binary search

binary search

binary search time complexity = O(logn)

the question usually give you a sorted array and then find a target(index) in the value:
the biggest number which less than and euqall to 5

index	value	description
0	1
1	2	the biggest index which less than 3 (小于3的是这些 2是最大的index了)
2	3	the smallet index which bigger and equal than 3
3	3	any index which equal to 3
4	3	biggest index which less than and equal to 3
5	5	the smallest index which bigger than 3
6	7
7	9
8	10

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** the times of appearing 3 = the smallest index of bigger than 3 - the biggest index of less than 3**

Exponential backoff (倍增法)

sorted by non-decreasing array + big array + target value;

• 1.首先在非常大的数组中得到一个稳定的长度
  range=1； getValue(n*2-1) 因为index是 range的数值-1，
• 2 。