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;

	}