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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).
1 public class Main { 2 3 public static void main(String[] args) { 4 try{ 5 int [] arr1 = {2, 4, 8, 10, 12, 14}; 6 int [] arr2 = {1, 6, 11, 16, 21, 31}; 7 int [] arr3 = {1, 6}; 8 System.out.println(findMissing(arr1)); 9 System.out.println(findMissing(arr2)); 10 11 System.out.println(findMissing(arr3)); 12 13 }catch(IllegalArgumentException e){ 14 System.out.println(e.getMessage()); 15 } 16 } 17 18 private static int findMissing(int [] arr) throws IllegalArgumentException{ 19 if(arr == null || arr.length < 3){ 20 throw new IllegalArgumentException("Invalid input!"); 21 } 22 int len = arr.length; 23 int l = 0; 24 int r = len-1; 25 int diff = (arr[r] - arr[l])/len; 26 System.out.println(diff); 27 while(l <= r){ 28 int mid = l+(r-l)/2; 29 if(arr[mid] - arr[l] == (mid-l)*diff){ 30 l = mid+1; 31 }else{ 32 r = mid; 33 } 34 } 35 return arr[r] - diff; 36 } 37 }
Find Missing Term in Arithmetic Progression 等差数列缺失项
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原文地址:http://www.cnblogs.com/Dylan-Java-NYC/p/5335588.html