Submission #479412

#	Time	Username	Problem	Language	Result	Execution time	Memory
479412		tranxuanbach	Building Bridges (CEOI17_building)	C++17	100 / 100	116 ms	13604 KiB

building

#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;

// Optimization

#pragma GCC optimize("O3,unroll-loops,no-stack-protector")
#define endl '\n'

// Shortcut

#define int long long
#define eb emplace_back
#define pb push_back
#define pob pop_back
#define mp make_pair
#define upb upper_bound
#define lwb lower_bound
#define fi first
#define se second
#define For(i, l, r) for (int i = l; i < r; i++)
#define ForE(i, l, r) for (int i = l; i <= r; i++)
#define Ford(i, r, l) for (int i = r; i > l; i--)
#define FordE(i, r, l) for (int i = r; i >= l; i--)
#define Fora(i, a) for (auto i : a)

// I/O & Debug

#define PrintV(a) Fora(iiii, a) cout << iiii << ' '; cout << endl;
#define PrintVl(a) Fora(iiii, a) cout << iiii << endl;
#define PrintA(a, l, r) for (int iiii = l; iiii <= r; iiii++) cout << a[iiii] << ' '; cout << endl;
#define PrintAl(a, l, r) for (int iiii = l; iiii <= r; iiii++) cout << a[iiii] << endl;
#define Ptest(x) return cout << x, 0;
#define gl(s) getline(cin, s);
#define setpre(x) fixed << setprecision(x)
/*
#define debug(args...){ string _sDEB = #args; replace(_sDEB.begin(), _sDEB.end(), ',', ' '); stringstream _ssDEB(_sDEB); istream_iterator<string> _itDEB(_ssDEB); DEB(_itDEB, args); }
void DEB(istream_iterator<string> it) {}
template<typename T, typename... Args>
void DEB(istream_iterator<string> it, T a, Args... args){
    cout << *it << " = " << a << endl;
    DEB(++it, args...);
}
*/

// Functions

//#define isvowel(a) (a == 'a' || a == 'e' || a == 'i' || a == 'o' || a == 'u')
#define bend(a) a.begin(), a.end()
#define rbend(a) a.rbegin(), a.rend()
#define mset(a) memset(a, 0, sizeof(a))
#define mset1(a) memset(a, 1, sizeof(a))
#define msetn1(a) memset(a, -1, sizeof(a))
#define msetinf(a) memset(a, 0x3f, sizeof(a))
#define gcd __gcd
#define __builtin_popcount __builtin_popcountll
//mt19937 rando(chrono::steady_clock::now().time_since_epoch().count());
//int randt(int l, int r){ return (rando() % (r - l + 1) + l); }

// Data Structure

#define pque priority_queue
#define mts multiset
#define y0 _y0_
#define y1 _y1_
#define div divi
typedef long long ll;
typedef long double ld;
typedef vector <int> vi;
typedef vector <ll> vll;
typedef vector <ld> vld;
typedef vector <string> vs;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
typedef vector <vi > vvi;
typedef vector <vll > vvll;
typedef vector <pii > vpii;
typedef vector <pll > vpll;

const int N = 1e5 + 5;
int mod = 1e9 + 7, mod1 = 998244353, mod2 = 1e9 + 9, inf = 1e9 + 7;
ll infll = 1e18 + 7;

/*
 * Dynamic version of data structure
 * to be used in dynamic programming optimisation
 * called "Convex Hull trick"
 * 'Dynamic' means that there is no restriction on adding lines order
 */
class ConvexHullDynamic
{
    typedef long long coef_t;
    typedef long long coord_t;
    typedef long long val_t;
 
    /*
     * Line 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
     * and 'xLeft' which is intersection with previous line in hull(first line has -INF)
     */
private:
    struct Line
    {
        coef_t a, b;
        ld xLeft;
 
        enum Type {line, maxQuery, minQuery} type;
        coord_t val;
 
        explicit Line(coef_t aa=0, coef_t bb=0) : a(aa), b(bb), xLeft(-infll), type(Type::line), val(0) {}
        val_t valueAt(coord_t x) const { return a*x+b; }
        friend bool areParallel(const Line& l1, const Line& l2) { return l1.a==l2.a; }
        friend ld intersectX(const Line& l1, const Line& l2) { return areParallel(l1,l2)?infll: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;
        }
    };
 
private:
    bool            isMax; //whether or not saved envelope is top(search of max value)
    std::set<Line>  hull;  //envelope itself
 
private:
    /*
     * INFO:        Check position in hull by iterator
     * COMPLEXITY:  O(1)
     */
    bool hasPrev(std::set<Line>::iterator it) { return it!=hull.begin(); }
    bool hasNext(std::set<Line>::iterator it) { return it!=hull.end() && std::next(it)!=hull.end(); }
 
    /*
     * INFO:        Check whether line l2 is irrelevant
     * NOTE:        Following positioning in hull must be true
     *              l1 is next left to l2
     *              l2 is right between l1 and l3
     *              l3 is next right to l2
     * COMPLEXITY:  O(1)
     */
    bool irrelevant(const Line& l1, const Line& l2, const Line& l3) { return intersectX(l1,l3) <= intersectX(l1,l2); }
    bool irrelevant(std::set<Line>::iterator it)
    {
        return hasPrev(it) && hasNext(it)
               && (    isMax && irrelevant(*std::prev(it), *it, *std::next(it))
                       || !isMax && irrelevant(*std::next(it), *it, *std::prev(it)) );
    }
 
    /*
     * INFO:        Updates 'xValue' of line pointed by iterator 'it'
     * COMPLEXITY:  O(1)
     */
    std::set<Line>::iterator updateLeftBorder(std::set<Line>::iterator it)
    {
        if (isMax && !hasPrev(it) || !isMax && !hasNext(it))
            return it;
 
        double val = intersectX(*it, isMax?*std::prev(it):*std::next(it));
        Line buf(*it);
        it = hull.erase(it);
        buf.xLeft = val;
        it = hull.insert(it, buf);
        return it;
    }
 
public:
    explicit ConvexHullDynamic(bool isMax): isMax(isMax) {}
 
    /*
     * INFO:        Adding line to the envelope
     *              Line is of type 'y=a*x+b' represented by 2 coefficients 'a' and 'b'
     * COMPLEXITY:  Adding N lines(N calls of function) takes O(N*log N) time
     */
    void addLine(coef_t a, coef_t b)
    {
        //find the place where line will be inserted in set
        Line l3 = Line(a, b);
        auto it = hull.lower_bound(l3);
 
        //if parallel line is already in set, one of them becomes irrelevant
        if (it!=hull.end() && areParallel(*it, l3))
        {
            if (isMax && it->b < b || !isMax && it->b > b)
                it = hull.erase(it);
            else
                return;
        }
 
        //try to insert
        it = hull.insert(it, l3);
        if (irrelevant(it)) { hull.erase(it); return; }
 
        //remove lines which became irrelevant after inserting line
        while (hasPrev(it) && irrelevant(std::prev(it))) hull.erase(std::prev(it));
        while (hasNext(it) && irrelevant(std::next(it))) hull.erase(std::next(it));
 
        //refresh 'xLine'
        it = updateLeftBorder(it);
        if (hasPrev(it))
            updateLeftBorder(std::prev(it));
        if (hasNext(it))
            updateLeftBorder(std::next(it));
    }
    /*
     * INFO:        Query, which returns max/min(depends on hull type - see more info above) value in point with abscissa 'x'
     * COMPLEXITY:  O(log N), N-amount of lines in hull
     */
    val_t getBest(coord_t x) const
    {
        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);
    }
} dch(0);

int n;
int h[N], w[N], b[N], dp[N];

signed main(){
    ios_base::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);
    cin >> n;
    ForE(i, 1, n){
        cin >> h[i];
    }
    ForE(i, 1, n){
        cin >> w[i];
        b[i] = b[i - 1] + w[i];
    }
    dp[1] = 0;
    dch.addLine(-2 * h[1], dp[1] - b[1] + h[1] * h[1]);
    // cout << dch.getBest(h[1]) << ' ';
    ForE(i, 2, n){
        dp[i] = b[i - 1] + h[i] * h[i] + dch.getBest(h[i]);
        // cout << dch.getBest(h[i]) << ' ';
        dch.addLine(-2 * h[i], dp[i] - b[i] + h[i] * h[i]);
    }
    // cout << endl;
    // PrintA(dp, 1, n);
    cout << dp[n];
}

/*
==================================+
INPUT:                            |
------------------------------    |

------------------------------    |
==================================+
OUTPUT:                           |
------------------------------    |

------------------------------    |
==================================+
*/

Compilation message (stderr)

building.cpp: In member function 'bool ConvexHullDynamic::irrelevant(std::set<ConvexHullDynamic::Line>::iterator)':
building.cpp:150:30: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  150 |                && (    isMax && irrelevant(*std::prev(it), *it, *std::next(it))
      |                        ~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
building.cpp: In member function 'std::set<ConvexHullDynamic::Line>::iterator ConvexHullDynamic::updateLeftBorder(std::set<ConvexHullDynamic::Line>::iterator)':
building.cpp:160:19: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  160 |         if (isMax && !hasPrev(it) || !isMax && !hasNext(it))
      |             ~~~~~~^~~~~~~~~~~~~~~
building.cpp: In member function 'void ConvexHullDynamic::addLine(ConvexHullDynamic::coef_t, ConvexHullDynamic::coef_t)':
building.cpp:188:23: warning: suggest parentheses around '&&' within '||' [-Wparentheses]
  188 |             if (isMax && it->b < b || !isMax && it->b > b)
      |                 ~~~~~~^~~~~~~~~~~~
building.cpp: In member function 'bool ConvexHullDynamic::Line::operator<(const ConvexHullDynamic::Line&) const':
building.cpp:123:9: warning: control reaches end of non-void function [-Wreturn-type]
  123 |         }
      |         ^

• Subtask 1: 30 / 30
• Subtask 2: 30 / 30
• Subtask 3: 40 / 40