summaryrefslogtreecommitdiff
path: root/AlgoDesignAndTechniqueEdxJava/sources/PointsAndSegments.java
blob: bc20b4b0dd9c3faaac49a6474efb3a8fd4899095 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
import java.util.Arrays;
import java.util.Objects;
import java.util.Scanner;

public class PointsAndSegments {

    public static class Segment implements Comparable<Segment> {
        int start, end;

        Segment(int start, int end) {
            this.start = start;
            this.end = end;
        }

        public int compareTo(Segment that) {
            if (this.start > that.start)
                return 1;
            if (this.start == that.start) {
                if (this.end > that.end)
                    return 1;
                else if (this.end == that.end) {
                    return 0;
                } else
                    return -1;
            }
            return -1;
        }

        @Override
        public boolean equals(Object o) {
            if (o == this)
                return true;
            if (!(o instanceof Segment)) {
                return false;
            }
            Segment s = (Segment) o;
            return start == s.start && end == s.end;
        }

        @Override
        public int hashCode() {
            return Objects.hash(start, end);
        }

    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        int n, m;
        n = scanner.nextInt();
        m = scanner.nextInt();
        int[] starts = new int[n];
        int[] ends = new int[n];
        int[] points = new int[m];
        for (int i = 0; i < n; i++) {
            starts[i] = scanner.nextInt();
            ends[i] = scanner.nextInt();
        }
        for (int i = 0; i < m; i++) {
            points[i] = scanner.nextInt();
        }
        // use fastCountSegments
        int[] cnt = fastestCountSegments(starts, ends, points);
        for (int x : cnt) {
            System.out.print(x + " ");
        }
    }

    public static int[] naiveCountSegments(int[] starts, int[] ends, int[] points) {
        int[] cnt = new int[points.length];
        for (int i = 0; i < points.length; i++) {
            for (int j = 0; j < starts.length; j++) {
                if (starts[j] <= points[i] && points[i] <= ends[j]) {
                    cnt[i]++;
                }
            }
        }
        return cnt;
    }

    public static int[] fastCountSegments(int[] starts, int[] ends, int[] points) {
        Segment[] s = new Segment[starts.length];
        for (int i = 0; i < s.length; i++) {
            s[i] = new Segment(starts[i], ends[i]);
        }
        Arrays.sort(s);
        int[] results = new int[points.length];
        for (int i = 0; i < results.length; i++) {
            results[i] = segCounts(s, points[i], 0, s.length - 1);
        }
        return results;
    }

    public static int[] fasterCountSegments(int[] starts, int[] ends, int[] points) {
        Segment[] s = new Segment[starts.length];
        Segment[] p = new Segment[points.length];
        for (int i = 0; i < s.length; i++) {
            s[i] = new Segment(starts[i], ends[i]);
        }
        for (int i = 0; i < p.length; i++) {
            p[i] = new Segment(points[i], i);
        }
        Arrays.sort(s);
        Arrays.sort(p);
        int[] results = new int[points.length];
        int r = segCounts(s, p[0].start, 0, s.length - 1);
        results[p[0].end] = r;
        for (int i = 1; i < results.length; i++) {
            if (p[i].start == p[i - 1].start)
                results[p[i].end] = results[p[i - 1].end];
            else
                results[p[i].end] = segCounts(s, p[i].start, 0, s.length - 1);
        }
        return results;
    }

    public static int[] fastestCountSegments(int[] starts, int[] ends, int[] points) {
        // Implement algo described here, really clever:
        // https://www.coursera.org/learn/algorithmic-toolbox/discussions/all/threads/QJ1jK9wNEeWdPBL2iFTrAw/replies/Ihiw4txhEeWK5g7mfcS2Xw/comments/oyAMaeIiEeWyqwpvChh66Q
        // l->1, p->2, r->3 for Segment.end property
        Segment[] s = new Segment[starts.length + ends.length + points.length];
        Segment[] p = new Segment[points.length];
        for (int i = 0; i < p.length; i++) {
            p[i] = new Segment(points[i], i);
            s[2 * starts.length + i] = new Segment(points[i], 2);
        }
        for (int i = 0; i < starts.length; i++) {
            s[i] = new Segment(starts[i], 1);
            s[i + starts.length] = new Segment(ends[i], 3);
        }
        Arrays.sort(s);
        Arrays.sort(p);
        int[] results = new int[points.length];
        int count = 0;
        int j = 0;
        for (int i = 0; i < s.length; i++) {
            if (s[i].end == 1) {
                count = count + 1;
            }
            if (s[i].end == 2) {
                results[j] = count;
                j = j + 1;
            }
            if (s[i].end == 3) {
                count = count - 1;
            }
        }
        int[] finalResults = new int[points.length];
        for (int i = 0; i < finalResults.length; i++) {
           finalResults[p[i].end] = results[i]; 
        }
        return finalResults;
    }

    public static int segCounts(Segment[] s, int p, int low, int high) {
        if (high < low)
            return 0;
        int mid = low + (high - low) / 2;
        if (p < s[mid].start)
            return segCounts(s, p, low, mid - 1);
        if (p > s[mid].end)
            return segCounts(s, p, mid + 1, high);
        return 1 + segCounts(s, p, low, mid - 1) + segCounts(s, p, mid + 1, high);
    }

}