 1;
ct++;
}
if (x >= adj[id].size()) {
out[id] = ct - 1;
if (parent[id] != -1) {
sz[parent[id]] += sz[id];
}
st.pop();
}
else {
st.top().second++;
int p = adj[id][x];
if (parent[p] == -1) {
parent[p] = id;
depth[p] = depth[id] + 1;
sons[id].push_back(p);
st.push({ p, 0 });
}
}
}
int i = 0;
}
void eulerian_tour_dfs(int root, vector<int>& ans) {
ans.push_back(root);
for (auto p : sons[root]) {
eulerian_tour_dfs(p, ans);
ans.push_back(root);
}
}
vector<int> eulerian_tour(int root) {
vector<int> ans;
eulerian_tour_dfs(root, ans);
return ans;
}
void prep_LCA() { // prepare the sparse table for LCA calculation
MAXLEVEL = 1;
while ((1 << MAXLEVEL) < nn) MAXLEVEL++;
MAXLEVEL++;
pred.assign(MAXLEVEL, vector<int>(nn, 0));
pred[0] = parent;
int i, j, k;
for (i = 1; i < MAXLEVEL; i++) {
for (j = 0; j < nn; j++) {
if (pred[i - 1][j] != -1) pred[i][j] = pred[i - 1][pred[i - 1][j]];
}
}
}
int get_p_ancestor(int a, int p) { // get p-ancestor of node a; need to call set_root() and prep_LCA() first
int i;
for (i = MAXLEVEL - 1; (i >= 0) && (p > 0) && (a != -1); i--) {
if ((1 << i) & p) {
p -= (1 << i);
a = pred[i][a];
}
}
return a;
}
int LCA(int a, int b) { // get the LCA of a and b, need to call set_root() and prep_LCA() first
int da = depth[a], db = depth[b];
if (da > db) {
swap(da, db);
swap(a, b);
}
int i, j, k;
for (i = MAXLEVEL - 1; i >= 0; i--) {
if (db - (1 << i) >= da) {
db -= (1 << i);
b = pred[i][b];
}
}
if (a == b) return a;
for (i = MAXLEVEL - 1; i >= 0; i--) {
if (pred[i][a] != pred[i][b]) {
a = pred[i][a];
b = pred[i][b];
}
}
return parent[a];
}
int get_distance(int a, int b) { // get distance between a and b, need to call set_root() and prep_LCA() first
int c = LCA(a, b);
int ans = depth[a] + depth[b] - 2 * depth[c];
return ans;
}
int get_diameter() {
int a, b, c, i, j, k, id, INF = nn + 100, ans;
vector<int> dist(nn), last(nn);
queue<int> q;
if (nn == 1) return 0;
// first pass, start with 1 -- any node
a = 1;
dist.assign(nn, INF);
dist[a] = 0;
q.push(a);
while (!q.empty()) {
id = q.front();
q.pop();
for (auto p : adj[id]) {
if (dist[p] == INF) {
dist[p] = dist[id] + 1;
q.push(p);
}
}
}
// second pass, start from the most remote node id, collect last to get ID
a = id;
dist.assign(nn, INF);
last.assign(nn, -1);
dist[a] = 0;
q.push(a);
while (!q.empty()) {
id = q.front();
q.pop();
for (auto p : adj[id]) {
if (dist[p] == INF) {
dist[p] = dist[id] + 1;
last[p] = id;
q.push(p);
}
}
}
// a and id forms the diameter
ans = dist[id];
return ans;
// construct the path of diamter in path
vector<int> path;
b = id;
c = id;
do {
path.push_back(b);
b = last[b];
} while (b != -1);
return ans;
}
};
// Union-Find Disjoint Sets Library written in OOP manner, using both path compression and union by rank heuristics
// initialize: UnionFind UF(N)
class UnionFind { // OOP style
private:
vector<int> p, rank, setSize;
// p = path toward the root of disjoint set; p[i] = i means it is root
// rank = upper bound of the actual height of the tree; not reliable as accurate measure
// setSize = size of each disjoint set
int numSets;
public:
UnionFind(int N) {
setSize.assign(N, 1);
numSets = N;
rank.assign(N, 0);
p.assign(N, 0);
for (int i = 0; i < N; i++) p[i] = i; // each belongs to its own set
}
int findSet(int i) {
return (p[i] == i) ? i : (p[i] = findSet(p[i])); // path compression: cut short of the path if possible
}
bool isSameSet(int i, int j) {
return findSet(i) == findSet(j);
}
void unionSet(int i, int j) {
if (!isSameSet(i, j)) {
numSets--;
int x = findSet(i), y = findSet(j);
// rank is used to keep the tree short
if (rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y]; }
else {
p[x] = y; setSize[y] += setSize[x];
if (rank[x] == rank[y]) rank[y]++;
}
}
}
int numDisjointSets() { // # of disjoint sets
return numSets;
}
int sizeOfSet(int i) { // size of set
return setSize[findSet(i)];
}
};
#define MAXN 205000 // total # of prime numbers
#define MAXP 1001000 // highest number to test prime
int prime[MAXN]; // prime numbers: 2, 3, 5 ...
int lp[MAXP]; // lp[n] = n if n is prime; otherwise smallest prime factor of the number
int phi[MAXP]; // phii function
class prime_class {
public:
long top;
prime_class() { // generate all prime under MAXP
int i, i2, j;
top = 0;
lp[0] = 0;
lp[1] = 1;
for (i = 2; i < MAXP; i++) lp[i] = 0;
top = 0;
for (i = 2; i < MAXP; ++i) {
if (lp[i] == 0) {
lp[i] = i;
prime[top++] = i;
}
for (j = 0; (j < top) && (prime[j] <= lp[i]) && (i * prime[j] < MAXP); ++j)
lp[i * prime[j]] = prime[j];
}
}
bool isprime(long long key)
{
if (key < MAXP) return (lp[key] == key) && (key >= 2);
else {
int i;
for (i = 0; (i < top) && (prime[i] * prime[i] <= key); i++)
if (key % prime[i] == 0) return false;
return true;
}
}
unordered_map<int, int> factorize(int key) {
unordered_map<int, int> ans;
while (lp[key] != key) {
ans[lp[key]]++;
key /= lp[key];
}
if (key > 1) ans[key]++;
return ans;
}
vector<int> mobius(int n) { // generate mobius function of size n
int i, j, k, ct, curr, cct, x, last;
vector<int> mobius(n + 1);
for (i = 1; i <= n; i++) {
curr = i; ct = 0; last = -1;
while (lp[curr] != curr) {
x = lp[curr];
if (x != last) {
cct = 1;
last = x;
ct++;
}
else {
if (++cct >= 2) {
mobius[i] = 0;
goto outer;
}
}
curr /= lp[curr];
}
if (curr > 1) {
x = curr;
if (x != last) {
cct = 1;
last = x;
ct++;
}
else {
if (++cct >= 2) {
mobius[i] = 0;
goto outer;
}
}
}
if (ct % 2 == 0) mobius[i] = 1;
else mobius[i] = -1;
outer:;
}
return mobius;
}
int get_phi(int key) { // calculate Euler's totient function, also known as phi-function
int ans = key, last = 0;
while (lp[key] != key) {
if (lp[key] != last) {
last = lp[key];
ans -= ans / last;
}
key /= lp[key];
}
if ((key > 1) && (key != last)) ans -= ans / key;
return ans;
}
void calc_all_phi(int n) {
int i, j, k;
for (int i = 1; i < n; i++) phi[i] = i;
for (int i = 2; i < n; i++) {
if (phi[i] == i) {
for (int j = i; j < n; j += i) {
phi[j] /= i;
phi[j] *= i - 1;
}
}
}
}
vector<pair<long long, long long>> factorize_full(long long key) { // can be used to factorize numbers >= MAXP
vector<pair<long long, long long>> ans;
long i, ct, sq = sqrt(key) + 10;
for (i = 0; (i < top) && (prime[i] <= sq); i++)
if (key % prime[i] == 0) {
ct = 0;
while (key % prime[i] == 0) {
ct++;
key /= prime[i];
}
ans.push_back({ prime[i], ct });
}
if (key > 1) {
ans.push_back({ key, 1 });
}
return ans;
}
void generate_divisors(int step, int v, vector<pair<int, int>>& fp, vector<int>& ans) {
if (step < fp.size()) {
generate_divisors(step + 1, v, fp, ans);
for (int i = 1; i <= fp[step].second; i++) {
v *= fp[step].first;
generate_divisors(step + 1, v, fp, ans);
}
}
else ans.push_back(v);
}
void generate_divisors_full(long long step, long long v, vector<pair<long long, long long>>& fp, vector<long long>& ans) {
if (step < fp.size()) {
generate_divisors_full(step + 1, v, fp, ans);
for (int i = 1; i <= fp[step].second; i++) {
v *= fp[step].first;
generate_divisors_full(step + 1, v, fp, ans);
}
}
else ans.push_back(v);
}
vector<int> get_divisors(int key) {
unordered_map<int, int> f = factorize(key);
int n = f.size();
vector<pair<int, int>> fp;
for (auto p : f) fp.push_back(p);
vector<int> ans;
generate_divisors(0, 1, fp, ans);
return ans;
}
vector<long long> get_divisors_full(long long key) {
vector<pair<long long, long long>> f = factorize_full(key);
int n = f.size();
vector<pair<long long, long long>> fp;
for (auto p : f) fp.push_back(p);
vector<long long> ans;
generate_divisors_full(0, 1, fp, ans);
return ans;
}
long long get_divisors_count(long long key) {
vector<pair<long long, long long>> f = factorize_full(key);
long long ans = 1;
for (auto p : f) ans *= (p.second + 1);
return ans;
}
};
long long mul_inv(long long a, long long b)
{
long long b0 = b, t, q;
long long x0 = 0, x1 = 1;
if (b == 1) return 1;
while (a > 1) {
q = a / b;
t = b, b = a % b, a = t;
t = x0, x0 = x1 - q * x0, x1 = t;
}
if (x1 < 0) x1 += b0;
return x1;
}
long long division(long long a, long long b, long long p) { // (a / b) mod p = ((a mod p) * (b^(-1) mod p)) mod p
long long ans, inv;
inv = mul_inv(b, p);
ans = ((a % p) * inv) % p;
return ans;
}
#define MP make_pair
#define PB push_back
#define F first
#define S second
#define LB lower_bound
#define UB upper_bound
#define SZ(x) ((int)x.size())
#define LEN(x) ((int)x.length())
#define ALL(x) begin(x), end(x)
#define RSZ resize
#define ASS assign
#define REV(x) reverse(x.begin(), x.end());
#define MAX(x) *max_element(ALL(x))
#define MIN(x) *min_element(ALL(x))
#define FOR(i, n) for (int i = 0; i < n; i++)
#define FOR1(i, n) for (int i = 1; i <= n; i++)
#define SORT(x) sort(x.begin(), x.end())
#define RSORT(x) sort(x.rbegin(), x.rend())
#define SUM(x) accumulate(x.begin(), x.end(), 0LL)
#define IN(x) cin >> x;
#define OUT(x) cout << x << "\n";
#define INV(x, n) FOR(iiii, n) { cin >> x[iiii]; }
#define INV1(x, n) FOR1(iiii, n) { cin >> x[iiii]; }
#define OUTV(x, n) { FOR(iiii, n) { cout << x[iiii] << " "; } cout << "\n"; }
#define OUTV1(x, n) { FOR1(iiii, n) { cout << x[iiii] << " "; } cout << "\n"; }
#define OUTYN(x) { if (x) cout << "YES\n"; else cout << "NO\n"; }
#define OUTyn(x) { if (x) cout << "Yes\n"; else cout << "No\n"; }
#define MOD7 1000000007
#define MOD9 1000000009
#define MOD3 998244353
int main()
{
ios::sync_with_stdio(false);
cin.tie(0);
LL n, i, j, k, nn;
cin >> n;
nn = n / 2;
double a, b, c, x, xx;
vector<double> w(n), s(n), v(n);
FOR(i, n) {
cin >> w[i] >> s[i];
}
a = 0.4; b = 2.1;
while (b - a > 1E-7) {
c = (a + b) / 2;
FOR(i, n) {
v[i] = c * w[i] - s[i];
}
SORT(v);
bool valid = true;
FOR(i, nn) {
if (-v[i] - c * 20 < v[n - 1 - i] - 1E-6) {
valid = false;
break;
}
}
if (valid) a = c;
else b = c;
}
cout << setprecision(10) << fixed << a << "\n";
return 0;
}
Kayaks CodeChef Solution in C
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
int pair[100000][2];
int people;
double dist[100000];
int compare (const void * a, const void * b) {
return ( *(double*)a - *(double*)b );
}
mergesort(double a[], int low, int high) {
int mid;
if(low<high) {
mid=(low+high)/2;
mergesort(a,low,mid);
mergesort(a,mid+1,high);
merge(a,low,high,mid);
}
}
double c[100000];
merge(double a[], int low, int high, int mid) {
int i, j, k;
i=low;
j=mid+1;
k=low;
while((i<=mid)&&(j<=high)) {
if(a[i]<a[j]) {
c[k]=a[i];
k++;
i++;
} else {
c[k]=a[j];
k++;
j++;
}
}
while(i<=mid) {
c[k]=a[i];
k++;
i++;
}
while(j<=high) {
c[k]=a[j];
k++;
j++;
}
for(i=low;i<k;i++) {
a[i]=c[i];
}
}
void mysort(double data[], int N)
{
int i, j;
double v, t;
if(N<=1) return;
// Partition elements
v = data[0];
i = 0;
j = N;
for(;;)
{
while(data[++i] < v && i < N) { }
while(data[--j] > v) { }
if(i >= j) break;
t = data[i]; data[i] = data[j]; data[j] = t;
}
t = data[i-1]; data[i-1] = data[0]; data[0] = t;
mysort(data, i-1);
mysort(data+i, N-i);
}
int isOk (double a) {
double denominators = sqrt(a*a+1);
//printf("%f, %f\n", a, denominators);
int i;
for (i=0; i<people; i++)
dist[i] = (a*pair[i][0]-pair[i][1]) / denominators;
//qsort(dist, people, sizeof(double), compare);
mysort(dist, people);
//for (i=0; i<people; i++)
// printf("%f ", dist[i]);
//printf("\n");
for (i=0; i<<1<people; i++)
if (dist[i]+dist[people-1-i] > 0)
return 0;
return 1;
}
int main () {
scanf("%d", &people);
int i;
for (i=0; i<people; i++) {
scanf("%d %d", &pair[i][0], &pair[i][1]);
pair[i][0] += 10;
}
double min = 0.4, max = 1.7, mid = 0;
while (max-min>1e-8) {
mid = (min + max) / 2;
if (isOk(mid)) min = mid;
else max = mid;
}
printf("%f\n", (min+max) / 2);
return 0;
}
Kayaks CodeChef Solution in JAVA
/* package codechef; // don't place package name! */
import java.util.*;
import java.lang.*;
import java.io.*;
/* Name of the class has to be "Main" only if the class is public. */
class Codechef
{
public static void main(String[] args) throws Exception {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
StringTokenizer st ;
int n = Integer.parseInt(br.readLine());
int[] s = new int[n];
int[] w = new int[n];
for (int i = 0; i < n; i++) {
st = new StringTokenizer(br.readLine());
w[i] = Integer.parseInt(st.nextToken()) + 10;
s[i] = Integer.parseInt(st.nextToken());
}
double max = (100.0 + 100.0) / (120.0);
double min = (50.0 + 50.0) / (220.0);
double mid = 0.0;
double eps = 1e-8;
while (max - min > eps) {
mid = (max + min) / 2;
if (isPossible(mid, w, s)) {
min = mid;
} else {
max = mid;
}
}
System.out.printf("%.7f",mid);
}
static boolean isPossible(double mid, int[] w, int[] s) {
double[] delta = new double[w.length];
for (int i = 0; i < w.length; i++) {
delta[i] = s[i] - mid * w[i];
}
Arrays.sort(delta);
for (int i = 0; i < delta.length; i++) {
if (delta[i] + delta[delta.length - 1 - i] < 0)
return false;
}
return true;
}
}Kayaks CodeChef Solution in C#
using System;
using System.Collections.Generic;
namespace CodeChef_200910_H2
{
/// <summary>
/// split persons ; group by weight & strength
/// </summary>
class PersonGroup : IComparable<PersonGroup>
{
public int weight;
public int strength;
public int person_num;
// when fill the min speed, some stength left.
public decimal left_strength;
public int CompareTo(PersonGroup other)
{
if (left_strength > other.left_strength) return 1;
if (left_strength < other.left_strength) return -1;
return 0;
}
}
class CaseItem
{
int caseIndex;
int person_number;
int total_weight = 0;
int total_strengh = 0;
decimal aver_speed = 0;
// for add person numbers quickly
PersonGroup[,] groupTable = new PersonGroup[51, 51];
// for sort by left_strength
List<PersonGroup> personList = new List<PersonGroup>(51*51);
private void buildIndex()
{
for (int weight = 0; weight <= 50; weight++)
{
for (int strength = 0; strength <= 50; strength++)
{
PersonGroup p = new PersonGroup();
groupTable[weight, strength] = p;
p.weight = weight + 60;
p.strength = strength + 50;
personList.Add(p);
}
}
}
public CaseItem(int index)
{
this.buildIndex();
caseIndex = index;
person_number = int.Parse(System.Console.ReadLine());
for (int i = 0; i < person_number; i++)
{
string s = Console.ReadLine();
string[] a = s.Split(' ');
int weight = int.Parse(a[0]) + 10;
int strength = int.Parse(a[1]);
groupTable[weight - 60, strength - 50].person_num++;
total_weight += weight;
total_strengh += strength;
}
aver_speed = decimal.Round((0.0M + total_strengh) / total_weight, 8);
}
private decimal test_min_speed(decimal v)
{
foreach (PersonGroup pg in personList)
{
pg.left_strength = pg.strength - v * pg.weight;
}
QuickSort<PersonGroup>(personList, 0, personList.Count - 1);
int start = 0;
int end = personList.Count - 1;
decimal min_v = int.MaxValue;
while (personList[start].person_num == 0) start++;
while (personList[end].person_num == 0) end--;
int min_start_index = start, min_end_index = end;
int start_left = personList[start].person_num;
int end_left = personList[end].person_num;
PersonGroup pstart = personList[start];
PersonGroup pend = personList[end];
while (start <= end)
{
if (pstart.left_strength + pend.left_strength < min_v)
{
min_v = pstart.left_strength + pend.left_strength;
min_start_index = start;
min_end_index = end;
}
if (start_left > end_left)
{
start_left -= end_left;
end--;
pend = personList[end];
end_left = pend.person_num;
}
else if (start_left == end_left)
{
start++;
end--;
pstart = personList[start];
pend = personList[end];
start_left = pstart.person_num;
end_left = pend.person_num;
}
else
{
end_left -= start_left;
start++;
pstart = personList[start];
start_left = pstart.person_num;
}
}
min_v = (0.0M + personList[min_start_index].strength + personList[min_end_index].strength) /
(personList[min_start_index].weight + personList[min_end_index].weight);
return decimal.Round(min_v, 8);
}
public void Execute()
{
decimal min_speed = aver_speed;
decimal test_speed;
do
{
test_speed = min_speed;
min_speed = test_min_speed(test_speed);
} while (min_speed != test_speed);
System.Console.WriteLine(decimal.Round(min_speed, 6).ToString());
}
public void QuickSort<T>(List<T> a, int low, int high)
where T : IComparable<T>
{
if (high - low <= 0)
{
return;
}
else if (high - low == 1)
{
if (a[high].CompareTo(a[low]) < 0)
{
T t = a[high];
a[high] = a[low];
a[low] = t;
}
return;
}
int mid = (low + high) >> 1;
T pivot = a[mid];
T t2 = a[mid];
a[mid] = a[low];
a[low] = t2;
int up = low + 1;
int down = high;
do
{
while (up <= down && a[up].CompareTo(pivot) <= 0) up++;
while (up <= down && a[down].CompareTo(pivot) > 0) down--;
if (up < down)
{
T t = a[up];
a[up] = a[down];
a[down] = t;
}
} while (up < down);
a[low] = a[down];
a[down] = pivot;
if (low < down - 1)
{
QuickSort<T>(a, low, down - 1);
}
if (down + 1 < high)
{
QuickSort<T>(a, down + 1, high);
}
}
}
class Round
{
int case_num;
CaseItem[] items;
public Round()
{
case_num = 1;
items = new CaseItem[case_num];
for (int i = 0; i < case_num; i++)
{
items[i] = new CaseItem(i + 1);
}
}
public void Execute()
{
foreach (CaseItem item in items)
{
item.Execute();
}
}
}
class Program
{
static void Main(string[] args)
{
//BuildDebug();
(new Round()).Execute();
// Debug();
}
static void BuildDebug()
{
using (System.IO.StreamWriter writer = new System.IO.StreamWriter("a.in"))
{
int n = 100000;
Random r = new Random(1000000);
writer.WriteLine(n);
for (int i = 0; i < n; i++)
{
int w = r.Next(n) % 51 + 50;
int s = r.Next(n) % 51 + 50;
writer.WriteLine(w.ToString() + " " + s.ToString());
}
}
}
static void Debug()
{
System.IO.TextReader stdin = System.Console.In;
System.IO.TextWriter stdout = System.Console.Out;
try
{
using (System.IO.StreamReader reader = new System.IO.StreamReader("a.in"))
{
using (System.IO.StreamWriter writer = new System.IO.StreamWriter("out.txt"))
{
long datetime1 = DateTime.Now.Ticks;
System.Console.SetIn(reader);
System.Console.SetOut(writer);
(new Round()).Execute();
long datetime2 = DateTime.Now.Ticks;
DateTime datetime3 = DateTime.Now;
long seconds = (datetime2 - datetime1) / (datetime3.AddSeconds(1).Ticks - datetime3.Ticks);
System.Console.WriteLine(" second is : " + seconds.ToString());
System.Console.WriteLine(" ticks is : " + (datetime2 - datetime1).ToString());
System.Console.WriteLine(" ticks per seconds : " + (datetime3.AddSeconds(1).Ticks - datetime3.Ticks).ToString());
}
}
}
finally
{
System.Console.SetIn(stdin);
System.Console.SetOut(stdout);
}
}
}
}
Kayaks CodeChef Solution in GO
package main
import (
"bufio"
"fmt"
"os"
"sort"
)
func main() {
reader := bufio.NewReader(os.Stdin)
n := readNum(reader)
persons := make([][]int, n)
for i := 0; i < n; i++ {
persons[i] = readNNums(reader, 2)
}
res := solve(n, persons)
fmt.Printf("%.7f\n", res)
}
func readInt(bytes []byte, from int, val *int) int {
i := from
sign := 1
if bytes[i] == '-' {
sign = -1
i++
}
tmp := 0
for i < len(bytes) && bytes[i] >= '0' && bytes[i] <= '9' {
tmp = tmp*10 + int(bytes[i]-'0')
i++
}
*val = tmp * sign
return i
}
func readNum(reader *bufio.Reader) (a int) {
bs, _ := reader.ReadBytes('\n')
readInt(bs, 0, &a)
return
}
func readTwoNums(reader *bufio.Reader) (a int, b int) {
res := readNNums(reader, 2)
a, b = res[0], res[1]
return
}
func readThreeNums(reader *bufio.Reader) (a int, b int, c int) {
res := readNNums(reader, 3)
a, b, c = res[0], res[1], res[2]
return
}
func readNNums(reader *bufio.Reader, n int) []int {
res := make([]int, n)
x := 0
bs, _ := reader.ReadBytes('\n')
for i := 0; i < n; i++ {
for x < len(bs) && (bs[x] < '0' || bs[x] > '9') && bs[x] != '-' {
x++
}
x = readInt(bs, x, &res[i])
}
return res
}
func readUint64(bytes []byte, from int, val *uint64) int {
i := from
var tmp uint64
for i < len(bytes) && bytes[i] >= '0' && bytes[i] <= '9' {
tmp = tmp*10 + uint64(bytes[i]-'0')
i++
}
*val = tmp
return i
}
func solve(n int, people [][]int) float64 {
// strength >= 50 & <= 100
// weight >= 50 & <= 100
// so total unique pair would be <= 50 * 50
pairs := make(map[Pair]int)
for _, cur := range people {
pairs[Pair{cur[1], cur[0]}]++
}
arr := make([]Pair, 0, len(pairs))
for cur := range pairs {
arr = append(arr, cur)
}
arr2 := make([]Pair, n)
check := func(speed float64) bool {
comp := Comp{speed, arr}
sort.Sort(&comp)
var p int
for i := 0; i < len(arr); i++ {
for j := 0; j < pairs[arr[i]]; j++ {
arr2[p] = arr[i]
p++
}
}
for i, j := 0, n-1; i < j; i, j = i+1, j-1 {
a, b := arr2[i], arr2[j]
if float64(a.first+b.first)-speed*float64(a.second+b.second+20) < 0 {
return false
}
}
return true
}
var lo, hi float64 = 0, 2.0
for i := 0; i < 30; i++ {
mid := (lo + hi) / 2
if check(mid) {
lo = mid
} else {
hi = mid
}
}
return (lo + hi) / 2
}
type Pair struct {
first int
second int
}
func (p Pair) Value(speed float64) float64 {
return float64(p.first) - speed*float64(p.second)
}
type Comp struct {
speed float64
arr []Pair
}
func (this *Comp) Len() int {
return len(this.arr)
}
func (this *Comp) Less(i, j int) bool {
a, b := this.arr[i], this.arr[j]
return a.Value(this.speed) < b.Value(this.speed)
}
func (this *Comp) Swap(i, j int) {
this.arr[i], this.arr[j] = this.arr[j], this.arr[i]
}Kayaks CodeChef Solution Review:
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