my understanding of (lower bound,upper bound) binary search, in C++, thanks to two post

If you understand the comments below, never will you make mistakes with binary search!
thanks to A simple CPP solution with lower_bound
and C++ O(logn) Binary Search that handles duplicate, thanks to phu1ku ‘s answer on the second post.
http://en.cppreference.com/w/cpp/algorithm/upper_bound
Returns an iterator pointing to the first element in the range [first, last) that is greater than value.
http://en.cppreference.com/w/cpp/algorithm/lower_bound
Returns an iterator pointing to the first element in the range [first, last) that is not less than (i.e. greater or equal to) value.

If want to practice, code on your own, try https://leetcode.com/problems/search-insert-position/ , https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/ , https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/ and https://leetcode.com/problems/search-a-2d-matrix-ii/ , and see the discusses.

int binarySearch(vector<int>& nums, int target) {    /// return index of first one that comp(item,target)==true, or nums.size() if not found    /// comp is greater or equal to for lower_bound    /// comp is greater for upper_bound    int first=0, last=nums.size(), mid;    while (first<last) {        mid=first+((last-first)>>1); // first<=mid, mid<last        /// if comp(item,target)==false, advance first        // if(nums[mid]<=target) // for upper_bound        if (nums[mid]<target) // for lower_bound        first=mid+1; // first always increases        else /// else recede last        last=mid; // last always decreases (even last-first==1)    }    return first;}

def bsearch(seq, key):    """    return index of first item in seq such that key(item) is true,     if no such item exist, return len(seq)    """    l, r = 0, len(seq)    while l<r:        mid = l+(r-l)/2        if key(seq[mid]):            r = mid        else:            l = mid + 1    return r