Missing Number, Duplicate Number

268. Missing Number(0-n)
1. XOR
2. BinarySearch

 Arrays.sort(nums);  
   int left = 0, right = nums.length, mid= (left + right)/2;  
   while(left<right){  
     mid = (left + right)/2;  
     if(nums[mid]>mid) right = mid;  
     else left = mid+1;  
   }  
   return left;  

287. Find the Duplicate Number(1-n)
1.hash
2.BinarySearch

162. Find Peak Element
Find one local maximum with binary search.

https://discuss.leetcode.com/topic/29329/java-solution-and-explanation-using-invariants/2