为什么这个二分搜索实现会导致溢出

Question

In the implementation of binary search

int search(int[] A, int K) {
  int l = 0;
  int u = A.length - 1;
  int m
  while ( l <= u ) {
     m = (l+u)/2; // why this can cause overflow
     ...
  }
}

The correct method is as follows:

m = l + (u -l )/2;

I don't know why the updated statement has no overflow issue. Based on my understanding, soon or later, the updated statement will also have overflow issue.

Thank you

Answer 1

The orignal may have overflow because l+u could be greater than the maximum value an int can handle (eg if both l and u were INT_MAX then their sum would obviously exceed INT_MAX ).

The correct method can't overflow, because ul obviously won't overflow, and l+(ul)/2 is guaranteed to be <=u , so can't overflow either.

Answer 2

The initial Calculation of m = (l+u)/2 create overflow due to addition of very large numbers . So , Difference of these numbers does not cause this overflow condition ,that's why we are calculating m=l+(ul)/2 using this formula . Hope you got your answer