oj.uz

Submission #634756

# Submission time Handle Problem Language Result Execution time Memory
634756 2022-08-24T20:29:51 Z rainliofficial Triple Jump (JOI19_jumps) C++17
100 / 100
 1049 ms 61784 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
#define sz(x) (int)x.size()

/* 
Date: 2022/08/24 15:14
Problem Link: https://oj.uz/problem/view/JOI19_jumps
Topic(s):
Time Spent:
Solution Notes:
Consider pairs of possible (a, b), and let them be at indices (i, j). We observe that in range [i, j], a and b must
be the two largest element, and everything in between is smaller. 
Therefore, we can fix whichever one of a or b that's smaller, and then find the other endpoint in O(N) time in total
by using a monotone stack. 
One we have all (a, b), it is a matter of determining c. We can naively use a segment tree to query every c (subtask 2),
or use a suffix max (subtask 3). 
To get the full solution, let's store the value of a + b at the least location of c that it corresponds to. Each node in 
segment tree would essientially store the following values:
1. max a+b
2. max c
3. max a+b+c 
*/

void __print(int x) {cerr << x;}
void __print(long x) {cerr << x;}
void __print(long long x) {cerr << x;}
void __print(unsigned x) {cerr << x;}
void __print(unsigned long x) {cerr << x;}
void __print(unsigned long long x) {cerr << x;}
void __print(float x) {cerr << x;}
void __print(double x) {cerr << x;}
void __print(long double x) {cerr << x;}
void __print(char x) {cerr << '\'' << x << '\'';}
void __print(const char *x) {cerr << '\"' << x << '\"';}
void __print(const string &x) {cerr << '\"' << x << '\"';}
void __print(bool x) {cerr << (x ? "true" : "false");}

template<typename T, typename V>
void __print(const pair<T, V> &x);
template<typename T>
void __print(const T &x) {int f = 0; cerr << '{'; for (auto &i: x) cerr << (f++ ? ", " : ""), __print(i); cerr << "}";}
template<typename T, typename V>
void __print(const pair<T, V> &x) {cerr << '{'; __print(x.first); cerr << ", "; __print(x.second); cerr << '}';}
void _print() {cerr << "]\n";}
template <typename T, typename... V>
void _print(T t, V... v) {__print(t); if (sizeof...(v)) cerr << ", "; _print(v...);}
#ifdef DEBUG
#define dbg(x...) cerr << "\e[91m"<<__func__<<":"<<__LINE__<<" [" << #x << "] = ["; _print(x); cerr << "\e[39m" << endl;
#else
#define dbg(x...)
#endif

const int MAXN = 2e5+5, INF = 1e9;
int n, q;

struct Node{
    int ab, c, abc;
};

struct segtree{
    const int PO2 = 131072; // least power of 2 greater than MAXN; 
    int n;
    Node identity = {-INF, -INF, -INF};
    vector<Node> seg;
    vector<int> arr;
    void init(int n){
        this->n = n;
        seg.resize(4*n, identity); // change to 4*N if we want to reinitialize the segtree multiple times on difference values of N
    }
    ll query(int a, int b){
        if (a > b){
            return -INF;
        }
        return query(0, 0, n-1, a, b).abc;
    }
    Node query(int node, int l, int r, int a, int b) { // inclusive 0-indexed
		if (a <= l && r <= b) {
			return seg[node];
		}
		Node ans = identity;
		int mid = (l + r) / 2;
		if (a <= mid) {
			ans = combine(ans, query(node * 2 + 1, l, mid, a, b));
		}
        if (b > mid){
			ans = combine(ans, query(node * 2 + 2, mid + 1, r, a, b));
		}
		return ans;
	}
    void update(int a, int x, bool updC) { // inclusive 0-indexed
    if (a >= n){
        return;
    }
		update(0, 0, n-1, a, x, updC);
	}
    void update(int node, int l, int r, int a, int x, bool updC) {
		if (l == r) { 
            if (updC){
                ckmax(seg[node].c, x);
            }else{
                ckmax(seg[node].ab, x);
            }
			seg[node].abc = seg[node].ab + seg[node].c;
			return;
		}
		int mid = (l + r) / 2;
		if (a <= mid) {
			update(node * 2 + 1, l, mid, a, x, updC);
		}else{
			update(node * 2 + 2, mid + 1, r, a, x, updC);
		}
		seg[node] = combine(seg[node * 2 + 1], seg[node * 2 + 2]);
	}
    Node combine(Node a, Node b){
        return {max(a.ab, b.ab), max(a.c, b.c), max({a.abc, b.abc, a.ab + b.c})};
    }
};

int main(){
    cin.tie(0); ios_base::sync_with_stdio(0);
    // freopen("file.in", "r", stdin);
    // freopen("file.out", "w", stdout);
    cin >> n;
    vector<int> arr(n);
    for (int i=0; i<n; i++){
        cin >> arr[i];
    }
    // use monotonic stack to process the possible (a, b). 
    // assume a > b
    vector<pii> ab;
    stack<pii> st;
    for (int i=n-1; i>=0; i--){
        while (!st.empty() && st.top().first < arr[i]){
            st.pop();
        }
        if (!st.empty()){
            ab.push_back({i, st.top().second});
        }
        st.push({arr[i], i});
    }
    stack<pii> st2;
    swap(st2, st);
    for (int i=0; i<n; i++){
        while (!st.empty() && st.top().first < arr[i]){
            st.pop();
        }
        if (!st.empty()){
            ab.push_back({st.top().second, i});
        }
        st.push({arr[i], i});
    }
    dbg(ab)
    segtree seg;
    seg.init(n);
    sort(ab.begin(), ab.end(), greater<pii>());
    int pt = 0;
    vector<array<int, 3>> queries;
    cin >> q;
    for (int i=0; i<q; i++){
        int l, r;
        cin >> l >> r;
        l--; r--;
        queries.push_back({l, r, i});
    }
    sort(queries.begin(), queries.end(), [](const array<int, 3> a1, const array<int, 3> a2){
        return make_pair(a1[0], a1[1]) > make_pair(a2[0], a2[1]);
    });
    for (int i=0; i<n; i++){
        seg.update(i, arr[i], true);
    }
    vector<int> ans(q);
    for (int i=0; i<q; i++){
        while (pt < sz(ab) && ab[pt].first >= queries[i][0]){
            seg.update(ab[pt].second + (ab[pt].second - ab[pt].first), arr[ab[pt].first] + arr[ab[pt].second], false);
            pt++;
        }
        ans[queries[i][2]] = seg.query(queries[i][0], queries[i][1]);
    }
    for (int i : ans){
        cout << i << "\n";
    }
}

/**
 * Debugging checklist:
 * - Reset everything after each TC
 * - Integer overflow, index overflow
 * - Special cases?
 */

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 224 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 224 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 389 ms 18328 KB Output is correct
12 Correct 328 ms 18100 KB Output is correct
13 Correct 325 ms 18208 KB Output is correct
14 Correct 337 ms 18336 KB Output is correct
15 Correct 327 ms 18356 KB Output is correct
16 Correct 327 ms 17668 KB Output is correct
17 Correct 323 ms 17816 KB Output is correct
18 Correct 329 ms 17544 KB Output is correct
19 Correct 333 ms 18196 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 165 ms 13760 KB Output is correct
2 Correct 106 ms 13636 KB Output is correct
3 Correct 104 ms 13840 KB Output is correct
4 Correct 172 ms 13648 KB Output is correct
5 Correct 199 ms 13768 KB Output is correct
6 Correct 165 ms 13764 KB Output is correct
7 Correct 165 ms 13764 KB Output is correct
8 Correct 164 ms 13764 KB Output is correct
9 Correct 186 ms 13760 KB Output is correct

Subtask #4
54.0 / 54.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 224 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 0 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 1 ms 212 KB Output is correct
10 Correct 1 ms 212 KB Output is correct
11 Correct 389 ms 18328 KB Output is correct
12 Correct 328 ms 18100 KB Output is correct
13 Correct 325 ms 18208 KB Output is correct
14 Correct 337 ms 18336 KB Output is correct
15 Correct 327 ms 18356 KB Output is correct
16 Correct 327 ms 17668 KB Output is correct
17 Correct 323 ms 17816 KB Output is correct
18 Correct 329 ms 17544 KB Output is correct
19 Correct 333 ms 18196 KB Output is correct
20 Correct 165 ms 13760 KB Output is correct
21 Correct 106 ms 13636 KB Output is correct
22 Correct 104 ms 13840 KB Output is correct
23 Correct 172 ms 13648 KB Output is correct
24 Correct 199 ms 13768 KB Output is correct
25 Correct 165 ms 13764 KB Output is correct
26 Correct 165 ms 13764 KB Output is correct
27 Correct 164 ms 13764 KB Output is correct
28 Correct 186 ms 13760 KB Output is correct
29 Correct 1049 ms 61608 KB Output is correct
30 Correct 821 ms 58588 KB Output is correct
31 Correct 755 ms 58596 KB Output is correct
32 Correct 986 ms 61528 KB Output is correct
33 Correct 938 ms 61604 KB Output is correct
34 Correct 920 ms 59424 KB Output is correct
35 Correct 911 ms 58940 KB Output is correct
36 Correct 932 ms 58984 KB Output is correct
37 Correct 935 ms 60480 KB Output is correct
38 Correct 800 ms 61680 KB Output is correct
39 Correct 812 ms 61612 KB Output is correct
40 Correct 782 ms 58204 KB Output is correct
41 Correct 796 ms 57796 KB Output is correct
42 Correct 773 ms 57784 KB Output is correct
43 Correct 783 ms 59608 KB Output is correct
44 Correct 815 ms 61624 KB Output is correct
45 Correct 813 ms 61636 KB Output is correct
46 Correct 802 ms 58544 KB Output is correct
47 Correct 803 ms 58040 KB Output is correct
48 Correct 792 ms 58080 KB Output is correct
49 Correct 820 ms 60056 KB Output is correct
50 Correct 841 ms 61616 KB Output is correct
51 Correct 845 ms 61784 KB Output is correct
52 Correct 878 ms 59264 KB Output is correct
53 Correct 829 ms 59004 KB Output is correct
54 Correct 839 ms 58872 KB Output is correct
55 Correct 830 ms 60612 KB Output is correct