ConvexHullTrick.java

import java.util.*;
import java.io.*;
import java.math.*;

public class ConvexHullTrick {
    static int n;
    static int[] b, x, y;
    static long[] dp, a;
    static Deque<Line> dq;

    public static void main(String[] args) throws IOException {
        PrintWriter out = new PrintWriter(System.out);
        Reader in = new Reader();
        ConvexHullTrick solver = new ConvexHullTrick();
        solver.solve(out, in);
        out.flush();
        out.close();
    }

    void solve(PrintWriter out, Reader in) throws IOException {
        n = in.nextInt();

        x = new int[n];
        y = new int[n];
        a = new long[n];
        Integer[] indices = new Integer[n];
        for (int i = 0; i < n; i++) {
            indices[i] = i;
            x[i] = in.nextInt();
            y[i] = in.nextInt();
            a[i] = in.nextLong();
        }
        Arrays.sort(indices, Comparator.comparingInt(i -> x[i]));

        dq = new LinkedList<Line>();
        dp = new long[n];

        dq.addFirst(new Line(0, 0));

        for (int idx : indices) {
            dp[idx] = query(y[idx], idx);
            insert(-x[idx], dp[idx]);
        }

        long ans = 0;
        for (int i = 0; i < n; i++) ans = Math.max(dp[i], ans);
        out.println(ans);

    }

    static void insert(long mx, long cx) {
        Line ne = new Line(mx, cx);
        Line li = new Line(-1, -1);
        while (dq.size() >= 2) {
            li = dq.pollFirst();
            if (li.inter(ne) < li.inter(dq.peekFirst())) {
                dq.addFirst(li);
                break;
            }
        }
        dq.addFirst(ne);
        return;
    }

    static long query(int s, int i) {
        Line li = new Line(-1, -1);
        while (dq.size() >= 2 ) {
            li = dq.pollLast();
            if (li.eval(s) > dq.peekLast().eval(s)) {
                dq.addLast(li);
                break;
            }
        }

        li = dq.peekLast();
        return li.eval(s) + (long)x[i] * (long)y[i] - a[i];
    }

    static class Line {
        long m, c;

        Line(long m, long c) {
            this.m = m;
            this.c = c;
        }

        double inter(Line l) {
            return (double)(l.c - c) / (double)(m - l.m);
        }

        long eval(int x) {
            return m * x + c;
        }
    }

    static class Reader {

        private InputStream mIs;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public Reader() {
            this(System.in);
        }

        public Reader(InputStream is) {
            mIs = is;
        }

        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();

            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = mIs.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
}