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Submission #332945

# Submission time Handle Problem Language Result Execution time Memory
332945 2020-12-04T03:41:32 Z KWang31 Split the sequence (APIO14_sequence) Java 11
71 / 100
 708 ms 131072 KB 
//Convex Hull Trick, verified on CF319C (319 is ID)
import java.io.*; import java.util.*;
public class sequence{
  static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        
    } 
    
    static ArrayList<Integer> M=new ArrayList<>();
    static long[] B;
    static ArrayList<Integer> ind=new ArrayList<>();
    static int pointer=0;
    static short[][] ch; static boolean[][] b1; static boolean[][] b2;
    static int N;
    public static void main(String[] args){
        
        FastReader br=new FastReader();
        N=br.nextInt(); int K=br.nextInt();
        int[] s=new int[N]; 
        long[] dp=new long[N];
        long[] dp2=new long[N];
        ch=new short[N][K]; b1=new boolean[N][K];b2=new boolean[N][K];
        s[0]=br.nextInt(); for(int i=1;i<N;i++){s[i]=s[i-1]+br.nextInt(); }
        //System.out.println(Arrays.toString(s));
        for (int i = 0; i < K; i++) {
            M=new ArrayList<>();
            B=new long[N];
            ind=new ArrayList<>();
            add(s[0],-(long)s[0]*s[0],i);
            for (int j = 1; j < N; j++) {
                dp2[j]=query((long)s[j],N*i+j);
                add(s[j], dp[j]-(long)s[j]*s[j],Math.max(j,i));
                //System.out.println(M);
                //System.out.println(B);
            }
            
            for (int j = 0; j < N; j++) {
                dp[j]=dp2[j];
            }
            //System.out.println(Arrays.toString(dp));
        }
        //System.out.println(Arrays.toString(dp));
        System.out.println(dp[N-1]);
        StringBuilder sb=new StringBuilder();
        ArrayList<Integer> arl=new ArrayList<>();
        int cur=N-1;
        for (int i = K-1; i >=0; i--) {
            
            if(b1[cur][i] && b2[cur][i])cur=(int) 4*ch[cur][i]+3;
            else if(b1[cur][i]) cur=(int) 4*ch[cur][i]+1;
            else if(b2[cur][i]) cur=(int) 4*ch[cur][i]+2;
            else cur=(int) 4*ch[cur][i];
            arl.add(cur); 
        }
        //StringBuilder is actually quite memory consuming
        for (int i = K-1; i >=0; i--) {
            sb.append((arl.get(i)+1)+" ");
        }
        System.out.println(sb.toString());
    }
    public static boolean bad(int l1, int l2, int l3){//Using doubles to prevent overflow
        return (M.get(l1)-M.get(l3))*((double)B[l2]-B[l1])>=(M.get(l1)-M.get(l2))*((double)B[l3]-B[l1]);
        //Intersection of l1 and l3 must be ABOVE l2
        //For l2 to be added
        //l1.m>l2.m>l3.m, as sum is strictly increasing
    }
    public static void add(int m, long b, int i){
        M.add(m); B[ind.size()]=b; ind.add(i);
        while(M.size()>=3 && bad(M.size()-3,M.size()-2,M.size()-1)){
            M.remove(M.size()-2); B[ind.size()-2]=b; ind.remove(ind.size()-2);
        }
    }
    public static long query(long x, int j){
        if(pointer>=M.size()){pointer=M.size()-1;}
        while(pointer<M.size()-1 && 
                M.get(pointer+1)*x+B[pointer+1] > M.get(pointer)*x+B[pointer]){
            pointer++;
        }
        
        ch[j%N][j/N]=(short)(ind.get(pointer)/4);
        if(ind.get(pointer)%2==1){
            b1[j%N][j/N]=true;
        }
        if(ind.get(pointer)%4>=2){
            b2[j%N][j/N]=true;
        }
        return M.get(pointer)*x+B[pointer];
    }
    
    
}
//Debugging:
//Are you sure your algorithm is correct?
//Bounds: long
//Special cases: n=0,1?
//Make sure you remove your debugging code before you submit!

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 112 ms 9960 KB contestant found the optimal answer: 108 == 108
2 Correct 113 ms 9580 KB contestant found the optimal answer: 999 == 999
3 Correct 111 ms 9708 KB contestant found the optimal answer: 0 == 0
4 Correct 113 ms 9580 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 109 ms 9580 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 109 ms 9580 KB contestant found the optimal answer: 1 == 1
7 Correct 113 ms 9600 KB contestant found the optimal answer: 1 == 1
8 Correct 110 ms 9580 KB contestant found the optimal answer: 1 == 1
9 Correct 110 ms 9708 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 120 ms 9688 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 113 ms 9536 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 111 ms 9600 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 110 ms 9580 KB contestant found the optimal answer: 140072 == 140072
14 Correct 111 ms 9452 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 115 ms 9580 KB contestant found the optimal answer: 805 == 805
16 Correct 110 ms 9580 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 112 ms 9572 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 125 ms 9580 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 120 ms 9700 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 145 ms 9776 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 115 ms 9580 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 123 ms 9580 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 119 ms 9448 KB contestant found the optimal answer: 933702 == 933702
7 Correct 130 ms 9680 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 121 ms 9580 KB contestant found the optimal answer: 687136 == 687136
9 Correct 115 ms 9580 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 116 ms 9708 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 126 ms 9472 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 122 ms 9576 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 223 ms 13976 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 123 ms 9580 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 230 ms 14052 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 235 ms 14252 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 233 ms 14076 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 178 ms 11720 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 165 ms 10264 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 211 ms 12928 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 146 ms 9932 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 158 ms 10088 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 243 ms 14760 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 145 ms 9944 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 260 ms 15112 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 259 ms 14984 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 253 ms 15232 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 269 ms 15464 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 232 ms 13872 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 241 ms 14512 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 459 ms 18416 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 463 ms 18332 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 708 ms 27896 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 434 ms 17408 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 676 ms 24916 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 667 ms 26208 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 707 ms 26908 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 618 ms 25156 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 654 ms 25784 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 698 ms 27704 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 618 ms 43152 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 621 ms 43132 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Runtime error 639 ms 131072 KB Execution killed with signal 9 (could be triggered by violating memory limits)
4 Halted 0 ms 0 KB -