二分查找及变形

二分查找是在完全有序数组(或部分有序)中对某一元素进行快速查找的算法。时间复杂度为O(logn)。

实现方式有递归和非递归。

非递归实现

	public int binarySearch(int[] nums, int key) {
		if (nums == null || nums.length == 0) {
			return -1;
		}

		int low = 0, high = nums.length - 1;
		while (low <= high) {
			int mid = low + (high - low) / 2;
			if (nums[mid] == key) {
				return mid;
			}
			if (nums[mid] < key) {
				low = mid + 1;
			} else {
				high = mid - 1;
			}
		}

		return -1;
	}

变形1：查找数组中最接近某一元素（即小于）的元素位置。

	public int findMaxMin(int[] nums, int key) {
		if (nums == null || nums.length == 0) {
			return -1;
		}

		int low = 0, high = nums.length - 1;
		while (low + 1 < high) {
			int mid = low + (high - low) / 2;
			if (nums[mid] < key) {
				low = mid;
			} else {
				high = mid - 1;
			}
		}
		
		if (nums[high] < key) {
			return high;
		}
		if (nums[low] < key) {
			return low;
		}
		
		return -1;
	}