Problem
Given a sorted array of n integers, find the starting and ending position ofa given target value. If the target is not found in the array, return [-1, -1].
Example
Given [5, 7, 7, 8, 8, 10] and target value 8, return [3, 4]
题解
lower/upper bound 的结合,做两次搜索即可。
JAVA:
import java.io.*; class test { public static void main (String[] args) throws java.lang.Exception { int arr[] = {5, 7, 7, 8, 8, 10}; int target = 8; int range[] = searchRange(arr, target); System.out.println("range is " + range[0] + " - " + range[1]); } public static int[] searchRange(int[] A, int target) { int[] result = new int[]{-1, -1}; if (A == null || A.length == 0) return result; int lb = -1, ub = A.length; // lower bound while (lb + 1 < ub) { int mid = lb + (ub - lb) / 2; if (A[mid] < target) { lb = mid; } else { ub = mid; } } // whether A[lb + 1] == target, check lb + 1 first if ((lb + 1 < A.length) && (A[lb + 1] == target)) { result[0] = lb + 1; } else { result[0] = -1; result[1] = -1; // target is not in the array return result; } // upper bound, since ub >= lb, we do not reset lb ub = A.length; while (lb + 1 < ub) { int mid = lb + (ub - lb) / 2; if (A[mid] > target) { ub = mid; } else { lb = mid; } } // target must exist in the array result[1] = ub - 1; return result; } }
输出:
range is 3 - 4
源码分析
1. 首先对输入做异常处理,数组为空或者长度为0
2. 分 lower/upper bound 两次搜索,注意如果在 lower bound 阶段未找到目标值时,upper bound 也一定找不到。
3. 取A[lb + 1]
时一定要注意判断索引是否越界!
复杂度分析
两次二分搜索,时间复杂度仍为 O(logn).
原创文章,作者:奋斗,如若转载,请注明出处:https://blog.ytso.com/20717.html