局部最小问题

package class01;

/**
 * 局部最小问题
 * <p>
 * 对于一个数组，使用二分法的前提，一定是这个数组整体有序吗？
 * 答：不是。局部最小问题就是反例。
 */
public class Code07_BSAwesome {
    public static int getLessIndex(int[] arr) {
        if (arr == null || arr.length == 0) {
            return -1;
        }
        if (arr.length == 1 || arr[0] < arr[1]) {
            return 0;
        }
        if (arr[arr.length - 1] < arr[arr.length - 2]) {
            return arr.length - 1;
        }
        int L = 1;
        int R = arr.length - 2;
        while (L <= R) {
            int mid = L + ((R - L) >> 1);
            if (arr[mid] > arr[mid - 1]) {
                R = mid - 1;
            } else if (arr[mid] > arr[mid + 1]) {
                L = mid + 1;
            } else {
                return mid;
            }
        }
        System.out.println("===============================");
        return L;
    }

    public static void main(String[] args) {
        int maxSize = 50;
        int maxValue = 30;
        int testTimes = 10000;
        boolean flag = true;
        for (int i = 0; i < testTimes; i++) {
            int[] arr1 = generateRandomArr2(maxSize, maxValue);

            int num = getLessIndex(arr1);
            if (!test(arr1, num)) {
                printArr(arr1);
                for (int index = 0; index < arr1.length; index++) {
                    System.out.print(index + "\t");
                }
                System.out.println();
                System.out.println("num = " + num);
                flag = false;
                break;
            }
        }
        //至少打印一次
        int[] arr1 = generateRandomArr2(maxSize, maxValue);
        printArr(arr1);
        for (int index = 0; index < arr1.length; index++) {
            System.out.print(index + "\t");
        }
        System.out.println();
        int num = getLessIndex(arr1);
        System.out.println("num = " + num);
        System.out.println(flag ? "nice!" : "oops!");
    }

    public static int[] generateRandomArr(int maxSize, int maxValue) {
        int[] arr = new int[(int) (Math.random() * maxSize)];
        for (int i = 0; i < arr.length; i++) {
            arr[i] = (int) (Math.random() * maxValue) - (int) (Math.random() * maxValue);
        }
        return arr;
    }

    public static void printArr(int[] arr) {
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + "\t");
        }
        System.out.println();
    }

    //生成的随机数组中的数字，相邻不相等。
    public static int[] generateRandomArr2(int maxSize, int maxValue) {
        int[] arr = new int[(int) (Math.random() * maxSize) + 1];
        arr[0] = (int) (Math.random() * maxValue) - (int) (Math.random() * maxValue);
        for (int i = 1; i < arr.length; i++) {
            do {
                arr[i] = (int) (Math.random() * maxValue) - (int) (Math.random() * maxValue);
            } while (arr[i] == arr[i - 1]);
        }
        return arr;
    }

    //用于测试，num位置的数，是不是局部最小。
    public static boolean test(int[] arr, int num) {
        if (arr.length <= 1) {
            return true;
        }
        if (num == 0) {
            return arr[0] < arr[1];
        }
        if (num == arr.length - 1) {
            return arr[num] < arr[num - 1];
        }
        return (arr[num] < arr[num - 1] && arr[num] < arr[num + 1]);
    }

}