Hướng dẫn giải của Đường phố mùa lễ hội


Chỉ dùng lời giải này khi không có ý tưởng, và đừng copy-paste code từ lời giải này. Hãy tôn trọng người ra đề và người viết lời giải.
Nộp một lời giải chính thức trước khi tự giải là một hành động có thể bị ban.

Lưu ý: Các code mẫu dưới đây chỉ mang tính tham khảo và có thể không AC được bài tập này

Code mẫu của flashmt

#include <iostream>
#include <algorithm>
#include <cstdio>
#include <vector>
#include <utility>
using namespace std;

int clockwise(int x, int y, int xx, int yy, int xxx, int yyy)
{
    return 1LL * (x - xx) * (y + yy) + 1LL * (xx - xxx) * (yy + yyy) + 1LL * (xxx - x) * (yyy + y) < 0;
}

int main()
{
    int n, hullX[100100], hullY[100100], yIntercept[100100], H = 0, y;

    cin >> n;
    for (int x = 1; x <= n; x++)
    {
        scanf("%d", &y);
        while (H > 1 && clockwise(x, y, hullX[H - 1], hullY[H - 1], hullX[H - 2], hullY[H - 2]))
            H--;
        hullX[H] = x; hullY[H++] = y;
    }

    for (int i = 0; i + 1 < H; i++)
    {
        double slope = 1.0 * (hullY[i] - hullY[i + 1]) / (hullX[i] - hullX[i + 1]);
        yIntercept[i] = int(hullY[i] - slope * hullX[i] + 1e-8);
    }
    yIntercept[H - 1] = 1000111222;

    cin >> n;
    while (n--)
    {
        scanf("%d", &y);
        int i = lower_bound(yIntercept, yIntercept + H, y) - yIntercept;
        double slope = 1.0 * (hullY[i] - y) / hullX[i];
        printf("%.6lf\n", 1 / slope);
    }
}

Code mẫu của happyboy99x

#include<cstdio>

#define long long long

struct Line {
    long a, b, lim;

    Line(long a = 0, long b = 0, long lim = 0):
        a (a), b (b), lim (lim) {}

    double val(long x) const {
        return 1. * (a - x) / b;
    }

    long xCut(const Line &x) const {
        return (a * x.b - b * x.a) / (x.b - b);
    }

    bool bad(const Line &x, const Line &y) const {
        return (a*x.b - b*x.a) * (y.b-b) >= (a*y.b - b*y.a) * (x.b-b);
    }
};

const int N = 1e5, INF = 2e9;
Line l[N];
int nLine;

void addLine(const Line &a) {
    while(nLine > 1 && l[nLine-2].bad(l[nLine-1], a)) --nLine;
    if(nLine > 0) l[nLine-1].lim = l[nLine-1].xCut(a);
    l[nLine++] = a;
}

void enter() {
    int n; scanf("%d", &n);
    for(int i = 0; i < n; ++i) {
        int a; scanf("%d", &a);
        addLine(Line(a, i + 1, INF));
    }
}

void solve() {
    int m; scanf("%d", &m);
    for(int i = 0; i < m; ++i) {
        int s; scanf("%d", &s);
        int low = 0, high = nLine - 1;
        while(low < high) {
            int mid = (low + high) >> 1;
            if(l[mid].lim < s) low = mid + 1;
            else high = mid;
        }
        printf("%.6lf\n", 1 / l[low].val(s));
    }
}

int main() {
    enter();
    solve();
    return 0;
}

Code mẫu của ladpro98

#include <cstring>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <queue>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <climits>
#include <cstdlib>
#include <ctime>
#include <memory.h>
#include <cassert>
#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define REP(i, a, b) for(int i = (a); i <=(b); i++)
#define FORD(i, a, b) for(int i = (a); i > (b); i--)
#define REPD(i, a, b) for(int i = (a); i >=(b); i--)
#define TR(it, a) for(typeof((a).begin()) it = (a).begin(); it != (a).end(); it++)
#define SZ(a) (int((a).size()))
#define ALL(a) (a).begin(), (a).end()
#define PB push_back
#define MP make_pair
#define LL long long
#define LD long double
#define II pair<LL, LL>
#define X first
#define Y second
#define VI vector<int>
const int N = 100005;
using namespace std;

void operator -= (II &a, II b) {a.X -= b.X; a.Y -= b.Y;}
bool ccw(II a, II b, II c) {c -= b; b -= a; return b.X * c.Y >= b.Y * c.X;}
vector<II> hull;
II a[N], s[N];
double ans[N];
int n, m;

int main() {
    ios :: sync_with_stdio(0); cin.tie(0);
    cin >> m;
    FOR(i, 0, m) {
        cin >> a[i].Y;
        a[i].X = i + 1;
    }
    sort(a, a + m);
    #define nn (int(hull.size()))
    FOR(i, 0, m) {
        while (nn > 1 && ccw(hull[nn - 2], hull[nn - 1], a[i])) hull.pop_back();
        hull.PB(a[i]);
    }
    cin >> n;
    FOR(i, 0, n) {
        cin >> s[i].X;
        s[i].Y = i;
    }
    sort(s, s + n);
    int j = 0;
    FOR(i, 0, n) {
        while (j + 1 < nn && ccw(MP(0, s[i].X), hull[j], hull[j + 1])) j++;
        ans[s[i].Y] = (double)hull[j].X / (hull[j].Y - s[i].X);
    }
    FOR(i, 0, n) cout << setprecision(6) << fixed << ans[i] << '\n';
    return 0;
}

Code mẫu của hieult

#include <set>
#include <map>
#include <list>
#include <cmath>
#include <queue>
#include <stack>
#include <cstdio>
#include <string>
#include <vector>
#include <cstdlib>
#include <cstring>
#include <sstream>
#include <iomanip>
#include <iostream>
#include <algorithm>

#include <ctime>
#include <deque>
#include <bitset>
#include <cctype>
#include <utility>
#include <cassert>

using namespace std;

typedef long long ll;
typedef double ld;
typedef unsigned int ui;
typedef unsigned long long ull;

#define Rep(i,n) for(int i = 0; i < (n); ++i)
#define Repd(i,n) for(int i = (n)-1; i >= 0; --i)
#define For(i,a,b) for(int i = (a); i <= (b); ++i)
#define Ford(i,a,b) for(int i = (a); i >= (b); --i)
//#define Fit(i,v) for(__typeof((v).begin()) i = (v).begin(); i != (v).end(); ++i)
//#define Fitd(i,v) for(__typeof((v).rbegin()) i = (v).rbegin(); i != (v).rend(); ++i)
#define mp make_pair
#define pb push_back
#define fi first
#define se second
#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()
#define ms(a,x) memset(a, x, sizeof(a))

template<class F, class T> T convert(F a, int p = -1) { stringstream ss; if (p >= 0) ss << fixed << setprecision(p); ss << a; T r; ss >> r; return r; }
template<class T> T gcd(T a, T b) { T r; while (b != 0) { r = a % b; a = b; b = r; } return a; }
template<class T> T lcm(T a, T b) { return a / gcd(a, b) * b; }
template<class T> T sqr(T x) { return x * x; }
template<class T> T cube(T x) { return x * x * x; }
template<class T> int getbit(T s, int i) { return (s >> i) & 1; }
template<class T> T onbit(T s, int i) { return s | (T(1) << i); }
template<class T> T offbit(T s, int i) { return s & (~(T(1) << i)); }
template<class T> int cntbit(T s) { return s == 0 ? 0 : cntbit(s >> 1) + (s & 1); }

const int bfsz = 1 << 16;
char bf[bfsz + 5];
int rsz = 0;
int ptr = 0;
char gc() {
    if (rsz <= 0) {
        ptr = 0;
        rsz = (int) fread(bf, 1, bfsz, stdin);
        if (rsz <= 0)
            return EOF;
    }
    --rsz;
    return bf[ptr++];
}
void ga(char &c) {
    c = EOF;
    while (!isalpha(c))
        c = gc();
}
int gs(char s[]) {
    int l = 0;
    char c = gc();
    while (isspace(c))
        c = gc();
    while (c != EOF && !isspace(c)) {
        s[l++] = c;
        c = gc();
    }
    s[l] = '\0';
    return l;
}
template<class T> bool gi(T &v) {
    v = 0;
    char c = gc();
    while (c != EOF && c != '-' && !isdigit(c))
        c = gc();
    if (c == EOF)
        return false;
    bool neg = c == '-';
    if (neg)
        c = gc();
    while (isdigit(c)) {
        v = v * 10 + c - '0';
        c = gc();
    }
    if (neg)
        v = -v;
    return true;
}

typedef pair<int, int> II;

const ld PI = acos(-1.0);
const ld eps = 1e-9;

const int dr[] = {0, +1, 0, -1};
const int dc[] = {+1, 0, -1, 0};

const int inf = (int)1e9 + 5;
const ll linf = (ll)1e16 + 5;
const ll mod = (ll)1e9 + 7;

#define maxn 100005

int cmp(ll x, ll y){
    if(x == y) return 0;
    return x < y ? -1 : 1;
}

struct Point {
    ll x, y;
    Point(){};
    Point(ll _x, ll _y){
        x = _x; y = _y;
    }
    bool operator ==(const Point& that) const {
        return (cmp(x, that.x) == 0 && cmp(y, that.y) == 0);
    }
    bool operator <(const Point& that) const {
        if (cmp(x, that.x) != 0) return cmp(x, that.x) < 0;
        return cmp(y, that.y) < 0;
    }
};

ll sqrdist(Point P0, Point P1){
    return sqr(P0.x - P1.x) + sqr(P0.y - P1.y);
}

int ccw(Point p0, Point p1, Point p2) {
    ll dx1 = p1.x - p0.x, dy1 = p1.y - p0.y;
    ll dx2 = p2.x - p0.x, dy2 = p2.y - p0.y;
    return cmp(dx1 * dy2 - dx2 * dy1, 0);
}

Point O;
bool cmp_angle(Point P1, Point P2) {
    int ret = ccw(O, P1, P2);
    if (ret != 0) return ret > 0;
    return sqrdist(O, P1) < sqrdist(O, P2);
}

int convex_hull(Point a[], int n) {
    if (n <= 3) return n;

    int imin = 0;
    Rep(i, n) if (a[i].y < a[imin].y || (a[i].y == a[imin].y && a[i].x < a[imin].x)) imin = i;

    swap(a[imin], a[0]);
    O = a[0];
    sort(a + 1, a + n, cmp_angle);

    int m = 2;
    For(i, 2, n - 1) {
        while (m > 1 && ccw(a[i], a[m - 1], a[m - 2]) >= 0) --m;
        swap(a[m], a[i]);
        ++m;
    }

    return m;
}


int n, m, x;
II S[maxn];
ld res[maxn];
Point P[maxn * 2];

ld cal(ll h, int id){
    ld res = P[id].x * (ld)(1.0) / (P[id].y - h);
    if(h >= P[id].y) res = linf - P[id].y;
    return res;
}

int  main()
{
//  freopen("in.txt", "r", stdin);

    cin >> n;
    Rep(i, n){
        scanf("%d", &x);
        P[i] = Point(i + 1, x);
    }

    n = convex_hull(P, n);
    For(i, n, n + n) P[i] = P[i - n];

    cin >> m;
    S[0] = mp(0, 0);
    For(i, 1, m){
        scanf("%d", &S[i].fi);
        S[i].se = i;
    }
    sort(S + 1, S + m + 1);

    Rep(i, n / 2) swap(P[i], P[n - 1 - i]);

    ll MIN = linf;
    int run = -1;
    Rep(i, n) if(cal(0, i) < MIN){
        MIN = cal(0, i);
        run = i;
    }

    For(i, 1, m){
        while(cal(S[i].fi, run) > cal(S[i].fi, run + 1)) run++;
        res[S[i].se] = cal(S[i].fi, run);
    }

    For(i, 1, m){
        printf("%.6lf\n", res[i]);
    }
     // getch();
}

Code mẫu của skyvn97

#include<bits/stdc++.h>
#define FOR(i,a,b) for (int i=(a);i<=(b);i=i+1)
#define REP(i,n) for (int i=0;i<(n);i=i+1)
#define FORE(i,v) for (__typeof((v).begin()) i=(v).begin();i!=(v).end();i++)
#define fi   first
#define se   second
using namespace std;
const double INF=1e9+7;
const double eps=1e-7;
typedef pair<double,double> dd;
bool cmp(const dd &a,const dd &b) {
        return (a.fi<b.fi);
}
class ConvexHull {
    private:
    vector<dd> v;
    double L,R;
    int sz;
    bool empty;
    public: 
    ConvexHull() {
        L=0.0;R=0.0;sz=0;empty=true;
    }
    ConvexHull(double l,double r,int n) {
        L=l;R=r;
        empty=true;
        v=vector<dd>(2*n+7);
        sz=2;
        v[0]=dd(L,0.0);
        v[1]=dd(R,0.0);
    }
    void addline(double a,double b) {       
        if (empty) {
            v[0]=dd(L,a*L+b);
            v[1]=dd(R,a*R+b);
            empty=false;
            return;
        }
        int i;
        for (i=sz-1;i>=0;i=i-1) if (v[i].se>a*v[i].fi+b+eps) break;
        if (i==sz-1) return;
        if (i<0) {
            v[0]=dd(L,a*L+b);
            v[1]=dd(R,a*R+b);
            sz=2;
            return;
        }
        double a2=(v[i+1].se-v[i].se)/(v[i+1].fi-v[i].fi);
        double b2=v[i].se-a2*v[i].fi;
        double x=-(b2-b)/(a2-a);
        v[i+1]=dd(x,a*x+b);
        v[i+2]=dd(R,a*R+b);
        sz=i+3;     
    }
    double getmax(double x) const {     
        int p=lower_bound(v.begin(),v.begin()+sz,dd(x-eps,x-eps),cmp)-v.begin();
        if (p<1) p=1;       
        double a=(v[p].se-v[p-1].se)/(v[p].fi-v[p-1].fi);
        double b=v[p].se-a*v[p].fi;
        return (a*x+b);
    }
};
ConvexHull CH;
int n,m;
void process(void) {
    scanf("%d",&n); 
    CH=ConvexHull(0.0,INF,n);
    vector<dd> line;
    line.push_back(dd(0.0,0.0));
    FOR(i,1,n) {
        int t;
        scanf("%d",&t);
        line.push_back(dd(-1.0/i,1.0*t/i));     
    }
    sort(line.begin(),line.end());
    FORE(it,line) CH.addline(it->fi,it->se);
    scanf("%d",&m);
    REP(i,m) {
        int s;
        scanf("%d",&s);
        printf("%.6lf\n",1.0/CH.getmax(s));
    }
}
int main(void) {
    process();
    return 0;
}

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