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Submission #335775

# Submission time Handle Problem Language Result Execution time Memory
335775 2020-12-14T00:39:48 Z Agnimandur Discharging (NOI20_discharging) Java 11
100 / 100
 343 ms 35492 KB 
import java.util.*;
import java.io.*;

public class Discharging {
    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public int ni() throws IOException {
            int ret = 0;
            boolean flip = false;
            byte c = read();
            while (c < '0' || c > '9') {
                if (c == '-') flip = true;
                c = read();
            }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            return flip ? -ret : ret;
        }
        public long nl() throws IOException {
            long ret = 0;
            boolean flip = false;
            byte c = read();
            while (c < '0' || c > '9') {
                if (c == '-') flip = true;
                c = read();
            }
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            return flip ? -ret : ret;
        }

        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1) {
                buffer[0] = -1;
            }
        }

        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead) {
                fillBuffer();
            }
            return buffer[bufferPointer++];
        }
    }

    public static void main(String[] args) throws IOException {
        Reader sc = new Reader();
        PrintStream out = new PrintStream(new BufferedOutputStream(System.out));
        
        int N = sc.ni();
        long[] nums = new long[N+1];
        for (int i = 1; i <= N; i++) {
            nums[i] = Math.max(nums[i-1],sc.nl());
        }
        
        //dp with convex hull trick
        long[] dp = new long[N+1];
        Hull cht = new Hull();
        for (int i = 1; i <= N; i++) {
            cht.add(new Line(nums[N-(i-1)],dp[i-1]));
            dp[i] = cht.getMin(i);
        }
        
        out.print(dp[N]);
        out.flush(); // remember to flush just once, at the very end of your program
    }

    //convex hull
    static class Hull {
        ArrayDeque<Line> ad;
        
        public Hull() {
            ad = new ArrayDeque<Line>();
        }

        public void add(Line l) {
        	if (ad.isEmpty() || l.m < ad.peekLast().m) {
        		while (ad.size() >= 2) {
        			Line l1 = ad.pollLast();
                    Line l2 = ad.peekLast();
                    if (good(l2,l1,l)) {
                    	ad.addLast(l1);
                    	break;
                    }
        		}
        		ad.addLast(l);
        	}
        }
        
        public boolean good(Line l1, Line l2, Line l3) {
        	double d12 = (l2.b-l1.b+0.0)/(l1.m-l2.m);
        	double d23 = (l3.b-l2.b+0.0)/(l2.m-l3.m);
        	return (d12 < d23);
        }

        public long getMin(long x) {
            while (ad.size() >= 2) {
                Line f1 = ad.pollFirst();
                Line f2 = ad.peekFirst();
                if ((f2.b-f1.b) > x*(f1.m-f2.m)) {
                    ad.addFirst(f1);
                    break;
                }
            }
            return ad.peekFirst().eval(x);
        }
    }

    //line
    static class Line {
        long m;
        long b;
        public Line(long m, long b) {
            this.m=m;
            this.b=b;
        }

        public long eval(long x) {
            return m*x+b;
        }
    }
}

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 77 ms 8808 KB Output is correct
2 Correct 72 ms 8556 KB Output is correct
3 Correct 71 ms 8556 KB Output is correct
4 Correct 72 ms 8556 KB Output is correct
5 Correct 72 ms 8556 KB Output is correct
6 Correct 72 ms 8556 KB Output is correct
7 Correct 76 ms 8556 KB Output is correct
8 Correct 75 ms 8624 KB Output is correct
9 Correct 76 ms 8540 KB Output is correct
10 Correct 74 ms 8556 KB Output is correct
11 Correct 75 ms 8556 KB Output is correct
12 Correct 74 ms 8556 KB Output is correct
13 Correct 74 ms 8556 KB Output is correct
14 Correct 73 ms 8556 KB Output is correct

Subtask #2
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 91 ms 8684 KB Output is correct
2 Correct 92 ms 8668 KB Output is correct
3 Correct 88 ms 8560 KB Output is correct
4 Correct 81 ms 8684 KB Output is correct
5 Correct 86 ms 8552 KB Output is correct
6 Correct 93 ms 8556 KB Output is correct
7 Correct 83 ms 8744 KB Output is correct
8 Correct 89 ms 8812 KB Output is correct
9 Correct 89 ms 8812 KB Output is correct
10 Correct 90 ms 8784 KB Output is correct
11 Correct 94 ms 8656 KB Output is correct
12 Correct 85 ms 8636 KB Output is correct
13 Correct 83 ms 8556 KB Output is correct
14 Correct 84 ms 8556 KB Output is correct
15 Correct 84 ms 8572 KB Output is correct

Subtask #3
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 91 ms 8684 KB Output is correct
2 Correct 92 ms 8668 KB Output is correct
3 Correct 88 ms 8560 KB Output is correct
4 Correct 81 ms 8684 KB Output is correct
5 Correct 86 ms 8552 KB Output is correct
6 Correct 93 ms 8556 KB Output is correct
7 Correct 83 ms 8744 KB Output is correct
8 Correct 89 ms 8812 KB Output is correct
9 Correct 89 ms 8812 KB Output is correct
10 Correct 90 ms 8784 KB Output is correct
11 Correct 94 ms 8656 KB Output is correct
12 Correct 85 ms 8636 KB Output is correct
13 Correct 83 ms 8556 KB Output is correct
14 Correct 84 ms 8556 KB Output is correct
15 Correct 84 ms 8572 KB Output is correct
16 Correct 302 ms 31556 KB Output is correct
17 Correct 339 ms 34268 KB Output is correct
18 Correct 333 ms 35088 KB Output is correct
19 Correct 343 ms 35148 KB Output is correct
20 Correct 315 ms 33640 KB Output is correct
21 Correct 312 ms 33796 KB Output is correct
22 Correct 337 ms 35240 KB Output is correct
23 Correct 304 ms 33700 KB Output is correct
24 Correct 316 ms 33416 KB Output is correct
25 Correct 324 ms 33564 KB Output is correct
26 Correct 310 ms 33472 KB Output is correct
27 Correct 308 ms 33508 KB Output is correct
28 Correct 328 ms 33724 KB Output is correct
29 Correct 322 ms 33708 KB Output is correct
30 Correct 310 ms 33712 KB Output is correct

Subtask #4
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 180 ms 26732 KB Output is correct
2 Correct 184 ms 27380 KB Output is correct
3 Correct 184 ms 27500 KB Output is correct
4 Correct 188 ms 27692 KB Output is correct
5 Correct 181 ms 27344 KB Output is correct
6 Correct 180 ms 27388 KB Output is correct
7 Correct 180 ms 27360 KB Output is correct
8 Correct 183 ms 27252 KB Output is correct
9 Correct 180 ms 27380 KB Output is correct
10 Correct 179 ms 27484 KB Output is correct

Subtask #5
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 77 ms 8808 KB Output is correct
2 Correct 72 ms 8556 KB Output is correct
3 Correct 71 ms 8556 KB Output is correct
4 Correct 72 ms 8556 KB Output is correct
5 Correct 72 ms 8556 KB Output is correct
6 Correct 72 ms 8556 KB Output is correct
7 Correct 76 ms 8556 KB Output is correct
8 Correct 75 ms 8624 KB Output is correct
9 Correct 76 ms 8540 KB Output is correct
10 Correct 74 ms 8556 KB Output is correct
11 Correct 75 ms 8556 KB Output is correct
12 Correct 74 ms 8556 KB Output is correct
13 Correct 74 ms 8556 KB Output is correct
14 Correct 73 ms 8556 KB Output is correct
15 Correct 91 ms 8684 KB Output is correct
16 Correct 92 ms 8668 KB Output is correct
17 Correct 88 ms 8560 KB Output is correct
18 Correct 81 ms 8684 KB Output is correct
19 Correct 86 ms 8552 KB Output is correct
20 Correct 93 ms 8556 KB Output is correct
21 Correct 83 ms 8744 KB Output is correct
22 Correct 89 ms 8812 KB Output is correct
23 Correct 89 ms 8812 KB Output is correct
24 Correct 90 ms 8784 KB Output is correct
25 Correct 94 ms 8656 KB Output is correct
26 Correct 85 ms 8636 KB Output is correct
27 Correct 83 ms 8556 KB Output is correct
28 Correct 84 ms 8556 KB Output is correct
29 Correct 84 ms 8572 KB Output is correct
30 Correct 77 ms 8720 KB Output is correct
31 Correct 80 ms 8444 KB Output is correct
32 Correct 78 ms 8684 KB Output is correct
33 Correct 79 ms 8656 KB Output is correct
34 Correct 78 ms 8668 KB Output is correct
35 Correct 79 ms 8668 KB Output is correct
36 Correct 80 ms 8684 KB Output is correct
37 Correct 79 ms 8700 KB Output is correct
38 Correct 78 ms 8684 KB Output is correct
39 Correct 79 ms 8540 KB Output is correct
40 Correct 79 ms 8680 KB Output is correct
41 Correct 78 ms 8744 KB Output is correct
42 Correct 78 ms 8556 KB Output is correct
43 Correct 83 ms 8684 KB Output is correct
44 Correct 77 ms 8684 KB Output is correct
45 Correct 79 ms 8684 KB Output is correct
46 Correct 78 ms 8684 KB Output is correct
47 Correct 77 ms 8668 KB Output is correct
48 Correct 78 ms 8684 KB Output is correct
49 Correct 84 ms 8684 KB Output is correct
50 Correct 78 ms 8660 KB Output is correct

Subtask #6
28.0 / 28.0

# Verdict Execution time Memory Grader output
1 Correct 77 ms 8808 KB Output is correct
2 Correct 72 ms 8556 KB Output is correct
3 Correct 71 ms 8556 KB Output is correct
4 Correct 72 ms 8556 KB Output is correct
5 Correct 72 ms 8556 KB Output is correct
6 Correct 72 ms 8556 KB Output is correct
7 Correct 76 ms 8556 KB Output is correct
8 Correct 75 ms 8624 KB Output is correct
9 Correct 76 ms 8540 KB Output is correct
10 Correct 74 ms 8556 KB Output is correct
11 Correct 75 ms 8556 KB Output is correct
12 Correct 74 ms 8556 KB Output is correct
13 Correct 74 ms 8556 KB Output is correct
14 Correct 73 ms 8556 KB Output is correct
15 Correct 91 ms 8684 KB Output is correct
16 Correct 92 ms 8668 KB Output is correct
17 Correct 88 ms 8560 KB Output is correct
18 Correct 81 ms 8684 KB Output is correct
19 Correct 86 ms 8552 KB Output is correct
20 Correct 93 ms 8556 KB Output is correct
21 Correct 83 ms 8744 KB Output is correct
22 Correct 89 ms 8812 KB Output is correct
23 Correct 89 ms 8812 KB Output is correct
24 Correct 90 ms 8784 KB Output is correct
25 Correct 94 ms 8656 KB Output is correct
26 Correct 85 ms 8636 KB Output is correct
27 Correct 83 ms 8556 KB Output is correct
28 Correct 84 ms 8556 KB Output is correct
29 Correct 84 ms 8572 KB Output is correct
30 Correct 302 ms 31556 KB Output is correct
31 Correct 339 ms 34268 KB Output is correct
32 Correct 333 ms 35088 KB Output is correct
33 Correct 343 ms 35148 KB Output is correct
34 Correct 315 ms 33640 KB Output is correct
35 Correct 312 ms 33796 KB Output is correct
36 Correct 337 ms 35240 KB Output is correct
37 Correct 304 ms 33700 KB Output is correct
38 Correct 316 ms 33416 KB Output is correct
39 Correct 324 ms 33564 KB Output is correct
40 Correct 310 ms 33472 KB Output is correct
41 Correct 308 ms 33508 KB Output is correct
42 Correct 328 ms 33724 KB Output is correct
43 Correct 322 ms 33708 KB Output is correct
44 Correct 310 ms 33712 KB Output is correct
45 Correct 180 ms 26732 KB Output is correct
46 Correct 184 ms 27380 KB Output is correct
47 Correct 184 ms 27500 KB Output is correct
48 Correct 188 ms 27692 KB Output is correct
49 Correct 181 ms 27344 KB Output is correct
50 Correct 180 ms 27388 KB Output is correct
51 Correct 180 ms 27360 KB Output is correct
52 Correct 183 ms 27252 KB Output is correct
53 Correct 180 ms 27380 KB Output is correct
54 Correct 179 ms 27484 KB Output is correct
55 Correct 77 ms 8720 KB Output is correct
56 Correct 80 ms 8444 KB Output is correct
57 Correct 78 ms 8684 KB Output is correct
58 Correct 79 ms 8656 KB Output is correct
59 Correct 78 ms 8668 KB Output is correct
60 Correct 79 ms 8668 KB Output is correct
61 Correct 80 ms 8684 KB Output is correct
62 Correct 79 ms 8700 KB Output is correct
63 Correct 78 ms 8684 KB Output is correct
64 Correct 79 ms 8540 KB Output is correct
65 Correct 79 ms 8680 KB Output is correct
66 Correct 78 ms 8744 KB Output is correct
67 Correct 78 ms 8556 KB Output is correct
68 Correct 83 ms 8684 KB Output is correct
69 Correct 77 ms 8684 KB Output is correct
70 Correct 79 ms 8684 KB Output is correct
71 Correct 78 ms 8684 KB Output is correct
72 Correct 77 ms 8668 KB Output is correct
73 Correct 78 ms 8684 KB Output is correct
74 Correct 84 ms 8684 KB Output is correct
75 Correct 78 ms 8660 KB Output is correct
76 Correct 245 ms 35248 KB Output is correct
77 Correct 258 ms 35292 KB Output is correct
78 Correct 249 ms 35240 KB Output is correct
79 Correct 250 ms 35304 KB Output is correct
80 Correct 251 ms 35160 KB Output is correct
81 Correct 251 ms 35272 KB Output is correct
82 Correct 252 ms 35432 KB Output is correct
83 Correct 243 ms 35340 KB Output is correct
84 Correct 260 ms 35332 KB Output is correct
85 Correct 248 ms 35340 KB Output is correct
86 Correct 242 ms 35256 KB Output is correct
87 Correct 248 ms 35304 KB Output is correct
88 Correct 246 ms 35420 KB Output is correct
89 Correct 246 ms 35300 KB Output is correct
90 Correct 239 ms 35416 KB Output is correct
91 Correct 245 ms 35304 KB Output is correct
92 Correct 332 ms 34724 KB Output is correct
93 Correct 314 ms 33880 KB Output is correct
94 Correct 244 ms 35288 KB Output is correct
95 Correct 250 ms 35304 KB Output is correct
96 Correct 248 ms 35232 KB Output is correct
97 Correct 245 ms 35304 KB Output is correct
98 Correct 240 ms 35288 KB Output is correct
99 Correct 242 ms 35492 KB Output is correct
100 Correct 248 ms 35384 KB Output is correct