Algorithms | Learn for Master

Leetcode - Longest common prefix

July 26, 2016 Author: david
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Longest common prefix

Write a function to find the longest common prefix string amongst an array of strings.

Pay attention to the corner case: strs can be empty.

Analysis

We define cur to record the char at current round that is recorded by si.

If si equals to the current string’s length, we return the substring from 0 to si.

At the beginning of each round, cur is set as null.

So when cur is null, we know this is the first string to check in current round. We set cur as the letter of the current string at index si

For the following string,
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Leetcode - Roman to Integer (Java)

July 26, 2016 Author: david
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Given a roman numeral, convert it to an integer.

Input is guaranteed to be within the range from 1 to 3999.

Analysis

The rules to transfer a roman to an integer can be understood using the following examples:

I == 1 II == 2 III == 3 IV == 4 V == 5 VI == 6 VII == 7 VIII == 8 IX = 9 X== 10, XI == 11, XL == 40, L == 50, LX == 60

1

I == 1 II == 2 III == 3 IV == 4 V == 5 VI == 6 VII == 7 VIII == 8 IX = 9 X== 10, XI == 11, XL == 40, L == 50, LX == 60

So for any two Roman letters in the form: Left Right

if the left is smaller than the right, the result will be right - left.

if the left is larger or equal to the right, the result will right + left.

See this link for more examples of the roman numbers.
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binary search - first bad version

July 26, 2016 Author: david
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You are a product manager and currently leading a team to develop a new product. Unfortunately, the latest version of your product fails the quality check. Since each version is developed based on the previous version, all the versions after a bad version are also bad.

Suppose you have n versions [1, 2, …, n] and you want to find out the first bad one, which causes all the following ones to be bad.

You are given an API bool isBadVersion(version) which will return whether version is bad. Implement a function to find the first bad version.
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System design interview- consistent hash

July 25, 2016 Author: david
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Consistent hashing is a simple yet powerful solution to a popular problem: how to locate a server in a distributed environment to store or get a value identified by a key, while handle server failures and network change?

A simple method is number the servers from 0 to N - 1. To store or retrieve a value V, we can use Hash(V) % N to get the id of the server.

However, this method does not work well when 1) some servers failed in the network (e.g, N changes) or 2) new machines are added to the server.
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System design interview- tinyurl service

July 25, 2016 Author: david
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How to design a tinyurl service is one of the most popular interview questions. It is often asked in the third or fourth round as the big data design interview question. To master tinyurl design, you need to be familiar with Base Conversion of Numbers, and Consistent Hash algorithm.

So what is tinyutl service? It is a URL service that can provide a map between a shorter and unique url to a long URL provided by a user.

For instance, “http://wp.me/p7Eshi-o3” is the tiny url for the current page. Typically,
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Quicksort algorithm

July 24, 2016 Author: david
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Quicksort is one of the most famous sort algorithms because of its average good performance. Because of its importance and popularity, it is usually asked in technique interviews. It is also important to master QuickSort as its partitioning technique can also be used to find the Kth largest or smallest element of an array in O(n) time with O(1) space complexity.

How quickSort algorithm works

Given an array A[s … e], a pivot is chosen to rearrange the array into two parts: ALeft and Aright. All the elements in ALeft are less than or equal to the pivot,
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LeetCode – Merge Sorted Array without extra space

July 24, 2016 Author: david
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Given two sorted integer arrays A and B, merge B into A as one sorted array.

Note:
You may assume that A has enough space to hold additional elements from B. The number of elements initialized in A and B are m and n respectively.

Analysis

We have described how to merge two sorted arrays into a third sorted array. For this problem, as A is assumed to have enough space, we are not allowed to create a third array.

We cannot start the merge from the beginning of the two arrays,
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Merge two sorted arrays algorithm (Java)

July 24, 2016 Author: david
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Given two sorted arrays or lists, how to merge them into a sorted array?

This is a fundamental problem as it is a common requirement to merge two sorted arrays into one sorted array. The algorithm of merging two sorted arrays is also the basics of the one of the most famous sort algorithms: merge sort.

Suppose there are two sorted arrays A and B, and we want to merge them into a third Array C.

We define three indexes a, b, c, which points to the beginning of the three arrays A, B,
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LeetCode – Median of Two Sorted Arrays Java Solution

July 24, 2016 Author: david
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There are two sorted arrays nums1 and nums2 of size m and n respectively.

Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)).

Example 1:

nums1 = [1, 3] nums2 = [2] The median is 2.0

1
2
3
4
5

nums1 = [1, 3]
nums2 = [2]

The median is 2.0

Example 2:

nums1 = [1, 2] nums2 = [3, 4] The median is (2 + 3)/2 = 2.5

1
2
3
4

nums1 = [1, 2]
nums2 = [3, 4]

The median is (2 + 3)/2 = 2.5

Analysis

It is easy to come up with a O(n) solution. Then it is high likely that the interviewer will ask you to give the algorithm with time complexity O(logn).

For any problem with sorted array, to come up with a O(logN) solution, we should consider the binary search related algorithm.
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Chi Square test for feature selection

July 23, 2016 Author: david
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Feature selection is an important problem in Machine learning. There are many feature selection methods available such as mutual information, information gain, and chi square test. In this post, I will use simple examples to describe how to conduct feature selection using chi square test. I will show that it is easy to use Spark or MapReduce to conduct chi square test based feature selection on large scale data set.

Problem Statement

Suppose there are N instances, and two classes: positive and negative. Given a feature X, we can use Chi Square Test to evaluate its importance to distinguish the class.
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