题目:
Follow up for "Search in Rotated Sorted Array":
What if duplicates are allowed?
Would this affect the run-time complexity? How and why?
Write a function to determine if a given target is in the array.
题解:
这道题与之前Search in Rotated Sorted Array类似,问题只在于存在dupilcate。那么和之前那道题的解法区别就是,不能通过比较A[mid]和边缘值来确定哪边是有序的,会出现A[mid]与边缘值相等的状态。所以,解决方法就是对于A[mid]==A[low]和A[mid]==A[high]单独处理。
当中间值与边缘值相等时,让指向边缘值的指针分别往前移动,忽略掉这个相同点,再用之前的方法判断即可。
这一改变增加了时间复杂度,试想一个数组有同一数字组成{1,1,1,1,1},target=2, 那么这个算法就会将整个数组遍历,时间复杂度由O(logn)升到O(n)
实现代码如下:
1 public boolean search(int [] A,int target){ 2 if(A==null||A.length==0) 3 return false; 4 5 int low = 0; 6 int high = A.length-1; 7 8 while(low <= high){ 9 int mid = (low + high)/2; if(target < A[mid]){ if(A[mid]<A[high])//right side is sorted high = mid - 1;//target must in left side else if(A[mid]==A[high])//cannot tell right is sorted, move pointer high high--; else//left side is sorted if(target<A[low]) low = mid + 1; else high = mid - 1; }else if(target > A[mid]){ if(A[low]<A[mid])//left side is sorted low = mid + 1;//target must in right side else if(A[low]==A[mid])//cannot tell left is sorted, move pointer low low++; else//right side is sorted if(target>A[high]) high = mid - 1; else low = mid + 1; }else return true; } return false; }
Reference: http://blog.csdn.net/linhuanmars/article/details/20588511