Submission #320622

#	Time	Username	Problem	Language	Result	Execution time	Memory
320622		vivaan_gupta	Discharging (NOI20_discharging)	C++14	100 / 100	374 ms	16612 KiB

Discharging

#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using ld = long double;
using db = double; 
using str = string; // yay python!

using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;

using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>; 
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>; 
using vpd = vector<pd>;

#define tcT template<class T
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 

// pairs
#define mp make_pair
#define f first
#define s second
#define int ll
// vectors
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18; // not too close to LLONG_MAX
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

// helper funcs
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down

tcT> bool ckmin(T& a, const T& b) {
    return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
    return a < b ? a = b, 1 : 0; }

#define tcTU tcT, class U
tcTU> T fstTrue(T lo, T hi, U f) {
    hi ++; assert(lo <= hi); // assuming f is increasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo)/2;
        f(mid) ? hi = mid : lo = mid+1; 
    } 
    return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
    lo --; assert(lo <= hi); // assuming f is decreasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo+1)/2;
        f(mid) ? lo = mid : hi = mid-1;
    } 
    return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
    sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
    auto it = t.find(u); assert(it != end(t));
    t.erase(u); } // element that doesn't exist from (multi)set

// INPUT
#define tcTUU tcT, class ...U
tcT> void re(complex<T>& c);
tcTU> void re(pair<T,U>& p);
tcT> void re(vector<T>& v);
tcT, size_t SZ> void re(AR<T,SZ>& a);

tcT> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
tcTUU> void re(T& t, U&... u) { re(t); re(u...); }

tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; }
tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
tcT> void re(vector<T>& x) { trav(a,x) re(a); }
tcT, size_t SZ> void re(AR<T,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) { 
    #ifdef LOCAL
        return b ? "true" : "false"; 
    #else 
        return ts((int)b);
    #endif
}
tcT> str ts(complex<T> c) { 
    stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
    str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
    res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
    str res = ""; F0R(i,SZ) res += char('0'+b[i]);
    return res; }
tcTU> str ts(pair<T,U> p);
tcT> str ts(T v) { // containers with begin(), end()
    #ifdef LOCAL
        bool fst = 1; str res = "{";
        for (const auto& x: v) {
            if (!fst) res += ", ";
            fst = 0; res += ts(x);
        }
        res += "}"; return res;
    #else
        bool fst = 1; str res = "";
        for (const auto& x: v) {
            if (!fst) res += " ";
            fst = 0; res += ts(x);
        }
        return res;

    #endif
}
tcTU> str ts(pair<T,U> p) {
    #ifdef LOCAL
        return "("+ts(p.f)+", "+ts(p.s)+")"; 
    #else
        return ts(p.f)+" "+ts(p.s);
    #endif
}

// OUTPUT
tcT> void pr(T x) { cout << ts(x); }
tcTUU> void pr(const T& t, const U&... u) { 
    pr(t); pr(u...); }
void ps() { pr("\n"); } // print w/ spaces
tcTUU> void ps(const T& t, const U&... u) { 
    pr(t); if (sizeof...(u)) pr(" "); ps(u...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
tcTUU> void DBG(const T& t, const U&... u) {
    cerr << ts(t); if (sizeof...(u)) cerr << ", ";
    DBG(u...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
    #define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
    #define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
         << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
    #define dbg(...) 0
    #define chk(...) 0
#endif

// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
    unsyncIO();
    // cin.exceptions(cin.failbit); 
    // throws exception when do smth illegal
    // ex. try to read letter into int
    if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
const ll N = 1e6+5;
int a[N];
int dp[N];
int calc(int i,int j){
    int m = a[i];
    FOR(k,i+1,j+1)m=max(m,a[k]);
    return m;
}
struct ConvexHullDynamic
{
    // static const int INF=1e12;
 
    struct Line
    {
        int a, b; //y = ax + b
        double xLeft; //Stores the intersection wiith previous line in the convex hull. First line has -INF
 
        enum Type {line, maxQuery, minQuery} type;
        int val;
 
        explicit Line(int aa=0, int bb=0): a(aa), b(bb), xLeft(-INF), type(Type::line), val(0) {}
 
        int valueAt(int x) const
        {
            return a*x + b;
        }
        friend bool isParallel(const Line &l1, const Line &l2)
        {
            return l1.a == l2.a;
        }
        friend double intersectX(const Line &l1, const Line &l2)
        {
            return isParallel(l1, l2)?INF:1.0*(l2.b-l1.b)/(l1.a-l2.a);
        }
        bool operator<(const Line& l2) const
        {
            if(l2.type == line)
                return this->a < l2.a;
            if(l2.type == maxQuery)
                return this->xLeft < l2.val;
            if(l2.type == minQuery)
                return this->xLeft > l2.val;
        }
    };
 
    bool isMax;
    set<Line> hull;
 
    bool hasPrev(set<Line>::iterator it)
    {
        return it!=hull.begin();
    }   
    bool hasNext(set<Line>::iterator it)
    {
        return it!=hull.end() && next(it)!=hull.end();
    }
    bool irrelevant(const Line &l1, const Line &l2, const Line &l3)
    {
        return intersectX(l1, l3) <= intersectX(l1, l2);
    }
    bool irrelevant(    set<Line>::iterator it)
    {
        return hasPrev(it) && hasNext(it) && ( 
            (isMax && irrelevant(*prev(it), *it, *next(it))) 
            || (!isMax && irrelevant(*next(it), *it, *prev(it))));
    }
    //Updates xValue of line pointed by it
    set<Line>::iterator updateLeftBorder(set<Line>::iterator it)
    {
        if(isMax && !hasPrev(it) || !isMax && !hasNext(it))
            return it;
        double val=intersectX(*it, isMax?(*prev(it)):(*next(it)));
        Line temp(*it);
        it=hull.erase(it);
        temp.xLeft=val;
        it=hull.insert(it, temp);
        return it;
    }
 
    explicit ConvexHullDynamic(bool isMax): isMax(isMax) {}
 
    void addLine(int a, int b) //Add ax + b in logN time
    {
        Line l3=Line(a, b);
        auto it=hull.lower_bound(l3);
 
        //If parallel liune is already in set, one of the lines becomes irrelevant
        if(it!=hull.end() && isParallel(*it, l3))
        {
            if(isMax && it->b<b || !isMax && it->b>b)
                it=hull.erase(it);
            else
                return;
        }
 
        it=hull.insert(it, l3);
        if(irrelevant(it))
        {
            hull.erase(it);
            return;
        }
 
        //Remove lines which became irrelevant after inserting
        while(hasPrev(it) && irrelevant(prev(it)))
            hull.erase(prev(it));
        while(hasNext(it) && irrelevant(next(it)))
            hull.erase(next(it));
 
        //Update xLine
        it=updateLeftBorder(it);
        if(hasPrev(it))
            updateLeftBorder(prev(it));
        if(hasNext(it))
            updateLeftBorder(next(it));
    }
 
    int getBest(int x)
    {
        Line q;
        q.val=x;
        q.type = isMax?Line::Type::maxQuery : Line::Type::minQuery;
 
        auto bestLine=hull.lower_bound(q);
        if(isMax)
            --bestLine;
        return bestLine->valueAt(x);
    }
};
ConvexHullDynamic hull(0);

signed main() {
    setIO();    
    // you should actually read the stuff at the bottom
    int n;re(n);
    FOR(i,1,n+1) re(a[i]);
    dp[0]= 0;// (dpval,cost)
    hull.addLine(n,dp[0]);
    int ma = 0;
    FOR(i,1,n+1){
        ma = max(ma,a[i]);
        dp[i]=hull.getBest(ma);
        hull.addLine(n-i,dp[i]);
    }
    // FOR(i,1,n){
    //     ps(dp[i]);
    // }
    ps(dp[n]);
}

/* stuff you should look for
    * read the probem 3 more times in case of WA :)
    * int overflow, array bounds
    * special cases (n=1?)
    * do smth instead of nothing and stay organized
    * WRITE STUFF DOWN
    * DON'T GET STUCK ON ONE APPROACH
*/

Compilation message (stderr)

Discharging.cpp: In member function 'std::set<ConvexHullDynamic::Line>::iterator ConvexHullDynamic::updateLeftBorder(std::set<ConvexHullDynamic::Line>::iterator)':
Discharging.cpp:261:18: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  261 |         if(isMax && !hasPrev(it) || !isMax && !hasNext(it))
      |            ~~~~~~^~~~~~~~~~~~~~~
Discharging.cpp: In member function 'void ConvexHullDynamic::addLine(ll, ll)':
Discharging.cpp:281:22: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  281 |             if(isMax && it->b<b || !isMax && it->b>b)
      |                ~~~~~~^~~~~~~~~~
Discharging.cpp: In function 'void setIn(str)':
Discharging.cpp:182:28: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  182 | void setIn(str s) { freopen(s.c_str(),"r",stdin); }
      |                     ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
Discharging.cpp: In function 'void setOut(str)':
Discharging.cpp:183:29: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
  183 | void setOut(str s) { freopen(s.c_str(),"w",stdout); }
      |                      ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
Discharging.cpp: In member function 'bool ConvexHullDynamic::Line::operator<(const ConvexHullDynamic::Line&) const':
Discharging.cpp:234:9: warning: control reaches end of non-void function [-Wreturn-type]
  234 |         }
      |         ^

• Subtask 1: 9 / 9
• Subtask 2: 13 / 13
• Subtask 3: 25 / 25
• Subtask 4: 11 / 11
• Subtask 5: 14 / 14
• Subtask 6: 28 / 28