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Submission #308776

# Submission time Handle Problem Language Result Execution time Memory
308776 2020-10-01T23:01:15 Z exopeng Global Warming (CEOI18_glo) C++14
100 / 100
 754 ms 32316 KB 
#include <bits/stdc++.h>
using namespace std;
#define mp make_pair
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define f first
#define s second
#define pii pair<int,int>
#define is insert
const int INF = 2e9;
const int MOD = 1e9 + 7;
const int MAXN = 2e5 + 1;
//store test cases here
/*


*/
int n,x;
vector<int> a;
vector<int> d;
vector<int> r;

int f[MAXN];
int b[MAXN];

int l[MAXN];

vector<pii> sor;

int t[4*MAXN];

void build(int curr, int left, int right) {
	if (left == right ) {
		t[curr] = 0;
	} else {
		int mid = (right + left) / 2;
		//an edge's two children are the indices 2i && 2i+1
		//in this sum segtree, an edge's value is the values from it's left to right indices
		build(curr * 2, left, mid);
		build(curr*2 + 1, mid + 1, right);
		t[curr] = max(t[curr*2],t[curr*2+1]);
	}
	//cout << "tl: " << left << " tr: " << right << " val: " << t[curr] << "\n";

}

//tl-tr is the current segment, and l-r is the desired segment
int sum(int curr, int tl, int tr, int left, int right) {
	if (left > right) {
		return 0;
	}
	if (left == tl && right == tr) {
		return t[curr];
	}

	int mid = (tl + tr) / 2;
	//taking min of r and mid, because mid might be greater than r, same for max
	return max(sum(curr*2, tl, mid, left, min(right,mid)), sum(curr*2+1, mid +1, tr, max(left,mid+1), right));
}

void update(int curr, int tl, int tr, int pos, int val) {
	if (tl == tr) {
		t[curr] = val;
	} else {
		int mid = (tl+tr) / 2;
		//see which segment the index falls in, and change it
		if (pos <= mid) {
			update(curr*2, tl, mid, pos, val);
		} else {
			update(curr*2+1, mid+1, tr, pos, val);
		}
		//update the curr segmment to the new val once everything below it has been updated properly
		t[curr] = max(t[curr*2],t[curr*2+1]);
	}
	//cout << "tl: " << tl << " tr: " << tr << " val: " << t[curr] << "\n";
}

int bsearch(int a) {
	int lo = 0;
	int hi = n-1;
	while (lo != hi) {
		int mid = (lo+hi)/2;
		if (r[mid] < a) {
			hi = mid;
		} else {
			lo = mid+1;
		}
		//cout << lo << "\n";
	} 
	return lo;
}

int main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> x;
    for (int i = 0; i < n; i++) {
    	int m;
    	cin >> m;
    	a.pb(m);
    	sor.pb(mp(m,i));
    	d.pb(INF);
     	r.pb(-1*INF);
    }
    d.pb(INF);
    d[0] = -1*INF;
    r.pb(-1*INF);
    r[0] = INF;
    for (int i = 0; i < n; i++) {
    	int ind = lower_bound(d.begin(),d.end(),a[i]+1) - d.begin();
    	if (d[ind-1] < a[i] && a[i] < d[ind]) {
            d[ind] = a[i];
            f[i] = ind;
    	} else {
    		f[i] = 1;
    	}
    	//cout << "i: " << i << " val: " << f[i] << "\n";
    }
    
    for (int i = n-1; i > -1; i--) {
    	int ind = bsearch(a[i]-1);
    	if (r[ind] < a[i] && a[i] <= r[ind-1]) {
            r[ind] = a[i]-1;
            b[i] = ind;
    	} else {
    		b[i] = 1;
    	}
    	//cout << "i: " << i << " val: " << b[i] << "\n";
    }
	
    int ans = 0;
    for (int i = 0; i <= n; i++) {
    	if (d[i] < INF) {
    		ans = i;
    	}
    }    
   	//empty segtree with size n, point update each time, query minimum in a range
   	//find first index that is geq and last index that is leq
   	//put elements in set afterwards, and map each element to an index in sorted segtree
   	map< pii, int> p;
   	sort(sor.begin(), sor.end());
   	for (int i = 0; i < n; i++) {
   		p.insert(mp(sor[i],i));
   		//cout << "(" << sor[i].first << "," << sor[i].second << ") i: " << i << "\n";
   	}
   	
   	build(1,0,n-1);
		
   	set<pii> taken;
   	//insert beg
   	taken.insert(mp(INF, n));
   	taken.insert(mp(-1*INF, -1*INF));
   	taken.insert(mp(a[0], p[mp(a[0],0)]));
   	update(1,0,n-1,p[mp(a[0],0)],f[0]);
   	//cout << sum(1,0,n-1,5,6) << "\n";
   	
    for (int i = 1; i < n; i++) {
    	int lo = taken.lower_bound(mp(a[i],0))->second;
    	int hi = taken.lower_bound(mp(a[i]+x,0))->second;
    	//cout << "i:" << i << " a[i]:" << a[i] << " lo:" << lo << " hi:" << hi << " sum: " << sum(1,0,n-1,lo,hi-1) << "\n";
    	ans = max(ans,sum(1,0,n-1,lo,hi-1) + b[i]);
    	taken.insert(mp(a[i], p[mp(a[i],i)]));
    	update(1,0,n-1,p[mp(a[i],i)],f[i]);
    	//cout << "ind: " << p[mp(a[i],i)] << " f[i] " << f[i] << "\n";
    }
	
    cout << ans << "\n";


}
/* REMINDERS
 * CHECK ARRAY BOUNDS, HOW BIG ARRAY HAS TO BE
 * PLANNING!!!!!!!! Concrete plan before code
 * IF CAN'T FIGURE ANYTHING OUT, MAKE TEN TEST CASES TO EVALUATE ALL TYPES OF SCENARIOS, THEN CONSTRUCT SOLUTION TO FIT IT
 * IF CAN'T FIGURE ANYTHING OUT, MAKE TEN TEST CASES TO EVALUATE ALL TYPES OF SCENARIOS, THEN CONSTRUCT SOLUTION TO FIT IT
 * IF CAN'T FIGURE ANYTHING OUT, MAKE TEN TEST CASES TO EVALUATE ALL TYPES OF SCENARIOS, THEN CONSTRUCT SOLUTION TO FIT IT
 * NAIVE SOL FIRST TO CHECK AGAINST OPTIMIZED SOL
 * MOD OUT EVERY STEP
 * DON'T MAKE ASSUMPTIONS
 * DON'T OVERCOMPLICATE
 * CHECK INT VS LONG, IF YOU NEED TO STORE LARGE NUMBERS
 * CHECK CONSTRAINTS, C <= N <= F...
 * CHECK SPECIAL CASES, N = 1...
 * TO TEST TLE/MLE, PLUG IN MAX VALS ALLOWED AND SEE WHAT HAPPENS
 * ALSO CALCULATE BIG-O, OVERALL TIME COMPLEXITY
 * IF ALL ELSE FAILS, DO CASEWORK
 * compile with "g++ -std=c++11 filename.cpp" if using auto keyword
 */

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct

Subtask #2
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct
12 Correct 1 ms 384 KB Output is correct
13 Correct 0 ms 384 KB Output is correct
14 Correct 1 ms 384 KB Output is correct
15 Correct 1 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct

Subtask #3
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct
12 Correct 1 ms 384 KB Output is correct
13 Correct 0 ms 384 KB Output is correct
14 Correct 1 ms 384 KB Output is correct
15 Correct 1 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct
19 Correct 3 ms 544 KB Output is correct
20 Correct 2 ms 512 KB Output is correct
21 Correct 2 ms 512 KB Output is correct
22 Correct 2 ms 512 KB Output is correct
23 Correct 2 ms 512 KB Output is correct
24 Correct 1 ms 512 KB Output is correct
25 Correct 1 ms 512 KB Output is correct
26 Correct 1 ms 512 KB Output is correct

Subtask #4
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 671 ms 32112 KB Output is correct
2 Correct 657 ms 32060 KB Output is correct
3 Correct 666 ms 32060 KB Output is correct
4 Correct 664 ms 31932 KB Output is correct
5 Correct 333 ms 31164 KB Output is correct

Subtask #5
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 106 ms 8288 KB Output is correct
2 Correct 119 ms 8380 KB Output is correct
3 Correct 116 ms 8272 KB Output is correct
4 Correct 75 ms 8012 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 69 ms 8136 KB Output is correct
7 Correct 87 ms 8272 KB Output is correct

Subtask #6
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 286 ms 16068 KB Output is correct
2 Correct 287 ms 16200 KB Output is correct
3 Correct 731 ms 32316 KB Output is correct
4 Correct 350 ms 31300 KB Output is correct
5 Correct 146 ms 15816 KB Output is correct
6 Correct 297 ms 29884 KB Output is correct
7 Correct 285 ms 30644 KB Output is correct
8 Correct 193 ms 16072 KB Output is correct

Subtask #7
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 384 KB Output is correct
2 Correct 1 ms 384 KB Output is correct
3 Correct 0 ms 384 KB Output is correct
4 Correct 0 ms 384 KB Output is correct
5 Correct 1 ms 384 KB Output is correct
6 Correct 1 ms 384 KB Output is correct
7 Correct 0 ms 384 KB Output is correct
8 Correct 0 ms 384 KB Output is correct
9 Correct 1 ms 384 KB Output is correct
10 Correct 0 ms 384 KB Output is correct
11 Correct 1 ms 384 KB Output is correct
12 Correct 1 ms 384 KB Output is correct
13 Correct 0 ms 384 KB Output is correct
14 Correct 1 ms 384 KB Output is correct
15 Correct 1 ms 384 KB Output is correct
16 Correct 1 ms 384 KB Output is correct
17 Correct 1 ms 384 KB Output is correct
18 Correct 1 ms 384 KB Output is correct
19 Correct 3 ms 544 KB Output is correct
20 Correct 2 ms 512 KB Output is correct
21 Correct 2 ms 512 KB Output is correct
22 Correct 2 ms 512 KB Output is correct
23 Correct 2 ms 512 KB Output is correct
24 Correct 1 ms 512 KB Output is correct
25 Correct 1 ms 512 KB Output is correct
26 Correct 1 ms 512 KB Output is correct
27 Correct 671 ms 32112 KB Output is correct
28 Correct 657 ms 32060 KB Output is correct
29 Correct 666 ms 32060 KB Output is correct
30 Correct 664 ms 31932 KB Output is correct
31 Correct 333 ms 31164 KB Output is correct
32 Correct 106 ms 8288 KB Output is correct
33 Correct 119 ms 8380 KB Output is correct
34 Correct 116 ms 8272 KB Output is correct
35 Correct 75 ms 8012 KB Output is correct
36 Correct 1 ms 384 KB Output is correct
37 Correct 69 ms 8136 KB Output is correct
38 Correct 87 ms 8272 KB Output is correct
39 Correct 286 ms 16068 KB Output is correct
40 Correct 287 ms 16200 KB Output is correct
41 Correct 731 ms 32316 KB Output is correct
42 Correct 350 ms 31300 KB Output is correct
43 Correct 146 ms 15816 KB Output is correct
44 Correct 297 ms 29884 KB Output is correct
45 Correct 285 ms 30644 KB Output is correct
46 Correct 193 ms 16072 KB Output is correct
47 Correct 278 ms 16072 KB Output is correct
48 Correct 270 ms 16072 KB Output is correct
49 Correct 754 ms 32196 KB Output is correct
50 Correct 341 ms 31168 KB Output is correct
51 Correct 223 ms 24296 KB Output is correct
52 Correct 324 ms 31284 KB Output is correct
53 Correct 305 ms 31296 KB Output is correct
54 Correct 300 ms 32132 KB Output is correct
55 Correct 472 ms 32060 KB Output is correct