二分搜索

最新推荐文章于 2025-08-03 10:00:00 发布

原创最新推荐文章于 2025-08-03 10:00:00 发布 · 432 阅读

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本文深入探讨了二分查找算法的原理、实现方式及其在不同场景的应用，包括递归与非递归版本，以及如何查找数组中元素的首次和末次出现位置。通过实例演示，帮助读者掌握这一高效搜索算法。

public class BinarySearch {
	
	
	public static Range search(int[] a, int value) throws Exception{
		
		if(a == null || a.length==0){
			throw new Exception("a is not valid input.");
		}
		if((value < a[0]) || (value > a[a.length-1])){
			throw new Exception("a is not in the range.");
		}
		if(value == a[0]){
			return new Range(a[0], a[0]);
		}
		if(value == a[a.length-1]){
			return new Range(a[a.length-1], a[a.length-1]);
		}
		
		return binarySearch(a, 0, a.length-1, value);
	}
	
	private static Range binarySearch(int[] a, int left, int right, int value) {
		if((right-left) == 1){
			return new Range(a[left], a[right]);
		}
		int mid = (left + right)/2;
		if(value == a[mid]){
			return new Range(a[mid], a[mid]);
		}
		if(value < a[mid]){
			return binarySearch(a, left, mid, value);
		}else{
			return binarySearch(a, mid, right, value);
		}
	}
	
	/**
	 * 非递归二分搜索
	 * @param a
	 * @param b
	 * @return
	 */
	public static int bSearch(int[] a, int b){
		int begin = 0;
		int end = a.length-1;
		while(begin <= end){
			int mid = (begin+end)/2;
			if(b == a[mid]){
				return b;
			}else if(b < a[mid]){
				end = mid - 1;
			}else{
				begin = mid + 1;
			}
		}
		return -1;
	}
	/**
	 * 返回第一次出现的位置。
	 * @param a
	 * @param b
	 * @return
	 */
	public static int bSearchFirst(int[] a, int b){
		int begin = 0;
		int end = a.length-1;
		int p = -1;
		while(begin <= end){
			int mid = (begin+end)/2;
			if(b == a[mid]){
				end = mid - 1;
				p = mid;
			}else if(b < a[mid]){
				end = mid - 1;
			}else{
				begin = mid + 1;
			}
		}
		return p;
	}
	
	/**
	 * 返回最后一次出现的位置。
	 * @param a
	 * @param b
	 * @return
	 */
	public static int bSearchLast(int[] a, int b){
		int begin = 0;
		int end = a.length-1;
		int p = -1;
		while(begin <= end){
			int mid = (begin+end)/2;
			if(b == a[mid]){
				begin = mid + 1;
				p = mid;
			}else if(b < a[mid]){
				end = mid - 1;
			}else{
				begin = mid + 1;
			}
		}
		return p;
	}
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		int[] a = {1,2,3,4,6,7,8,8,8,9};

		try {
			Range result = BinarySearch.search(a, 5);
			System.out.println(result.left + "   " + result.right);
		} catch (Exception e) {
			// TODO Auto-generated catch block
			e.printStackTrace();
		}
		
		
		int x = BinarySearch.bSearch(a, 9);
		System.out.println(x);
		
		x = BinarySearch.bSearchFirst(a, 8);
		System.out.println(x);
		
		x = BinarySearch.bSearchLast(a, 8);
		System.out.println(x);
	}
	
	public static class Range{
		public int left;
		public int right;
		
		public Range(int left, int right){
			this.left = left;
			this.right = right;
		}
	}

}