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Submission #1065552

# Submission time Handle Problem Language Result Execution time Memory
1065552 2024-08-19T09:11:35 Z anango Horses (IOI15_horses) C++17
100 / 100
 540 ms 65656 KB 
#include "horses.h"
#include <bits/stdc++.h>
#define int long long
using namespace std;

int MOD = 1000000007;
int INF = 1LL<<60;

//maintain a set of all indices such that X[i]>1
//consider the last 30 such indices
//then using a max segtree calculate the maximum Y[i] in between these indices, and thus compute the max X[i]*Y[i] at that index
//we can compute the prefix products of the X[i] using another segtree, which allows us to make point updates
//and range product queries

int exp(int base, int exponent) {
    int t = base;
    int p = 1;
    for (int i=0; i<32; i++) {
        if (exponent&(1LL<<i)) {
            p*=t; p%=MOD;
        }
        t*=t;
        t%=MOD;
    }
    return p;
}

int inv(int base) {
    return exp(base,MOD-2);
}

class productSegTree {
public:
    const int sz = 1048576;
    vector<int> tree;
    productSegTree() {
        tree=vector<int>(sz,1);
    }
    //each node carries the product of its children
    void update(int v, int l, int r, int tl, int tr, int assignment) {
        if (l>tr || r<tl) return;
        if (l<=tl && tr<=r) {
            tree[v]=assignment;
            tree[v]%=MOD;
            return;
        }
        int m = (tl+tr)/2;
        update(2*v,l,r,tl,m,assignment);
        update(2*v+1,l,r,m+1,tr,assignment);
        tree[v] = tree[2*v]*tree[2*v+1];
        tree[v]%=MOD;
    }
    int query(int v, int l, int r, int tl, int tr) {
        if (l>tr || r<tl) return 1;
        if (l<=tl && tr<=r) {
            return tree[v];
        }
        int m = (tl+tr)/2;
        int a = query(2*v,l,r,tl,m);
        int b = query(2*v+1,l,r,m+1,tr);
        return (a*b)%MOD;
    }

    void update_wrapper(int index, int mult) {
        update(1,index,index,0,sz/2-1,mult);
    }
    int query_wrapper(int index) {
        //0...index
        return query(1,0,index,0,sz/2-1);
    }
};

class maxSegTree {
public:
    const int sz = 1048576;
    vector<int> tree;
    maxSegTree() {
        tree=vector<int>(sz,0);
    }
    //each node carries the max of its children
    void update(int v, int l, int r, int tl, int tr, int assignment) {
        if (l>tr || r<tl) return;
        if (l<=tl && tr<=r) {
            tree[v]=assignment;
            return;
        }
        int m = (tl+tr)/2;
        update(2*v,l,r,tl,m,assignment);
        update(2*v+1,l,r,m+1,tr,assignment);
        tree[v] = max(tree[2*v],tree[2*v+1]);
    }
    int query(int v, int l, int r, int tl, int tr) {
        if (l>tr || r<tl) return -INF;
        if (l<=tl && tr<=r) {
            return tree[v];
        }
        int m = (tl+tr)/2;
        int a = query(2*v,l,r,tl,m);
        int b = query(2*v+1,l,r,m+1,tr);
        return max(a,b);
    }
    void update_wrapper(int index, int assignment) {
        update(1,index,index,0,sz/2-1,assignment);
    }
    int query_wrapper(int l, int r) {
        return query(1,l,r,0,sz/2-1);
    }
};

set<int> usefulX;
vector<int> xval,yval;
maxSegTree yseg;
productSegTree xseg;
int n;

signed get_answer() {
    vector<int> needcheck={0};
    auto it = usefulX.end();
    for (int i=0; i<32; i++) {
        if (it==usefulX.begin()) break;
        it--;
        int r = *it;
        needcheck.push_back(r);
    }
    needcheck.push_back(n);
    sort(needcheck.begin(), needcheck.end());
    int answer = -1;
    int suffprod = 1;
    int bestyval = 0;
    int bestsuffprod = 1;
    //want maximum value of maxyval / suffprod
    int k = needcheck.size();
    for (int i=k-2; i>=0; i--) {
        if (suffprod>1073741824) break;
        int maxyval = yseg.query_wrapper(needcheck[i],needcheck[i+1]-1);
        if (maxyval*bestsuffprod>bestyval*suffprod) {
            //cout << "changed " << i << " " << maxyval <<" " << bestsuffprod <<" " << bestyval <<" " << suffprod << endl;
            bestsuffprod = suffprod;
            bestyval = maxyval;
            answer = maxyval*xseg.query_wrapper(needcheck[i]); 
            answer%=MOD;
        }
        //cout << "trying " << i <<" " << needcheck[i] <<" " << needcheck[i+1] <<" " << maxyval <<" " << suffprod << " " << maxyval*xseg.query_wrapper(needcheck[i]) << endl;

        suffprod*=xval[needcheck[i]];
    }
    return (signed)answer;

}

signed init(signed N, signed X[], signed Y[]) {
    n=N;
    xval=yval=vector<int>(N,0);
    for (int i=0; i<N; i++) {
        xval[i] = X[i]; yval[i] = Y[i];
        if (xval[i]!=1) usefulX.insert(i);
    }
    for (int i=0; i<N; i++) {
        xseg.update_wrapper(i,X[i]);
        yseg.update_wrapper(i,Y[i]);
    }
	return get_answer();
}

signed updateX(signed pos, signed val) {
    if (val==1 && xval[pos]!=1) {
        usefulX.erase(pos);
    }
    if (val!=1 && xval[pos]==1) {
        usefulX.insert(pos);
    }
    xval[pos] = val;	
    xseg.update_wrapper(pos,val);
	return get_answer();
}

signed updateY(signed pos, signed val) {
    yval[pos] = val;
    yseg.update_wrapper(pos,val);
	return get_answer();
}

Subtask #1
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 16732 KB Output is correct
2 Correct 10 ms 16824 KB Output is correct
3 Correct 8 ms 16732 KB Output is correct
4 Correct 6 ms 16732 KB Output is correct
5 Correct 7 ms 16728 KB Output is correct
6 Correct 7 ms 16708 KB Output is correct
7 Correct 9 ms 16684 KB Output is correct
8 Correct 6 ms 16872 KB Output is correct
9 Correct 6 ms 16732 KB Output is correct
10 Correct 7 ms 16732 KB Output is correct
11 Correct 6 ms 16856 KB Output is correct
12 Correct 6 ms 16732 KB Output is correct
13 Correct 6 ms 16792 KB Output is correct
14 Correct 7 ms 16732 KB Output is correct
15 Correct 6 ms 16784 KB Output is correct
16 Correct 8 ms 16728 KB Output is correct
17 Correct 7 ms 16732 KB Output is correct
18 Correct 6 ms 16732 KB Output is correct
19 Correct 9 ms 16728 KB Output is correct
20 Correct 8 ms 16732 KB Output is correct

Subtask #2
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 8 ms 16728 KB Output is correct
2 Correct 7 ms 16732 KB Output is correct
3 Correct 6 ms 16732 KB Output is correct
4 Correct 6 ms 16728 KB Output is correct
5 Correct 7 ms 16824 KB Output is correct
6 Correct 7 ms 16732 KB Output is correct
7 Correct 7 ms 16776 KB Output is correct
8 Correct 6 ms 16728 KB Output is correct
9 Correct 7 ms 16732 KB Output is correct
10 Correct 6 ms 16732 KB Output is correct
11 Correct 8 ms 16732 KB Output is correct
12 Correct 7 ms 16876 KB Output is correct
13 Correct 6 ms 16732 KB Output is correct
14 Correct 8 ms 16732 KB Output is correct
15 Correct 7 ms 16732 KB Output is correct
16 Correct 7 ms 16708 KB Output is correct
17 Correct 7 ms 16728 KB Output is correct
18 Correct 7 ms 16732 KB Output is correct
19 Correct 7 ms 16732 KB Output is correct
20 Correct 7 ms 16712 KB Output is correct
21 Correct 7 ms 16732 KB Output is correct
22 Correct 7 ms 16868 KB Output is correct
23 Correct 8 ms 16732 KB Output is correct
24 Correct 10 ms 16732 KB Output is correct
25 Correct 9 ms 16732 KB Output is correct
26 Correct 9 ms 16936 KB Output is correct
27 Correct 10 ms 16888 KB Output is correct
28 Correct 10 ms 16884 KB Output is correct
29 Correct 7 ms 16732 KB Output is correct
30 Correct 8 ms 16960 KB Output is correct
31 Correct 9 ms 16732 KB Output is correct
32 Correct 10 ms 16728 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 537 ms 56656 KB Output is correct
2 Correct 400 ms 65620 KB Output is correct
3 Correct 427 ms 56656 KB Output is correct
4 Correct 414 ms 60496 KB Output is correct

Subtask #4
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 16732 KB Output is correct
2 Correct 6 ms 16732 KB Output is correct
3 Correct 9 ms 16632 KB Output is correct
4 Correct 6 ms 16732 KB Output is correct
5 Correct 7 ms 16732 KB Output is correct
6 Correct 6 ms 16984 KB Output is correct
7 Correct 6 ms 16732 KB Output is correct
8 Correct 7 ms 16732 KB Output is correct
9 Correct 6 ms 16668 KB Output is correct
10 Correct 6 ms 16732 KB Output is correct
11 Correct 6 ms 16732 KB Output is correct
12 Correct 6 ms 16796 KB Output is correct
13 Correct 6 ms 16776 KB Output is correct
14 Correct 9 ms 16732 KB Output is correct
15 Correct 6 ms 16728 KB Output is correct
16 Correct 6 ms 16984 KB Output is correct
17 Correct 8 ms 16732 KB Output is correct
18 Correct 6 ms 16732 KB Output is correct
19 Correct 6 ms 16732 KB Output is correct
20 Correct 6 ms 16732 KB Output is correct
21 Correct 6 ms 16732 KB Output is correct
22 Correct 6 ms 16732 KB Output is correct
23 Correct 13 ms 16788 KB Output is correct
24 Correct 8 ms 16732 KB Output is correct
25 Correct 8 ms 16732 KB Output is correct
26 Correct 8 ms 16732 KB Output is correct
27 Correct 10 ms 16732 KB Output is correct
28 Correct 9 ms 16944 KB Output is correct
29 Correct 7 ms 16732 KB Output is correct
30 Correct 8 ms 16732 KB Output is correct
31 Correct 8 ms 16828 KB Output is correct
32 Correct 10 ms 16732 KB Output is correct
33 Correct 175 ms 32540 KB Output is correct
34 Correct 164 ms 32592 KB Output is correct
35 Correct 282 ms 62956 KB Output is correct
36 Correct 292 ms 62804 KB Output is correct
37 Correct 184 ms 30704 KB Output is correct
38 Correct 219 ms 43604 KB Output is correct
39 Correct 168 ms 30660 KB Output is correct
40 Correct 292 ms 57932 KB Output is correct
41 Correct 170 ms 30552 KB Output is correct
42 Correct 209 ms 30692 KB Output is correct
43 Correct 306 ms 58708 KB Output is correct
44 Correct 284 ms 58464 KB Output is correct

Subtask #5
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 7 ms 16728 KB Output is correct
2 Correct 8 ms 16732 KB Output is correct
3 Correct 8 ms 16884 KB Output is correct
4 Correct 6 ms 16732 KB Output is correct
5 Correct 7 ms 16668 KB Output is correct
6 Correct 7 ms 16732 KB Output is correct
7 Correct 7 ms 16732 KB Output is correct
8 Correct 7 ms 16728 KB Output is correct
9 Correct 7 ms 16660 KB Output is correct
10 Correct 6 ms 16872 KB Output is correct
11 Correct 6 ms 16732 KB Output is correct
12 Correct 6 ms 16732 KB Output is correct
13 Correct 6 ms 16844 KB Output is correct
14 Correct 7 ms 16732 KB Output is correct
15 Correct 6 ms 16676 KB Output is correct
16 Correct 6 ms 16768 KB Output is correct
17 Correct 6 ms 16644 KB Output is correct
18 Correct 6 ms 16656 KB Output is correct
19 Correct 8 ms 16732 KB Output is correct
20 Correct 6 ms 16844 KB Output is correct
21 Correct 6 ms 16732 KB Output is correct
22 Correct 7 ms 16732 KB Output is correct
23 Correct 8 ms 16732 KB Output is correct
24 Correct 8 ms 16732 KB Output is correct
25 Correct 8 ms 16772 KB Output is correct
26 Correct 8 ms 16732 KB Output is correct
27 Correct 10 ms 16728 KB Output is correct
28 Correct 10 ms 16732 KB Output is correct
29 Correct 8 ms 16676 KB Output is correct
30 Correct 9 ms 16732 KB Output is correct
31 Correct 9 ms 16732 KB Output is correct
32 Correct 10 ms 16732 KB Output is correct
33 Correct 540 ms 56816 KB Output is correct
34 Correct 437 ms 65656 KB Output is correct
35 Correct 386 ms 56912 KB Output is correct
36 Correct 458 ms 60500 KB Output is correct
37 Correct 166 ms 32668 KB Output is correct
38 Correct 165 ms 32540 KB Output is correct
39 Correct 284 ms 63056 KB Output is correct
40 Correct 278 ms 63000 KB Output is correct
41 Correct 180 ms 30776 KB Output is correct
42 Correct 213 ms 43556 KB Output is correct
43 Correct 151 ms 30672 KB Output is correct
44 Correct 264 ms 57896 KB Output is correct
45 Correct 164 ms 30544 KB Output is correct
46 Correct 177 ms 30584 KB Output is correct
47 Correct 289 ms 58468 KB Output is correct
48 Correct 275 ms 58444 KB Output is correct
49 Correct 301 ms 35664 KB Output is correct
50 Correct 273 ms 35664 KB Output is correct
51 Correct 455 ms 64852 KB Output is correct
52 Correct 397 ms 64352 KB Output is correct
53 Correct 513 ms 33872 KB Output is correct
54 Correct 368 ms 47404 KB Output is correct
55 Correct 245 ms 31536 KB Output is correct
56 Correct 407 ms 59732 KB Output is correct
57 Correct 366 ms 32364 KB Output is correct
58 Correct 408 ms 32852 KB Output is correct
59 Correct 260 ms 58452 KB Output is correct