算法时间复杂度

对增长数量级的常见假设的总结

二分法查找：

package chapter1;

import java.util.Arrays;

public class BinarySearch {
    private static int[] source = {3, 9, 5, 2, 7 ,3, 6};
    private static int key = 7;

    private static int Search(int[] a, int mid) {
        int length = a.length;
        if (a[mid] == key) {
            return a[mid];
        } else if (a[mid] > key) {
            mid = (length - mid) / 2;
            return Search(a, mid);
        } else if (a[mid] < key) {
            mid = (length - mid) / 2 + mid;
            return Search(a, mid);
        }
        return -1;
    }

    public static void main(String[] args) {
        Arrays.sort(BinarySearch.source);
        int result = Search(BinarySearch.source, BinarySearch.source.length / 2);
        System.out.print(result);
    }
}

归并排序：

package chapter2;

/**
 * Created by Blue on 2017/6/3.
 */
public class Merge {
    private static Comparable[] aux;

    public static void sort(Comparable[] a) {
        aux = new Comparable[a.length];
        sort(a, 0, a.length - 1);
    }

    private static void sort(Comparable[] a, int lo, int hi) {
        if (hi <= lo) {
            return;
        }
        int mid = lo + (hi - lo) / 2;
        sort(a, lo, mid);
        sort(a, mid + 1, hi);
        merge(a, lo, mid, hi);
    }

    private static void merge(Comparable[] a, int lo, int mid, int hi) {
        int i = lo, j = mid + 1;
        for (int k = lo; k <= hi; k++) {
            aux[k] = a[k];
        }
        for (int k = lo; k <= hi; k++) {
            if (i > mid) {
                a[k] = aux[j++];
            } else if (j > hi) {
                a[k] = aux[i++];
            } else if (less(aux[j], aux[i])) {
                a[k] = aux[j++];
            } else {
                a[k] = aux[i++];
            }
        }
    }

    public static boolean less(Comparable v, Comparable w) {
        return v.compareTo(w) < 0;
    }

    public static void exch(Comparable[] a, int i, int j) {
        Comparable t = a[i];
        a[i] = a[j];
        a[j] = t;
    }

    public static boolean isSorted(Comparable[] a) {
        for (int i = 1; i < a.length; i++) {
            if (less(a[i], a[i - 1])) {
                return false;
            }
        }
        return true;
    }

    public static void show(Comparable[] a) {
        for (int i = 0; i < a.length; i++) {
            System.out.print(a[i] + " ");
        }
        System.out.println();
    }

    public static void main(String[] args) {
        String[] a = {"80", "30", "60", "40", "20", "10", "50", "70"};
        sort(a);
        assert isSorted(a);
        show(a);
    }
}