Binary Search

二分Index

287. Find the Duplicate Number

Given an array nums containing n + 1 integers where each integer is between 1 and n (inclusive), prove that at least one duplicate number must exist. Assume that there is only one duplicate number, find the duplicate one.
You must not modify the array (assume the array is read only).
You must use only constant, O(1) extra space.
Your runtime complexity should be less than O(n2).
There is only one duplicate number in the array, but it could be repeated more than once.

367. Valid Perfect Square

Given a positive integer num, write a function which returns True if num is a perfect square else False.
Note: Do not use any built-in library function such as sqrt.
Example 1:
Input: 16
Returns: True

用long防止int最大值情况。while的条件是小于等于

    public boolean isPerfectSquare(int num) {
        if (num < 1) return false;
        long start = 1;
        long end = num; // long type to avoid 2147483647 case
        while (start <= end) {
            long mid = (start + end) / 2; 
            if (mid * mid == num) {
                return true;
            } else if (mid * mid > num) {
                // check right half
                end = mid - 1;
            } else {
                // left half
                start =  mid + 1 ;
            }
        }
        return false;
    }