挑战程序竞赛系列（61）：4.6平面上的分治法（1）

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挑战程序竞赛系列（61）：4.6平面上的分治法（1）

传送门：Uva 10245: The Closest Pair Problem
传送门：POJ 3714: Raid

Uva 10245: The Closest Pair Problem

思路：
分治，参考《挑战》P365：
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利用分治后左平面和右平面的最小d来限制第二种情况的查询，绝了。关于第二种情形的算法采用平面扫描法，但前提y需要排序。

注意一些细节：比如如何确定矩形y的范围，先来看看代码：

import java.io.BufferedReader;import java.io.File;import java.io.FileInputStream;import java.io.IOException;import java.io.InputStream;import java.io.InputStreamReader;import java.io.PrintWriter;import java.util.ArrayList;import java.util.Arrays;import java.util.List;import java.util.StringTokenizer;public class Main{    String INPUT = "./data/judge/201709/U0245.txt";    public static void main(String[] args) throws IOException {        new Main().run();    }    static final int    MAX_N = 10000 + 16;    static final double INF   = 1e4;    class Pair implements Comparable<Pair>{        double x;        double y;        Pair(double x, double y){            this.x = x;            this.y = y;        }        @Override        public String toString() {            return x + " " + y;        }        @Override        public int compareTo(Pair that) {            if (this.x != that.x) return Double.compare(this.x, that.x);            return Double.compare(this.y, that.y);        }    }    Pair[] tmp = new Pair[MAX_N];    double solve(Pair[] p, int l, int r) {        if (r - l <= 1) return 12341234;        int mid = (l + r) / 2;        double x = p[mid].x;        double d = Math.min(solve(p, l, mid), solve(p, mid, r));        int k = 0;        int ll = l, rr = mid;        while (ll < mid && rr < r) {            if (p[ll].y < p[rr].y) tmp[k++] = p[ll++];            else tmp[k++] = p[rr++];        }        while (ll < mid) tmp[k++] = p[ll++];        while (rr < r) tmp[k++] = p[rr++];        for (int i = l; i < r; ++i) p[i] = tmp[i - l];//      for (int i = l, j = mid, k = l; k < r;) {//          if (j >= r || i < mid && p[i].y < p[j].y) tmp[k++] = p[i++];//          else tmp[k++] = p[j++];//      }//      for (int i = l; i < r; ++i) p[i] = tmp[i];        List<Pair> b = new ArrayList<>();        for (int i = l; i < r; ++i) {            if (Math.abs(p[i].x - x) >= d) continue;            for (int j = b.size() - 1; j >= 0; --j) {                double dx = p[i].x - b.get(j).x;                double dy = p[i].y - b.get(j).y;                if (Math.abs(dy) >= d) break;                d = Math.min(d, Math.sqrt(dx * dx + dy * dy));            }            b.add(p[i]);        }        return d;    }    void read() {        while (true) {            int N = ni();            if (N == 0) break;            Pair[] points = new Pair[N];            for (int i = 0; i < N; ++i) {                double x = nd();                double y = nd();                points[i] = new Pair(x, y);            }            Arrays.sort(points);            double ans = solve(points, 0, N);            if (ans >= INF) out.println("INFINITY");            else {                out.printf("%.4f\n", ans);            }        }    }    FastScanner in;    PrintWriter out;    void run() throws IOException {        boolean oj;        try {            oj = ! System.getProperty("user.dir").equals("F:\\java_workspace\\leetcode");        } catch (Exception e) {            oj = System.getProperty("ONLINE_JUDGE") != null;        }        InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));        in = new FastScanner(is);        out = new PrintWriter(System.out);        long s = System.currentTimeMillis();        read();        out.flush();        if (!oj){            System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");        }    }    public boolean more(){        return in.hasNext();    }    public int ni(){        return in.nextInt();    }    public long nl(){        return in.nextLong();    }    public double nd(){        return in.nextDouble();    }    public String ns(){        return in.nextString();    }    public char nc(){        return in.nextChar();    }    class FastScanner {        BufferedReader br;        StringTokenizer st;        boolean hasNext;        public FastScanner(InputStream is) throws IOException {            br = new BufferedReader(new InputStreamReader(is));            hasNext = true;        }        public String nextToken() {            while (st == null || !st.hasMoreTokens()) {                try {                    st = new StringTokenizer(br.readLine());                } catch (Exception e) {                    hasNext = false;                    return "##";                }            }            return st.nextToken();        }        String next = null;        public boolean hasNext(){            next = nextToken();            return hasNext;        }        public int nextInt() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Integer.parseInt(more);        }        public long nextLong() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Long.parseLong(more);        }        public double nextDouble() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Double.parseDouble(more);        }        public String nextString(){            if (next == null){                hasNext();            }            String more = next;            next = null;            return more;        }        public char nextChar(){            if (next == null){                hasNext();            }            String more = next;            next = null;            return more.charAt(0);        }    }    static class ArrayUtils {        public static void fill(int[][] f, int value) {            for (int i = 0; i < f.length; ++i) {                Arrays.fill(f[i], value);            }        }        public static void fill(int[][][] f, int value) {            for (int i = 0; i < f.length; ++i) {                fill(f[i], value);            }        }        public static void fill(int[][][][] f, int value) {            for (int i = 0; i < f.length; ++i) {                fill(f[i], value);            }        }    }}

此处：

        List<Pair> b = new ArrayList<>();        for (int i = l; i < r; ++i) {            if (Math.abs(p[i].x - x) >= d) continue;            for (int j = b.size() - 1; j >= 0; --j) {                double dx = p[i].x - b.get(j).x;                double dy = p[i].y - b.get(j).y;                if (Math.abs(dy) >= d) break;                d = Math.min(d, Math.sqrt(dx * dx + dy * dy));            }            b.add(p[i]);        }

纠结了很久，注意第二个循环的break，使用break，说明dy >= d的情况都不需要比较，那么必须满足当前点和之前最大的那些点进行比较，continue的话，就与顺序无关，因为遍历了所有情况，但估计数据量一大就超时，根据书上的定义该for循环不会超过6次，可以认为是常数级的。

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POJ 3714: Raid

求能量站和人之间的最短顶点对。

思路：
多了个限制，人与能量站之间的最短距离，那么在分治求解时，当且仅当遇到两个顶点分别是人和能量站时进行最短距更新即可。

代码如下：

import java.io.BufferedReader;import java.io.File;import java.io.FileInputStream;import java.io.IOException;import java.io.InputStream;import java.io.InputStreamReader;import java.io.PrintWriter;import java.util.ArrayList;import java.util.Arrays;import java.util.List;import java.util.StringTokenizer;public class Main{    String INPUT = "./data/judge/201709/P3714.txt";    public static void main(String[] args) throws IOException {        new Main().run();    }    static final int MAX_N = 100000 + 16;    static final int INF   = 0x3f3f3f3f;    class Pair implements Comparable<Pair>{        double x;        double y;        boolean man;        Pair(double x, double y, boolean man){            this.x = x;            this.y = y;            this.man = man;        }        @Override        public String toString() {            return x + " " + y;        }        @Override        public int compareTo(Pair o) {            return x > o.x ? -1 : 1;        }    }    Pair[] tmp = new Pair[2 * MAX_N];    double solve(Pair[] p, int l, int r) {        if (r - l <= 1) return INF;        int m = (l + r) / 2;        double x = p[m].x;        double d = Math.min(solve(p, l, m), solve(p, m, r));        // merge        for (int i = l, j = m, k = l; k < r;) {            if (j >= r || i < m && p[i].y < p[j].y) tmp[k++] = p[i++];            else tmp[k++] = p[j++];        }        for (int i = l; i < r; ++i) p[i] = tmp[i];        List<Pair> b = new ArrayList<Pair>();        for (int i = l; i < r; ++i) {            if (Math.abs(p[i].x - x) >= d) continue;            for (int j = b.size() - 1; j >= 0; --j) {                double dx = p[i].x - b.get(j).x;                double dy = p[i].y - b.get(j).y;                if (p[i].man ^ b.get(j).man) {                    if (Math.abs(dy) >= d) break;                    d = Math.min(d, Math.sqrt(dx * dx + dy * dy));                }            }            b.add(p[i]);        }        return d;    }    void read() {        int T = ni();        while (T --> 0) {            int N = ni();            Pair[] points = new Pair[2 * N];            for (int i = 0; i < N; ++i) {                points[i] = new Pair(nd(), nd(), false);            }            for (int i = 0; i < N; ++i) {                points[i + N] = new Pair(nd(), nd(), true);            }            Arrays.sort(points);            out.printf("%.3f\n", solve(points, 0, 2 * N));        }    }    FastScanner in;    PrintWriter out;    void run() throws IOException {        boolean oj;        try {            oj = ! System.getProperty("user.dir").equals("F:\\java_workspace\\leetcode");        } catch (Exception e) {            oj = System.getProperty("ONLINE_JUDGE") != null;        }        InputStream is = oj ? System.in : new FileInputStream(new File(INPUT));        in = new FastScanner(is);        out = new PrintWriter(System.out);        long s = System.currentTimeMillis();        read();        out.flush();        if (!oj){            System.out.println("[" + (System.currentTimeMillis() - s) + "ms]");        }    }    public boolean more(){        return in.hasNext();    }    public int ni(){        return in.nextInt();    }    public long nl(){        return in.nextLong();    }    public double nd(){        return in.nextDouble();    }    public String ns(){        return in.nextString();    }    public char nc(){        return in.nextChar();    }    class FastScanner {        BufferedReader br;        StringTokenizer st;        boolean hasNext;        public FastScanner(InputStream is) throws IOException {            br = new BufferedReader(new InputStreamReader(is));            hasNext = true;        }        public String nextToken() {            while (st == null || !st.hasMoreTokens()) {                try {                    st = new StringTokenizer(br.readLine());                } catch (Exception e) {                    hasNext = false;                    return "##";                }            }            return st.nextToken();        }        String next = null;        public boolean hasNext(){            next = nextToken();            return hasNext;        }        public int nextInt() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Integer.parseInt(more);        }        public long nextLong() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Long.parseLong(more);        }        public double nextDouble() {            if (next == null){                hasNext();            }            String more = next;            next = null;            return Double.parseDouble(more);        }        public String nextString(){            if (next == null){                hasNext();            }            String more = next;            next = null;            return more;        }        public char nextChar(){            if (next == null){                hasNext();            }            String more = next;            next = null;            return more.charAt(0);        }    }    static class ArrayUtils {        public static void fill(int[][] f, int value) {            for (int i = 0; i < f.length; ++i) {                Arrays.fill(f[i], value);            }        }        public static void fill(int[][][] f, int value) {            for (int i = 0; i < f.length; ++i) {                fill(f[i], value);            }        }        public static void fill(int[][][][] f, int value) {            for (int i = 0; i < f.length; ++i) {                fill(f[i], value);            }        }    }}

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