Max Points on a Line

Given n points on a 2D plane, find the maximum number of points that lie on the same straight line.

Essentially this problem is equivalent to find all unique lines. Note that each line can be represented by a pair: slope and a fixed point. Here, we use the point where y = 0. If y = 0 is impossible, we use the point where x = 0. Also, we use a map to store the line and the points which lie on this line.


Comments

Post a Comment

Popular posts from this blog

Maximum Gap

Given an unsorted array, find the maximum difference between the successive elements in its sorted form.  Try to solve it in linear time/space.  Return 0 if the array contains less than 2 elements. You may assume all elements in the array are non-negative integers and fit in the 32-bit signed integer range. In order to solve this in linear time, we cannot use general sorting algorithm. Here we use bucket sort. First, we scan the array to find the min and the max values.   We can then create n - 1 buckets with equal size. Suppose we have n elements in total, then we have n - 2 elements except the min and the max. Scan the array again to put the n - 2 elements into these buckets. We should have at least one empty bucket. For each bucket, we record the min and the max for all the elements within that bucket.  Finally, we scan all the buckets, and maintain the maximum gap. Note that the maximum gap between the successive elements in the sorted array can only be the gap between
Read more

[ITint5] Maximum Subarray for a Circular Array

http://www.itint5.com/oj/#8 Classic DP problem, which has also appeared in Leetcode as Maximum subarray . The only difference is, in this problem, empty subarray (where sum is 0) is allowed. So instead of return ret, we could simply return max(0, ret). http://www.itint5.com/oj/#9 Calculate the maximum subarray for a circular array. For example, [1, 3, -2, 6, -1], we should return 9 since 6 + (-1) + 1 + 3 = 9. The following solution might not be optimized. Suppose that the maximum subarray is from A[i] to A[j]. The idea is, consider the following different scenarios: i <= j: it is the same as classic problem. i > j: the sum is A[i : end] + A[start : j]. So we can use two additional arrays: left[j] = maximum subarray, starts from A[start] and ends no later than A[j] right[i] = maximum subarray, starts no earlier than A[i] and ends at A[end] The following code passes the online judge. However, we need O(4n) in time and O(2n) in space. Not sure how to improve this.
Read more

[CC150] Chapter 8 Object-Oriented Design

8.1 Design the data structure for a generic deck of cards. Explain how you would subclass the data structures to implement blackjack. Following codes implement blackjack. Note that syntax highlighter automatically changes some upper case letters to lower case.   8.2 Imagine you have a call center with three levels of employees: respondent, manager, and director. An incoming telephone call must be first allocated to a respondent who is free. If the respondent can't handle the call, he or she must escalate the call to a manager. If the manager is not free or not able to handle it, then the call should be escalated to a director. Design the classes and data structures for this problem. Implement a method dispatchCall() which assigns a call to the first available employee. 8.3 Design a musical jukebox using object-oriented principles. 8.4 Design a parking lot using object-oriented principles. 8.5 Design the data structures for an online book reader system. 8.6 Implement a ji
Read more