oj.uz

Submission #244802

# Submission time Handle Problem Language Result Execution time Memory
244802 2020-07-05T05:12:27 Z kshitij_sodani K blocks (IZhO14_blocks) C++17
100 / 100
 256 ms 4628 KB 
/*
let dp[i][j] denote minimum answer for splitting first i in j segments
naive dp is n^2*k
we can optimize using  observations

let x be max index element with a_x>a_i(classical problem in o(N) using stacks)

notice answer is min(dp[x][j],min(dp[x][j-1],dp[x+1][j-1],,,,,,,,(dp[i-1][j-1]))+a_i)
observe that x to (i-1) segments intersect only at endpoints
can be done using stack
amortized O(nk)


note nk*log(n) wit segment tree gets TLE
I first tried that

*/
#include <bits/stdc++.h>
using namespace std;
typedef int64_t llo;
#define mp make_pair
#define pb push_back
#define a first 
#define b second
//#define endl '\n'

int n,k;

int dp[100001];
int dp2[100001];

int it[100001];
int tree[400001];
int pre[100001];
/*void build(int no,int l,int r){
	if(l==r){
		tree[no]=dp[l];
	}
	else{
		int mid=(l+r)/2;
		build(no*2+1,l,mid);
		build(no*2+2,mid+1,r);
		tree[no]=min(tree[no*2+1],tree[no*2+2]);
	}
}
int query(int no,int l,int r,int aa,int bb){
	if(r<aa or l>bb){
		return 1e9;
	}
	if(aa<=l and r<=bb){
		return tree[no];
	}
	else{
		int mid=(l+r)/2;
		return min(query(no*2+1,l,mid,aa,bb),query(no*2+2,mid+1,r,aa,bb));
	}
}*/
int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	cin>>n>>k;
	vector<pair<int,int>> ac;
	for(int i=0;i<n;i++){
		cin>>it[i];

		while(ac.size()){
			if(ac.back().a<=it[i]){
				ac.pop_back();
			}
			else{
				break;
			}
		}
		if(ac.size()==0){
			pre[i]=-1;
		}
		else{
			pre[i]=ac.back().b;
			
		}
		ac.pb({it[i],i});
	/*	for(int kk=pre[i]+1;kk<i;kk++){
			if(it[kk]>it[i]){
				while(true){
					continue;
				}
			}
		}*/

	//	cout<<pre[i]<<",";
	}
	//cout<<endl;


	int ma=0;
	for(int i=0;i<n;i++){
		ma=max(ma,it[i]);
		dp[i]=ma;
		dp2[i]=1e9;
	}


	for(int i=1;i<k;i++){
		//build(0,0,n-1);
		vector<pair<pair<int,int>,int>> cur;
		int mo=1e9;
		for(int j=i;j<n;j++){
			
			mo=min(mo,dp[j-1]);
			if(pre[j]>=i){
				dp2[j]=dp2[pre[j]];
			}
			cur.pb({{j-1,j-1},dp[j-1]});
		//	cout<<j<<endl;
			if(pre[j]==-1){
				dp2[j]=min(dp2[j],mo+it[j]);
			}
			else{
				pair<pair<int,int>,int> mi={{-1,-1},1e9};
				int mk=1e9;
				while(cur.size()){
					if(cur.back().a.a>=pre[j]){
						if(mi.a.a==-1){
							mi=cur.back();
						}
						else{
							mi.a.a=min(mi.a.a,cur.back().a.a);
							mi.a.b=max(mi.a.b,cur.back().a.b);
							mi.b=min(mi.b,cur.back().b);
						}
						mk=mi.b;
						cur.pop_back();
				//		cout<<mi.a.a<<","<<mi.a.b<<","<<mi.b<<endl;
					}
					else{
						if(mi.a.a-pre[j]>1){
							while(true){
								continue;
							}
						}
						for(int kk=pre[j];kk<mi.a.a;kk++){
							mk=min(mk,dp[kk]);
						}
						break;
					}
				}
				cur.pb(mi);

				dp2[j]=min(dp2[j],mk+it[j]);
			}
		}
		for(int j=0;j<n;j++){
			dp[j]=dp2[j];
			dp2[j]=1e9;
		}
	}

	cout<<dp[n-1]<<endl;






	return 0;
}

Subtask #1
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 5 ms 384 KB Output is correct
3 Correct 4 ms 384 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 4 ms 384 KB Output is correct
9 Correct 4 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 4 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 4 ms 384 KB Output is correct
14 Correct 4 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 512 KB Output is correct
18 Correct 5 ms 384 KB Output is correct

Subtask #2
18.0 / 18.0

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

Subtask #3
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB Output is correct
2 Correct 4 ms 384 KB Output is correct
3 Correct 5 ms 512 KB Output is correct
4 Correct 4 ms 384 KB Output is correct
5 Correct 5 ms 384 KB Output is correct
6 Correct 5 ms 384 KB Output is correct
7 Correct 5 ms 384 KB Output is correct
8 Correct 4 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 4 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 5 ms 384 KB Output is correct
15 Correct 5 ms 384 KB Output is correct
16 Correct 5 ms 384 KB Output is correct
17 Correct 5 ms 384 KB Output is correct
18 Correct 5 ms 384 KB Output is correct
19 Correct 5 ms 384 KB Output is correct

Subtask #4
47.0 / 47.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 768 KB Output is correct
2 Correct 11 ms 1152 KB Output is correct
3 Correct 18 ms 2340 KB Output is correct
4 Correct 91 ms 2464 KB Output is correct
5 Correct 256 ms 4628 KB Output is correct
6 Correct 23 ms 4444 KB Output is correct
7 Correct 144 ms 4440 KB Output is correct
8 Correct 5 ms 384 KB Output is correct
9 Correct 5 ms 384 KB Output is correct
10 Correct 5 ms 384 KB Output is correct
11 Correct 5 ms 384 KB Output is correct
12 Correct 5 ms 384 KB Output is correct
13 Correct 5 ms 384 KB Output is correct
14 Correct 29 ms 632 KB Output is correct
15 Correct 6 ms 512 KB Output is correct
16 Correct 11 ms 512 KB Output is correct
17 Correct 13 ms 1024 KB Output is correct
18 Correct 16 ms 1024 KB Output is correct
19 Correct 84 ms 1024 KB Output is correct
20 Correct 237 ms 1920 KB Output is correct
21 Correct 23 ms 1920 KB Output is correct
22 Correct 115 ms 1920 KB Output is correct
23 Correct 19 ms 1920 KB Output is correct
24 Correct 38 ms 1920 KB Output is correct
25 Correct 233 ms 2040 KB Output is correct
26 Correct 5 ms 384 KB Output is correct
27 Correct 5 ms 384 KB Output is correct
28 Correct 26 ms 640 KB Output is correct
29 Correct 6 ms 640 KB Output is correct
30 Correct 11 ms 640 KB Output is correct
31 Correct 11 ms 1280 KB Output is correct
32 Correct 17 ms 1652 KB Output is correct
33 Correct 81 ms 1652 KB Output is correct
34 Correct 251 ms 3552 KB Output is correct
35 Correct 24 ms 3420 KB Output is correct
36 Correct 124 ms 3416 KB Output is correct
37 Correct 6 ms 768 KB Output is correct
38 Correct 23 ms 704 KB Output is correct
39 Correct 5 ms 384 KB Output is correct
40 Correct 5 ms 384 KB Output is correct
41 Correct 5 ms 384 KB Output is correct
42 Correct 5 ms 384 KB Output is correct