Find Missing Term in Arithmetic Progression 等差数列缺失项

查找等差数列中的缺失项.

e.g.Input: arr[] = {2, 4, 8, 10, 12, 14}

Output: 6

Input: arr[] = {1, 6, 11, 16, 21, 31};

Output: 26.

采用binary search. 若是arr[mid] - arr[left] == (mid - left) * diff, 说明missing 部分在mid右侧.

否则missing部分在包括mid的左侧.

Time complexity: O(logn). Space: O(1).

 public class Main {

     public static void main(String[] args) {
         try{
             int [] arr1 = {2, 4, 8, 10, 12, 14};
             int [] arr2 = {1, 6, 11, 16, 21, 31};
             int [] arr3 = {1, 6};
             System.out.println(findMissing(arr1));
             System.out.println(findMissing(arr2));

             System.out.println(findMissing(arr3));

         }catch(IllegalArgumentException e){
             System.out.println(e.getMessage());
         }
     }

     private static int findMissing(int [] arr) throws IllegalArgumentException{
         if(arr == null || arr.length < 3){
             throw new IllegalArgumentException("Invalid input!");
         }
         int len = arr.length;
         int l = 0;
         int r = len-1;
         int diff = (arr[r] - arr[l])/len;
         System.out.println(diff);
         while(l <= r){
             int mid = l+(r-l)/2;
             if(arr[mid] - arr[l] == (mid-l)*diff){
                 l = mid+1;
             }else{
                 r = mid;
             }
         }
         return arr[r] - diff;
     }
 }