题解 | 撞车-Java

import java.util.*;

public class Main {
    static class Car {
        long x;  // 使用long避免位置值过大导致溢出
        int v;

        Car(long x, int v) {
            this.x = x;
            this.v = v;
        }
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();

        Car[] cars = new Car[n];
        for (int i = 0; i < n; i++) {
            long x = scanner.nextLong();
            int v = scanner.nextInt();
            cars[i] = new Car(x, v);
        }

        // 按位置排序，位置小的车在后面，位置大的车在前面
        Arrays.sort(cars, (a, b) -> Long.compare(a.x, b.x));

        // 提取速度序列
        int[] speeds = new int[n];
        for (int i = 0; i < n; i++) {
            speeds[i] = cars[i].v;
        }

        // 找出最长非递增子序列的长度
        int maxNonIncreasing = longestNonIncreasingSubsequence(speeds);

        // 需要移除的车辆数 = 总车辆数 - 最长非递增子序列的长度
        System.out.println(n - maxNonIncreasing);
    }

    // 计算最长非递增子序列的长度，使用O(n log n)算法
    private static int longestNonIncreasingSubsequence(int[] nums) {
        if (nums == null || nums.length == 0) {
            return 0;
        }

        List<Integer> tails = new ArrayList<>();

        for (int num : nums) {
            // 找到第一个小于num的位置（二分查找）
            int left = 0, right = tails.size() - 1;
            while (left <= right) {
                int mid = left + (right - left) / 2;
                if (tails.get(mid) <= num) {
                    left = mid + 1;
                } else {
                    right = mid - 1;
                }
            }

            if (left == tails.size()) {
                tails.add(num);
            } else {
                tails.set(left, num);
            }
        }

        return tails.size();
    }
}