答复: 一道算法题，百思不得其解，求指导[非降序列找目标项，二分法变体]

正确解看此链接
http://www.cnblogs.com/sunyongyue/archive/2010/12/04/1896675.html
这个条件粗看起来不是很靠谱，事实上却很好用

代码实现如下，

import java.util.Arrays;

public class AiEqualsISearcher {
	private static int ARR_LENGTH = 100;
	private int[] numArr = new int[ARR_LENGTH];
	private int stepCount = 0;

	private void init() {
		int targetElement = (int) (Math.random() * (ARR_LENGTH - 1));
		numArr[targetElement] = targetElement;
		int num = targetElement - 1;
		while (num >= 0) {
			int tmp = (int) (Math.random() * 3);
			numArr[num] = numArr[num + 1] - tmp;
			if (numArr[num] == num) {
				numArr[num] = num - 1;
			}
			num--;
		}
		for (int i = targetElement + 1; i < ARR_LENGTH; i++) {
			int tmp = (int) (Math.random() * 5);
			numArr[i] = numArr[i - 1] + tmp;
			if (numArr[i] == i) {
				numArr[i] = i + 1;
			}
		}
		System.out.println("the num arr init as " + Arrays.toString(numArr));
		System.out.println("the target index is " + targetElement);
	}

	private int search(int start, int end) {
		System.out.println("check a[" + start + "," + end + "]");
		stepCount++;
		int middle = (start + end) / 2;
		if (numArr[middle] == middle) {
			return middle;
		}
		if (start >= end) {
			return -1;
		}
		if (end >= numArr[middle]) { // && numArr[end] >= middle
			int result = search(middle + 1, end);
			if (result != -1) {
				return result;
			} else {
				return search(start, middle - 1);
			}
		} else {
			System.out
					.println("a[" + middle + "," + end + "] no need to check");
			return search(start, middle - 1);
		}
	}

	public static void main(String[] args) {
		AiEqualsISearcher searchAi = new AiEqualsISearcher();
		searchAi.init();
		System.out.println("\nstart to search...");
		int i = searchAi.search(0, AiEqualsISearcher.ARR_LENGTH - 1);
		if (i >= 0) {
			System.out.println("find a[" + i + "]=" + i + " with "
					+ searchAi.stepCount + " steps ");
		} else {
			System.out.println("can't find the element");
		}
	}
}