oj.uz

Submission #937448

# Submission time Handle Problem Language Result Execution time Memory
937448 2024-03-04T04:27:36 Z GrindMachine Rectangles (IOI19_rect) C++17
100 / 100
 2754 ms 660276 KB 
#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;

template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;

#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl

#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)

template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}

template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}

#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif

/*

read some solutions long back, recollected some ideas from there

look at a given row
how many (i,j) exist s.t i < j and a[i] > a[i+1],a[i+2],...,a[j-1] and a[j] > a[i+1],a[i+2],...,a[j-1]
i.e the ends have stricly larger value than the values in the middle

claim:
the #of such pairs is O(n)

proof:
for simplicity, assume all elems are distinct
we can count such pairs using a stack
maintain a decreasing stack
when pushing index i, pop off all smaller values
(j,i) forms a valid pair, and j is no longer useful (i has bigger value), so it's popped
what about indices in the stack with bigger value?
only 1 such index can form a good pair
15 10 6 5 => assume a[i] = 5, [15,10,6] = contents of stack after popping all guys smaller than 5 (stack contains values for this explanation, not indices)
        ^
(6,5) forms a valid pair
(10,5) does not, because 6 > 5
so only the closest greater to the left of i can form a pair with i (when considering greater elements)
for j to the left of this position, there would exist an index in the middle with value bigger than the right end
so we have proved this by construction

find the valid segments for each row and each col
tot #of valid segments over all rows = O(nm)
tot #of valid segments over all cols = O(nm)

now, fix the lowest horizontal segment of the rectangle
find how far up this horizontal segment can be extended
leftmost vertical segment is also known once the lowest horizontal segment is fixed

vertical segment (k,i) is valid for a given (l,r) if:
k >= horizontal_extend_up-1
vertical_extend_right >= r-1
counting naively is O(nm*max(n,m)) (or something similar), gives 72 points

queries could be answered offline with a fenwick tree for 100 points

*/

const int MOD = 1e9 + 7;
const int N = 1e5 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;

#include "rect.h"
 
template<typename T>
struct fenwick {
    int siz;
    vector<T> tree;
 
    fenwick() {
 
    }
 
    fenwick(int n) {
        siz = n;
        tree = vector<T>(n + 1);
    }
 
    int lsb(int x) {
        return x & -x;
    }
 
    void build(vector<T> &a, int n) {
        for (int i = 1; i <= n; ++i) {
            int par = i + lsb(i);
            tree[i] += a[i];
 
            if (par <= siz) {
                tree[par] += tree[i];
            }
        }
    }
 
    void pupd(int i, T v) {
        i++;
        while (i <= siz) {
            tree[i] += v;
            i += lsb(i);
        }
    }
 
    T sum(int i) {
        i++;
        T res = 0;
 
        while (i) {
            res += tree[i];
            i -= lsb(i);
        }
 
        return res;
    }
 
    T query(int l, int r) {
        if (l > r) return 0;
        T res = sum(r) - sum(l - 1);
        return res;
    }
};
 
long long count_rectangles(std::vector<std::vector<int> > a) {
    int n = sz(a), m = sz(a[0]);
    if(n <= 2 or m <= 2) return 0;
 
    vector<pii> up[n][m];
    int ptr = 0;
 
    rep(j,m){
        stack<int> st;
        rep(i,n){
            bool eq = false;
            while(!st.empty() and a[i][j] >= a[st.top()][j]){
                int k = st.top();
                st.pop();
                if(a[i][j] == a[k][j]){
                    eq = true;
                }
                if(i-k >= 2){
                    up[i][j].pb({k,ptr++});
                }
            }
 
            if(!st.empty() and !eq){
                int k = st.top();
                if(i-k >= 2){
                    up[i][j].pb({k,ptr++});
                }
            }
 
            st.push(i);
        }
    }
 
    vector<int> farthest(ptr);
    int seg_ptr[n][n];
    memset(seg_ptr,-1,sizeof seg_ptr);

    rev(j,m-1,0){
        if(j+2 < m){
            rep(i,n){
                for(auto [k,ptr] : up[i][j+2]){
                    seg_ptr[k][i] = -1;
                }
            }   
        }

        if(j+1 < m){
            rep(i,n){
                for(auto [k,ptr] : up[i][j+1]){
                    seg_ptr[k][i] = ptr;
                }
            }   
        }

        rep(i,n){
            for(auto [k,ptr] : up[i][j]){
                if(seg_ptr[k][i] != -1){
                    farthest[ptr] = farthest[seg_ptr[k][i]];
                }
                else{
                    farthest[ptr] = j;
                }
            }
        }
    }
 
    int prev_occ[m][m], first_occ[m][m];
    memset(prev_occ,-1,sizeof prev_occ);
    memset(first_occ,-1,sizeof first_occ);
 
    ll ans = 0;
    vector<int> queries[ptr];
 
    rep1(i,n-2){
        stack<int> st;
        vector<pii> good;
        rep(j,m){
            bool eq = false;
            while(!st.empty() and a[i][j] >= a[i][st.top()]){
                int k = st.top();
                st.pop();
                if(a[i][j] == a[i][k]){
                    eq = true;
                }
                if(j-k >= 2){
                    good.pb({k,j});
                }
            }
 
            // cout << j << endl;
            // cout << eq << endl;
            // auto st_copy = st;
            // while(!st_copy.empty()){
            //  cout << st_copy.top() << " ";
            //  st_copy.pop();
            // }
            // cout << endl;
 
            if(!st.empty() and !eq){
                int k = st.top();
                if(j-k >= 2){
                    // cout << k << " " << j << endl;
                    good.pb({k,j});
                }
            }
 
            st.push(j);
        }
 
        for(auto [l,r] : good){
            if(prev_occ[l][r] != i-1){
                first_occ[l][r] = i;
            }
 
            prev_occ[l][r] = i;
 
            int lo = 0, hi = sz(up[i+1][l+1])-1;
            int pos = -1;
 
            while(lo <= hi){
                int mid = (lo+hi) >> 1;
                if(up[i+1][l+1][mid].ff >= first_occ[l][r]-1){
                    pos = mid;
                    lo = mid+1;
                }
                else{
                    hi = mid-1;
                }
            }
 
            if(pos != -1){
                int ind = up[i+1][l+1][pos].ss;
                queries[ind].pb(r);
            }
 
            /*
 
            for(auto [k,ptr] : up[i+1][l+1]){
                if(k >= first_occ[l][r]-1){
                    if(farthest[ptr] >= r-1){
                        ans++;
                    }
                }
                else{
                    break;
                }
            }
 
            */
        }
    }
 
    fenwick<int> fenw(m);
 
    rep(i,n){
        rep(j,m){
            for(auto [k,ptr] : up[i][j]){
                fenw.pupd(farthest[ptr],1);
                trav(r,queries[ptr]){
                    ans += fenw.query(r-1,m-1);
                }
            }
 
            for(auto [k,ptr] : up[i][j]){
                fenw.pupd(farthest[ptr],-1);
            }
        }
    }
 
    /*
 
    int oans = 0;
 
    rep1(i1,n-2){
        rep1(j1,m-2){
            for(int i2 = i1; i2 < n-1; ++i2){
                for(int j2 = j1; j2 < m-1; ++j2){
                    bool ok = true;
                    for(int r = i1; r <= i2; ++r){
                        for(int c = j1; c <= j2; ++c){
                            if(a[r][c] >= min({a[i1-1][c],a[i2+1][c],a[r][j1-1],a[r][j2+1]})){
                                ok = false;
                                break;
                            }
                        }
                        if(!ok) break;
                    }
 
                    if(ok){
                        oans++;
                        cout << i1 << " " << j1 << " " << i2 << " " << j2 << endl;
                    }
                }
            }
        }
    }
    
    */
    
    // cout << ans << endl;
    // cout << oans << endl;
    // cout << endl;
 
    // assert(ans == oans);
 
    return ans;
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 ms 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct

Subtask #2
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 0 ms 348 KB Output is correct
18 Correct 1 ms 344 KB Output is correct
19 Correct 1 ms 348 KB Output is correct
20 Correct 1 ms 348 KB Output is correct
21 Correct 1 ms 348 KB Output is correct
22 Correct 1 ms 860 KB Output is correct
23 Correct 1 ms 860 KB Output is correct
24 Correct 1 ms 860 KB Output is correct
25 Correct 1 ms 704 KB Output is correct
26 Correct 2 ms 860 KB Output is correct
27 Correct 2 ms 860 KB Output is correct
28 Correct 2 ms 856 KB Output is correct
29 Correct 1 ms 604 KB Output is correct

Subtask #3
12.0 / 12.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 860 KB Output is correct
18 Correct 1 ms 860 KB Output is correct
19 Correct 1 ms 860 KB Output is correct
20 Correct 1 ms 704 KB Output is correct
21 Correct 2 ms 860 KB Output is correct
22 Correct 2 ms 860 KB Output is correct
23 Correct 2 ms 856 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 0 ms 348 KB Output is correct
26 Correct 1 ms 344 KB Output is correct
27 Correct 1 ms 348 KB Output is correct
28 Correct 1 ms 348 KB Output is correct
29 Correct 1 ms 348 KB Output is correct
30 Correct 5 ms 3676 KB Output is correct
31 Correct 5 ms 3672 KB Output is correct
32 Correct 5 ms 3928 KB Output is correct
33 Correct 6 ms 3160 KB Output is correct
34 Correct 10 ms 4444 KB Output is correct
35 Correct 10 ms 4444 KB Output is correct
36 Correct 10 ms 4452 KB Output is correct
37 Correct 10 ms 4188 KB Output is correct

Subtask #4
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 860 KB Output is correct
18 Correct 1 ms 860 KB Output is correct
19 Correct 1 ms 860 KB Output is correct
20 Correct 1 ms 704 KB Output is correct
21 Correct 2 ms 860 KB Output is correct
22 Correct 2 ms 860 KB Output is correct
23 Correct 2 ms 856 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 5 ms 3676 KB Output is correct
26 Correct 5 ms 3672 KB Output is correct
27 Correct 5 ms 3928 KB Output is correct
28 Correct 6 ms 3160 KB Output is correct
29 Correct 10 ms 4444 KB Output is correct
30 Correct 10 ms 4444 KB Output is correct
31 Correct 10 ms 4452 KB Output is correct
32 Correct 10 ms 4188 KB Output is correct
33 Correct 0 ms 348 KB Output is correct
34 Correct 1 ms 344 KB Output is correct
35 Correct 1 ms 348 KB Output is correct
36 Correct 1 ms 348 KB Output is correct
37 Correct 1 ms 348 KB Output is correct
38 Correct 53 ms 34192 KB Output is correct
39 Correct 52 ms 35716 KB Output is correct
40 Correct 65 ms 38996 KB Output is correct
41 Correct 69 ms 40276 KB Output is correct
42 Correct 57 ms 43644 KB Output is correct
43 Correct 58 ms 43780 KB Output is correct
44 Correct 61 ms 44068 KB Output is correct
45 Correct 55 ms 41808 KB Output is correct
46 Correct 62 ms 30548 KB Output is correct
47 Correct 84 ms 34640 KB Output is correct
48 Correct 161 ms 50084 KB Output is correct
49 Correct 167 ms 52088 KB Output is correct
50 Correct 76 ms 26296 KB Output is correct
51 Correct 77 ms 27608 KB Output is correct
52 Correct 154 ms 49196 KB Output is correct
53 Correct 158 ms 50512 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 30 ms 49888 KB Output is correct
2 Correct 21 ms 35928 KB Output is correct
3 Correct 28 ms 49492 KB Output is correct
4 Correct 0 ms 344 KB Output is correct
5 Correct 29 ms 49536 KB Output is correct
6 Correct 29 ms 49680 KB Output is correct
7 Correct 28 ms 49500 KB Output is correct
8 Correct 30 ms 49492 KB Output is correct
9 Correct 28 ms 49492 KB Output is correct
10 Correct 0 ms 348 KB Output is correct
11 Correct 0 ms 348 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 1 ms 344 KB Output is correct
3 Correct 1 ms 348 KB Output is correct
4 Correct 1 ms 348 KB Output is correct
5 Correct 1 ms 348 KB Output is correct
6 Correct 0 ms 348 KB Output is correct
7 Correct 500 ms 191844 KB Output is correct
8 Correct 1245 ms 384588 KB Output is correct
9 Correct 1225 ms 386296 KB Output is correct
10 Correct 1248 ms 386480 KB Output is correct
11 Correct 167 ms 157776 KB Output is correct
12 Correct 410 ms 262660 KB Output is correct
13 Correct 425 ms 281648 KB Output is correct

Subtask #7
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 348 KB Output is correct
2 Correct 0 ms 348 KB Output is correct
3 Correct 0 ms 348 KB Output is correct
4 Correct 0 ms 348 KB Output is correct
5 Correct 0 ms 348 KB Output is correct
6 Correct 1 ms 348 KB Output is correct
7 Correct 0 ms 348 KB Output is correct
8 Correct 1 ms 348 KB Output is correct
9 Correct 1 ms 344 KB Output is correct
10 Correct 1 ms 348 KB Output is correct
11 Correct 1 ms 348 KB Output is correct
12 Correct 1 ms 348 KB Output is correct
13 Correct 0 ms 436 KB Output is correct
14 Correct 0 ms 344 KB Output is correct
15 Correct 0 ms 348 KB Output is correct
16 Correct 1 ms 348 KB Output is correct
17 Correct 1 ms 860 KB Output is correct
18 Correct 1 ms 860 KB Output is correct
19 Correct 1 ms 860 KB Output is correct
20 Correct 1 ms 704 KB Output is correct
21 Correct 2 ms 860 KB Output is correct
22 Correct 2 ms 860 KB Output is correct
23 Correct 2 ms 856 KB Output is correct
24 Correct 1 ms 604 KB Output is correct
25 Correct 5 ms 3676 KB Output is correct
26 Correct 5 ms 3672 KB Output is correct
27 Correct 5 ms 3928 KB Output is correct
28 Correct 6 ms 3160 KB Output is correct
29 Correct 10 ms 4444 KB Output is correct
30 Correct 10 ms 4444 KB Output is correct
31 Correct 10 ms 4452 KB Output is correct
32 Correct 10 ms 4188 KB Output is correct
33 Correct 53 ms 34192 KB Output is correct
34 Correct 52 ms 35716 KB Output is correct
35 Correct 65 ms 38996 KB Output is correct
36 Correct 69 ms 40276 KB Output is correct
37 Correct 57 ms 43644 KB Output is correct
38 Correct 58 ms 43780 KB Output is correct
39 Correct 61 ms 44068 KB Output is correct
40 Correct 55 ms 41808 KB Output is correct
41 Correct 62 ms 30548 KB Output is correct
42 Correct 84 ms 34640 KB Output is correct
43 Correct 161 ms 50084 KB Output is correct
44 Correct 167 ms 52088 KB Output is correct
45 Correct 76 ms 26296 KB Output is correct
46 Correct 77 ms 27608 KB Output is correct
47 Correct 154 ms 49196 KB Output is correct
48 Correct 158 ms 50512 KB Output is correct
49 Correct 30 ms 49888 KB Output is correct
50 Correct 21 ms 35928 KB Output is correct
51 Correct 28 ms 49492 KB Output is correct
52 Correct 0 ms 344 KB Output is correct
53 Correct 29 ms 49536 KB Output is correct
54 Correct 29 ms 49680 KB Output is correct
55 Correct 28 ms 49500 KB Output is correct
56 Correct 30 ms 49492 KB Output is correct
57 Correct 28 ms 49492 KB Output is correct
58 Correct 0 ms 348 KB Output is correct
59 Correct 0 ms 348 KB Output is correct
60 Correct 0 ms 348 KB Output is correct
61 Correct 500 ms 191844 KB Output is correct
62 Correct 1245 ms 384588 KB Output is correct
63 Correct 1225 ms 386296 KB Output is correct
64 Correct 1248 ms 386480 KB Output is correct
65 Correct 167 ms 157776 KB Output is correct
66 Correct 410 ms 262660 KB Output is correct
67 Correct 425 ms 281648 KB Output is correct
68 Correct 0 ms 348 KB Output is correct
69 Correct 1 ms 344 KB Output is correct
70 Correct 1 ms 348 KB Output is correct
71 Correct 1 ms 348 KB Output is correct
72 Correct 1 ms 348 KB Output is correct
73 Correct 885 ms 430360 KB Output is correct
74 Correct 894 ms 448524 KB Output is correct
75 Correct 1297 ms 494688 KB Output is correct
76 Correct 1334 ms 515336 KB Output is correct
77 Correct 1053 ms 545020 KB Output is correct
78 Correct 1538 ms 395144 KB Output is correct
79 Correct 1615 ms 408516 KB Output is correct
80 Correct 2694 ms 633880 KB Output is correct
81 Correct 1583 ms 411468 KB Output is correct
82 Correct 2081 ms 527500 KB Output is correct
83 Correct 2754 ms 660276 KB Output is correct
84 Correct 1436 ms 388560 KB Output is correct
85 Correct 2574 ms 638192 KB Output is correct
86 Correct 2537 ms 623328 KB Output is correct
87 Correct 599 ms 325488 KB Output is correct
88 Correct 1041 ms 544788 KB Output is correct
89 Correct 1050 ms 545228 KB Output is correct
90 Correct 1069 ms 542880 KB Output is correct