제출 #1317735

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
1317735		spetr	모자이크 (IOI24_mosaic)	C++20	12 / 100	113 ms	48784 KiB

mosaic

#include <bits/stdc++.h>

using namespace std;

#define ll long long
const ll mmod = 998244353;  
#define vl vector<long long>
#define vll vector<vector<long long>>
#define pl pair<long long, long long>
#define vb vector<bool>

std::vector<long long> mosaic(
    std::vector<int> X, std::vector<int> Y,
    std::vector<int> T, std::vector<int> B,
    std::vector<int> L, std::vector<int> R){

    ll n, q;
    n = X.size();
    q = T.size();

    vll row3;
    vll col3;
    vl x1, y1;
    for (ll i = 0; i <n; i++){
        x1.push_back(X[i]);
        y1.push_back(Y[i]);
    }
    row3.push_back(x1); col3.push_back(y1);
    row3.push_back({Y[1]}); row3.push_back({Y[2]}); 
    col3.push_back({X[1]}); col3.push_back({X[2]}); 

    for (ll i = 1; i < 3; i++){
        for (ll j = 1; j < n; j++){
            ll v1 = 0; ll v2 = 0;
            if (row3[i][j-1] == 0 && row3[i-1][j] == 0){
                v1 = 1;
            }
            if (col3[i][j-1] == 0 && col3[i-1][j] == 0){
                v2 = 1;
            }
            row3[i].push_back(v1);
            col3[i].push_back(v2);
        }
    }

    vl s1, s2, s3;
    for (ll i = n-1; i>=0; i--){
        s1.push_back(col3[0][i]);
    }
    for (ll i = 1; i < n; i++){
        s1.push_back(row3[0][i]);
    }

    for (ll i = n-1; i>=1; i--){
        s2.push_back(col3[1][i]);
    }
    for (ll i = 2; i < n; i++){
        s2.push_back(row3[1][i]);
    }

    for (ll i = n-1; i>=2; i--){
        s3.push_back(col3[2][i]);
    }
    for (ll i = 3; i < n; i++){
        s3.push_back(row3[2][i]);
    }

    vl p1, p2, p3;
    p1 = p2 = p3 = {0};
    for (ll i = 0; i < s1.size(); i++){
        p1.push_back(s1[i] + p1[i]);
    }
    for (ll i = 0; i < s2.size(); i++){
        p2.push_back(s2[i] + p2[i]);
    }
    for (ll i = 0; i < s3.size(); i++){
        p3.push_back(s3[i] + p3[i]);
    }


    vl q1; // q2 smazáno/zakomentováno, viz níže
    q1 = {0}; 
    for (ll i = 0; i < s3.size(); i++){
        q1.push_back(q1[i] + s3[i]*(i+1));
        // q2.push_back... TOTO ZPŮSOBUJE PROBLÉMY, nahradíme to vzorcem
    }

    vl ans;
    for (ll i = 0; i < q; i++){
        ll l, r, u, d;
        l = L[i]; r = R[i]; u = T[i]; d = B[i];
        ll a, b;
        ll suma = 0;
        //Layer1
        b = 0; a = 1e9;
        if (l == 0){
            a = min(a, n-d-1);
            b = max(b, n-u);
        }
        if (u == 0){
            a = min(a, n + l - 1);
            b = max(b, n + r);
        }
        if (a < b){
            suma += p1[b] - p1[a];
        }
        //Layer2
        b = 0; a = 1e9;
        if (l <= 1 && r >= 1){
            a = min(a, n-d-1);
            b = max(b, n-max(u,1ll));
        }
        if (u <= 1 && d >= 1){
            a = min(a, n + max(l,1ll) - 3);
            b = max(b, n + r - 2);
        }
        if (a < b){
            suma += p2[b] - p2[a];
        }
        
        // Layer3 - ZDE JSOU HLAVNÍ OPRAVY
        // FIX 1: Musí být &&, jinak indexy s3 vyletí mimo
        if (r >= 2 && d >= 2){ 
            l = max(2ll, l);
            u = max(2ll, u);
            ll a = l - 2 + (n-1)-d;
            ll b = r - 2 + n - u;
            ll t = min(d-u, r-l); 
            // ll v = q2.size(); <-- Není potřeba

            // FIX 2: Všude přidáno +1 k horní mezi (protože prefix sums jsou [L, R))
            
            // Rostoucí část (Rising slope)
            // Interval [a, a+t] -> prefix indexy [a, a+t+1]
            suma += q1[a+t+1] - q1[a];
            suma -= (p3[a+t+1] - p3[a])*a;

            // Klesající část (Falling slope)
            // Interval [b-t, b] -> prefix indexy [b-t, b+1]
            // Místo q2 použijeme matematiku: (b+2)*SUMA - VÁŽENÁ_SUMA
            // Tím se vyhneme složitému indexování q2 pozpátku
            ll range_sum = p3[b+1] - p3[b-t];
            ll range_w_sum = q1[b+1] - q1[b-t];
            suma += range_sum * (b + 2) - range_w_sum;

            // Plošina (Plateau)
            // Interval (a+t, b-t) -> prefix indexy [a+t+1, b-t]
            // Podmínka b-t > a+t zajišťuje, že se nepřekrývají
            if (b-t > a+t) {
                suma += (p3[b-t] - p3[a+t+1])*(t+1);
            }
        }

        ans.push_back(suma);
    }
    return ans;
}

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