线段重合

链接
来源：牛客网

每一个线段都有start和end两个数据项，表示这条线段在X轴上从start位置开始到end位置结束。
给定一批线段，求所有重合区域中最多重合了几个线段，首尾相接的线段不算重合。
例如：线段[1,2]和线段[2.3]不重合。
线段[1,3]和线段[2,3]重合

串气球

import java.util.Scanner;

public class Main {


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

        while (in.hasNext()) {
            int n = in.nextInt();

            int[] count = new int[100001];

            while (n -- > 0) {
                int a = in.nextInt();
                int b = in.nextInt();

                count[a] ++;
                count[b] --;
            }

            int res = 0, sum = 0;

            for (int i = 1; i <= 100000; ++i) {
                sum += count[i];
                res = Math.max(res, sum);
            }
            System.out.println(res);
        }
    }
}

串气球（离散化）

import java.util.Map;
import java.util.Scanner;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {


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

        while (in.hasNext()) {
            int n = in.nextInt();

            Map<Integer, Integer> countMap = new TreeMap<>();
            while (n -- > 0) {
                int a = in.nextInt();
                int b = in.nextInt();

                Integer exist = countMap.getOrDefault(a, 0);
                countMap.put(a, exist + 1);

                exist = countMap.getOrDefault(b, 0);
                countMap.put(b, exist - 1);
            }

            int res = 0, sum = 0;

            for (Map.Entry<Integer, Integer> entry: countMap.entrySet()) {

                sum += entry.getValue();

                res = Math.max(sum, res);
            }

            System.out.println(res);

        }
    }
}

线段树

import java.util.*;

public class Main {

    static class SegmentTree {

        private int[] max;
        private int[] lazy;

        public SegmentTree(int n) {
            this.max = new int[n << 2 ^ 1];
            this.lazy = new int[n << 2 ^ 1];
        }

        private void pushUp(int rt) {
            max[rt] = Math.max(max[rt << 1], max[rt << 1 ^ 1]);
        }

        private void pushDown(int rt) {
            if (lazy[rt] != 0) {
                max[rt << 1] += lazy[rt];
                lazy[rt << 1] += lazy[rt];
                max[rt << 1 ^ 1] += lazy[rt];
                lazy[rt << 1 ^ 1] += lazy[rt];
                lazy[rt] = 0;
            }
        }

        public void add(int L, int R, int C, int l, int r, int rt) {
            if (L <= l && r <= R) {
                max[rt] += C;
                lazy[rt] += C;
                return;
            }

            int mid = (l + r) >> 1;

            pushDown(rt);

            if (L <= mid) {
                add(L, R, C, l, mid, rt << 1);
            }

            if (mid < R) {
                add(L, R, C, mid + 1, r, rt << 1 ^ 1);
            }
            pushUp(rt);
        }

        public int query(int L, int R, int l, int r, int rt) {
            if (L <= l && r <= R) {
                return max[rt];
            }

            int mid = (l + r) >> 1;

            pushDown(rt);

            int res = 0;

            if (L <= mid) {
                res = Math.max(res, query(L, R, l, mid, rt << 1));
            }

            if (mid < R) {
                res = Math.max(res, query(L, R, mid + 1, r, rt << 1 ^ 1));
            }

            return res;
        }
    }


    private static Map<Integer, Integer> discrete(int[][] data) {
        if (data == null || data.length == 0) {
            return new HashMap<>(0);
        }
        TreeSet<Integer> treeSet = new TreeSet<>();
        for (int[] item : data) {
            treeSet.add(item[0]);
            treeSet.add(item[1] - 1);
        }
        Map<Integer, Integer> res = new HashMap<>();
        int count = 0;
        for (int item : treeSet) {
            res.put(item, ++count);
        }
        return res;
    }


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

        while (in.hasNext()) {
            int n = in.nextInt();

            int[][] arr = new int[n][2];

            for (int i = 0; i < n; ++i) {
                arr[i][0] = in.nextInt();
                arr[i][1] = in.nextInt();
            }

            Map<Integer, Integer> discrete = discrete(arr);

            int m = discrete.size();

            SegmentTree segmentTree = new SegmentTree(m);

            int res = 0;
            for (int[] item : arr) {

                int L = discrete.get(item[0]);
                int R = discrete.get(item[1] - 1);

                segmentTree.add(L, R, 1, 1, m, 1);

                int max = segmentTree.query(L, R, 1, m, 1);
                res = Math.max(res, max);
            }
            System.out.println(res);

        }
    }
}

堆

import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {


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

        while (in.hasNext()) {
            int n = in.nextInt();
            int[][] data = new int[n][2];

            for (int i = 0; i < n; ++i) {
                data[i][0] = in.nextInt();
                data[i][1] = in.nextInt();
            }


            Arrays.sort(data, new Comparator<int[]>() {
                @Override
                public int compare(int[] o1, int[] o2) {
                    return o1[0] - o2[0];
                }
            });

            PriorityQueue<Integer> priorityQueue = new PriorityQueue<>();

            int res = 0;

            for (int i = 0; i < n; ++i) {

                while (! priorityQueue.isEmpty() && priorityQueue.peek() <= data[i][0]) {
                    priorityQueue.poll();
                }

                priorityQueue.offer(data[i][1]);

                res = Math.max(res, priorityQueue.size());
            }

            System.out.println(res);
        }
    }
}