Khoa Nguyen

The Neuroscience of Artificial Intelligence

2017-05-03T15:41:19+00:00

Abstract

Artificial intelligence (AI) has been on a steady rise for the last 20 years, inspired by the improved understanding of the brain and implemented with mathematics. It has achieved several feats, including driving cars, beating humans at Go and poker, and even creating art works and music. Yet there are still limitations to what AI can do, such as detecting sarcasm or recognizing features in low-resolution images, which may be explain in part by limited computing power and our lack of a total understanding of the human brain. This article explores the history and connection between the state of AI and what we currently know about the human brain, and compares the learning process in humans and AI alike.

Introduction to Artificial Intelligence (AI)

The idea of a “thinking” machine has been around for more than half a century, as long as the existence of computers itself, starting with Alan Turing proposing the Turing Test in the 1950s. A machine would pass the Turing Test if it can fool humans into thinking the machine is also a human ¹. The interest in machine learning (ML) and artificial intelligence (AI) was restrained by the limited computing power of the time, but has become stronger and stronger as technology develops into what we have today. Now, chatbots are regularly deployed in Facebook Messenger and Slack chat groups, ML algorithms choose what ads you should see on a website, and the AIs of tech companies are beating human champions at poker and Go, two of the most difficult strategy games even for humans to master. People are worried that ultimately, automatons would replace all humans at what we used to be the best at. And yet, AIs are still not at the same level as humans on understanding nuanced speech, sarcasm, or body language, for example. Sometimes, the line between “easy” and “difficult” can be blurry.

(Photo credit: xkcd.com) Well, for a computer, knowing the national park where the photo is taken is easier than knowing that there is a bird in it. On the other hand, any normally developed 4-year-old toddler can tell you that’s a bird, but they might have no idea what national park it’s in.

The Love Story of Neuroscience and Artificial Intelligence

Researchers thought of modeling a “smart” machine after the human brain surprisingly early in 1957, when Frank Rosenblatt designed the perceptron after the neurons, and created the first neural network ¹. A perceptron is binary, meaning it takes the value 1 if a certain condition is met, and 0 otherwise ². It is similar to the way a neuron only fires an action potential when it reaches a certain threshold. An action potential is one of the ways neurons communicate with each other, and that is also how perceptrons in a network connect with each other to learn a certain concept. It did not take long for researchers to realize that a network of perceptrons were not capable of many things, which now makes sense when we compare it with the complex, definitely non-binary functionality of neurons. They need better networks of units, appropriately named “neural networks” and “neurons” respectively, in order for the machines to get smarter.

The perceptron signals the start of computer science research looking at nature, especially the mammal brain, for inspirations, although much of the theory and implementation rely on mathematical and computer science knowledge. More algorithms are created, notably recurrent neural networks and deep learning networks. Comparing these networks (left) with the drawings of human hippocampus stained with Golgi’s method (right) below, can you see the similarities? (Photo credit: Wikipedia and Wikimedia Commons)

The Classification Problem, Or, Teaching A Toddler How To Recognize Objects

Perhaps you remember all those years you’ve spent as a toddler learning how to recognize the different shapes, animals, things, or parts of your body by your caregivers telling you what is what and answering all of your silly questions. Perhaps not, but you might have seen somebody else’s child going through the same phase. The child looks at the object and her brain takes in its image. Then she points to it and asks you, “What’s that?” And you answer, “Honey it’s a cat.” Enough times of the child asking and you answering, and the child’s brain registers in some cluster of neurons that this thing is identified as a “cat”.

The same process applies to training a neural network. You feed the computer not one, but many, many images of cats taken from different angles, in different settings, of different breeds, so that it can extract features of cats from these pictures, and calibrate the weights on the connections of its neurons to respond to those features. Eventually, at some point after a lot of pictures, it should be able to reliably tell if it’s looking at a cat or not. Sometimes it can be wrong, but hey, humans do that sometimes too. Incidentally, differentiating between cats and dogs was a classic classification problem for AI researchers in the 1980s and 1990s ³. Now, advances in AI give us something like https://quickdraw.withgoogle.com or https://www.autodraw.com. You can click on the links to contribute your doodles to training a super-toddler AI created by Google in solving the very classic problem of classification!

Limits of AI

Nature has spent million of years on evolution to reach the wonder that is the human brain. Technology has just begun little more than 50 years ago, barely scratching the surface of what our brain is capable of. No AI has yet the ability to process such an enormous amount of sensory input and combine this data in unique ways every second during the decades of a human lifespan without overheating. Tugui ⁴ successfully summarizes the limitations of AI into the following points:

Nature follows the law of entropy to reach stabilization in any system. AI does not (but it needs to).
The foundations of AI is based on procedures that may restrict the successful mimicking of actual neural activity.
AI is founded upon computer science, and computer science is founded upon 0 and 1 (or True and False). Nature is very non-binary.
AI uses symbolic logic based on True/False, while natural intelligence (i.e. human’s intelligence) is much more fluid.

Our job is to increase the currently limited flow of knowledge between neuroscience and AI research, because even though the two fields would help each other tremendously, current advances in AI and neuroscience are often disconnected ⁵. Understanding the human brain, and the relationship between neuroscience and artificial intelligence, is the key to help the currently toddler-AI grow into an adult one.

References

Marr, Bernard. “A Short History of Machine Learning.” Forbes. Forbes Magazine, 08 Mar. 2016. Web. 03 May 2017. https://www.forbes.com/sites/bernardmarr/2016/02/19/a-short-history-of-machine-learning-every-manager-should-read/#1e7cdec15e78. ↩ ↩²
Mitchell, Tom M. 1. Machine Learning. McGraw-Hill, New York, 1997. ↩
Lewis-kraus, Gideon. “The Great A.I. Awakening.” The New York Times. The New York Times, 14 Dec. 2016. Web. 04 May 2017. https://www.nytimes.com/2016/12/14/magazine/the-great-ai-awakening.html. ↩
Tugui, Alexandru. 2004. “Reflections on the Limits of Artificial Intelligence”. Ubiquity 2004, December (December 2004), 2-2. DOI=http://dx.doi.org/10.1145/1041062.1041064 ↩
Potter, Steve M. “What Can AI Get from Neuroscience?” Lecture Notes in Computer Science (including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 4850. 2007. 174-85. Web. 2 Feb. 2017. ↩

One Year Later, or How Grace Hopper Conference Is Totally Worth It

2017-03-17T22:41:19+00:00

A year after my very first interview with a tech company outside my college campus, a lot of things have changed. I’ve changed. It feels good to make that first interview snowball into a year of asking forerunners for advice, practicing algorithms, finding a hidden obsession (almost) with programming competitions, and embracing myself as a woman in tech.

I let go most of the emotional baggage of past failures. Some I keep for motivational purposes. A quote I read somewhere (probably an answer on Quora) finally stopped me from questioning the college choices I made as a high school senior. It was along the line of, “Don’t be proud of the school you go to, do something that makes your school proud.”

Late March 2016. I reached out and connected with people in different parts of the world whom I may or may not have known well, but could give me helpful advice. One of my closest friends suggested I applied for Grace Hopper Conference (GHC) after I shared the news of Facebook’s rejection with him. Coincidentally, as luck would have it, this happened when the original deadline for GHC scholarship was extended due to some technical difficulties. Within little more than a week before the final deadline, I asked my amazing professor to write me a recommendation letter, wrote my scholarship essay and my poster proposal, and sent the application away in April.

In the meantime, I set a small goal of doing at least 1 problem on LeetCode OJ a week. I got frustrated with myself for being slow at first, but as time went on, I didn’t have to look up language reference as much, I solved some hard-level problems myself, and stuff from my Algorithm Analysis course came back to me. I knew I had one last shot at a software engineering internship as an undergraduate for the summer after my junior year, and I was determined to make it count.

The GHC scholarship acceptance email came in June. The GHC resume database got online shortly after, and I immediately sent mine in. Emails from recruiters started to arrive. In late August, a Google recruiter contacted me. She was one of the nicest, most helpful, and prompt people I’ve ever worked with. Google became my first coding interview experience in late September with 2 back-to-back phone/Google Docs interviews. I had my 3rd one with them in late October and got to the host matching stage, but at that point I had another pressing deadline and couldn’t wait out the host-matching timeline :(

In October, being at GHC in Houston, Texas was surreal. Not wanting to waste any second at GHC, I woke up at 6am everyday, took the first bus from the hotel to the conference site, and scheduled my 3 days out in advance, filling it with as many workshops/talks/interviews/sponsored events as I could from 8am to 8-9pm. My first Software Engineer internship offer came from Intuit. My most memorable interview experience came from Pure Storage. That interview was supposed to be an hour long. It actually lasted an hour and 40 minutes. 20 minutes in, I already ran out of knowledge from the Intro to Operating Systems course I was taking at the time, but I tried my best to catch up with what my interviewer was saying about multithreaded programming, and applied it to the problem in front of me that kept being added more and more conditions to. I learned more during that interview than any other. After GHC, they told me I was in for the next round of interviews, but I had to decline because I already accepted Intuit’s offer, and didn’t want to waste their resources, but they left quite an impression on me for sure! Also, I got to make a tech joke with my poster slot:

A week after I got back from GHC, it was the ACM Regional. My team solved 2 problems out of 10, just like the team last year, and the year before. I got the competitive programming bug ever since. We went again to Denison Spring Programming Contest 2017 in February where we ranked 7th out of 22 teams total, but we could have ranked 3rd or 4th if I hadn’t missed 2 lines in my code in the last 15 minutes of the competition that would have made another successful submission. I’m out for blood this coming ACM Regional, not exactly to reach the World Finals, but at least to break the 2-problem-per-year curse that my college seems to be stuck with. I really look forward to Google Code Jam this April for the same rush of both frustration and instant gratification. Why I choose to go on such emotional roller coaster rides, I don’t know entirely, but it’s fun!

Now, I look forward to the future. Just gotta finish my senior thesis first :) After GHC, I’m more aware of my status as a woman in tech than ever. We’ve all seen stories about the current situation in the tech industry regarding diversity, but I always have hopes, maybe a little more than allowed, in everything :)

Configure hostednetwork (WiFi Hotspot) on Windows 7

2016-12-20T22:41:19+00:00

A few years ago I visited a home where there was only a Dell desktop with Windows 7 and cabled Internet in the house, and no WiFi. My host gave me the administrator account on the computer to use while she went on vacation. I wanted to use wifi on my laptop and phone so badly, so I tried to figure out whether it was possible to set up a WiFi hotspot on this desktop. It took me more hours than I’d like to admit, so to save you some pain in the posterior, below are the steps to follow. (It might work on other Windows versions too, but no guarantee).

Make sure your hardware supports a wireless hotspot, and is connected to the Internet. Google if needed. You probably will need to know the brand and model number of your computer. If yes, continue. If no, sorry - I guess you’ll have to buy a WiFi hub/router/etc.
In File Explorer, search for a folder named RtBackup, delete all files in it, then changed the folder’s name to ANYTHING other than its original name. The last time I did this hack, this folder resides in C:\Windows\System32\LogFiles\WMI.
Go to Start and search for Windows Services tool. *IMPORTANT: Start the Windows Event Log service FIRST. Then start SSTP (Secure Socket Tunneling Protocol Service). Without these 2, the rest won’t work. By “the rest,” I mean to start the following services:

Application Layer Gateway Service
Network Connections
Network Location Awareness (NLA)
Plug And Play
Remote Access Auto Connection Manager
Remote Access Connection Manager
Remote Procedure Call (RPC)
Telephony

After the little hack above, we are ready to follow the official instructions posted on Dell’s website at http://www.dell.com/support/article/us/en/04/SLN208643/EN. The entire content of this article is reproduced here for your convenience.

The adapter for the connection is Microsoft Virtual WiFi Miniport Adapter. If there is problem setting this up, go to Start -> search for Device Manager -> Network -> reinstall driver for this adapter.
Hit the Start button, and type “Command Prompt” or “cmd” on the search box. If your computer is based on Windows 8, you’ll need to press the keyboard’s Windows logo key to switch to the system’s Modern UI Style and type “Command Prompt” or “cmd.” Run Command Prompt with admin rights. To do that, right-click on the Command Prompt icon and select “Run as administrator.”
Type “netsh wlan show drivers” (without the quotation marks) in Command Prompt to check whether or not your computer supports a hosted network. The “Hosted network supported” field should indicate “Yes” if your unit supports WiFi sharing. If it says “No,” you’ll have to download the corresponding driver for your WiFi adapter first before proceeding.
To create a hotspot, type “netsh wlan set hostednetwork mode=allow ssid=yournetworkname key=yournetworkpassword,” and hit Enter on your keyboard. Remember, “ssid” refers to the WiFi hotspot’s name while “key” is said network’s password. You can also use the aforementioned command to change the hotspot’s name and password.
To get the hotspot up and running, type “netsh wlan start hostednetwork.” Make sure your computer’s WiFi adapter is also switched on, or the hotspot won’t work at all.
Again, hit the Start button. Type “Network and Sharing Center,” and left-click on it. If you’re using a Windows-based unit, you probably know what to do by now. (Switch to Modern UI Style, and type “Network and Sharing Center.”)
Select “Change adapter settings,” which can be found on the left-hand side of the window. Both the network connection you want to share and your newly created WiFi hotspot are shown here. Choose the network connection you wish to share. Right click on it, select “Properties,” and go to the “Sharing” tab. Check the option “Allow other network users to connect through this computer’s Internet connection.” This time, select the WiFi hotspot you created earlier.
To turn off your hotspot, type “netsh wlan stop hostednetwork” in Command Prompt.

Best of luck! I hope you won’t have to spend so much time wading through useless answers on Microsoft’s help forum or Yahoo! Answers like I did :)

Cryptography: Cracking Codes

2016-10-10T22:41:19+00:00

I did the problem below as an optional programming assignment for the course Cryptography on Coursera, offered by the University of Maryland in their Cybersecurity Specialization.

Problem Statement:

Numbered below are 7 ciphertexts, each of which was generated by encrypting some 31-character ASCII plaintext with the one-time pad using the same key (code for the encryption program used is given below). Decrypt them and recover all 7 plaintexts, each of which is a grammatically correct English sentence. Note: for this problem it is easiest to use a combination of automated analysis plus human insight and even occasional guessing. As long as you can decrypt them all, it doesn’t matter how you do it.

1. BB 3A 65 F6 F0 03 4F A9 57 F6 A7 67 69 9C E7 FA BA 85 5A FB 4F 2B 52 0A EA D6 12 94 4A 80 1E

2. BA 7F 24 F2 A3 53 57 A0 5C B8 A1 67 62 C5 A6 AA AC 92 4A E6 44 7F 06 08 A3 D1 13 88 56 9A 1E

3. A6 72 61 BB B3 06 51 BA 5C F6 BA 29 7E D0 E7 B4 E9 89 4A A9 5E 30 02 47 F0 C0 02 8F 40 9A 1E

4. A5 72 61 F5 F0 00 4B A7 4C F4 AA 29 79 D9 A6 B7 AC 85 4D A9 5E 30 52 03 EC 85 15 95 4C 9D 0F

5. BB 3A 70 F3 B9 1D 48 E8 4D F0 AB 70 2E CF EE B5 BC 8C 5D A9 4C 30 1E 0B EC D2 41 95 4C 83 1E

6. A6 72 6D E8 F0 1A 50 E8 49 ED BC 6C 7C 9C F2 B2 A8 8E 19 FD 42 3E 06 47 EC CB 04 DD 4C 9D 1E

7. BC 75 70 BB BF 1D 46 E8 5A F9 AA 6C 7A 9C EF A9 E9 82 5C FD 5E 3A 00 47 F7 CD 00 93 05 A7 1E

Here is the code of the encryption program:

#include 
#define KEY_LENGTH 31
 
main(){
  unsigned char ch;
  FILE *fpIn, *fpOut;
  int i;
  unsigned char key[KEY_LENGTH] = {0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00, 0x00,
  0x00, 0x00, 0x00};
  // Of course, I did not use the all-0 key when generating the 7 ciphertexts above!
 
  fpIn = fopen("messages.txt", "r");
  fpOut = fopen("ctexts.txt", "w");
 
  i=0;
 
  while (fscanf(fpIn, "%c", &ch) != EOF) {
    fprintf(fpOut, "%02X", ch^key[i]);
    i++;
    if (i==31) {
      fprintf(fpOut, "\n");
      i=0;
      fscanf(fpIn, "%c", &ch);
    }
  }
 
  fclose(fpIn);
  fclose(fpOut);
 
  return;
}

My Solution:

This problem gave me unusual excitement, because quite honestly I really enjoy cracking codes. It’s like you’re in a detective movie :)

After reading the encryption code (it basically XORed each character of the key with the corresponding character of the plaintexts), I decided to look over the ciphertexts to see if there was any pattern a human could recognize. It was pretty easy to see that the last character of 6 out of 7 ciphertexts was all 0x1E except for (4) with 0x0F. Because they were all grammatically correct English sentences, I guessed that 0x1E stood for the period (.) and 0x0F stood for the question mark (?). And so I broke the last byte of the key, which was 0x30.

Now… I was stuck.

The rest of the ciphertexts made little sense. For a while I tried (stupidly) to find other patterns, but there were none. Then I suddenly realized that because they all used the same 31-byte key, and they were all English sentences, the characters must be either space (ASCII decimal #32), or uppercase letters (ASCII decimal #65-90), or lowercase letters (ASCII decimal #97-122). I excluded punctuations to prevent diluting the results, since most of the characters in the sentences would be English letters and spaces anyway. If I could figure out enough letters, I could use them to infer what the others were.

So I wrote a little code in C++ that tried every possible character from 0x00 to 0xFF as key to XOR against each character of the 7 ciphertexts to see which one resulted in the desired ASCII ranges above, then output that key character and the corresponding decrypted characters. Below is an example screenshot of the raw output (this means for the 4th character of every ciphertext, the only key that works is 0x9b which produces letter m for ciphertext (1), letter i for ciphertext (2), and so forth at that position. For the 7th character, there are many possibilities):

…and partial & complete outputs (after I did some manual fill-in-the-blanks):

So there it was! The key in hexadecimal is:

key[31] = {0xf2, 0x1a, 0x04, 0x9b, 0xd0, 0x73, 0x23, 0xc8, 0x39, 0x98, 0xce, 0x09, 0x0e, 0xbc, 0x86, 0xda, 0xc9, 0xe0, 0x39, 0x89, 0x2a, 0x5f, 0x72, 0x67, 0x83, 0xa5, 0x61, 0xfd, 0x25, 0xee, 0x30};

You can find the code I wrote below:

#include <iostream>
using namespace std;
 
int main() {
// ciphertexts
    unsigned char ciphertext[7][31] = {
{0xBB, 0x3A, 0x65, 0xF6, 0xF0, 0x03, 0x4F, 0xA9, 0x57, 0xF6, 0xA7, 0x67, 0x69, 
0x9C, 0xE7, 0xFA, 0xBA, 0x85, 0x5A, 0xFB, 0x4F, 0x2B, 0x52, 0x0A, 0xEA, 0xD6, 
0x12, 0x94, 0x4A, 0x80, 0x1E},
 
{0xBA, 0x7F, 0x24, 0xF2, 0xA3, 0x53, 0x57, 0xA0, 0x5C,0xB8, 0xA1, 0x67, 0x62, 
0xC5, 0xA6, 0xAA, 0xAC, 0x92, 0x4A, 0xE6, 0x44, 0x7F, 0x06, 0x08, 0xA3, 0xD1, 
0x13, 0x88, 0x56, 0x9A, 0x1E},
 
{0xA6, 0x72, 0x61, 0xBB, 0xB3, 0x06, 0x51, 0xBA, 0x5C, 0xF6, 0xBA, 0x29, 0x7E, 
0xD0, 0xE7, 0xB4, 0xE9, 0x89, 0x4A, 0xA9, 0x5E, 0x30, 0x02, 0x47, 0xF0, 0xC0, 
0x02, 0x8F, 0x40, 0x9A, 0x1E},
 
{0xA5, 0x72, 0x61, 0xF5, 0xF0, 0x00, 0x4B, 0xA7, 0x4C, 0xF4, 0xAA, 0x29, 0x79, 
0xD9, 0xA6, 0xB7, 0xAC, 0x85, 0x4D, 0xA9, 0x5E, 0x30, 0x52, 0x03, 0xEC, 0x85, 
0x15, 0x95, 0x4C, 0x9D, 0x0F},
 
{0xBB, 0x3A, 0x70, 0xF3, 0xB9, 0x1D, 0x48, 0xE8, 0x4D, 0xF0, 0xAB, 0x70, 0x2E, 
0xCF, 0xEE, 0xB5, 0xBC, 0x8C, 0x5D, 0xA9, 0x4C, 0x30, 0x1E, 0x0B, 0xEC, 0xD2, 
0x41, 0x95, 0x4C, 0x83, 0x1E},
 
{0xA6, 0x72, 0x6D, 0xE8, 0xF0, 0x1A, 0x50, 0xE8, 0x49, 0xED, 0xBC, 0x6C, 0x7C, 
0x9C, 0xF2, 0xB2, 0xA8, 0x8E, 0x19, 0xFD, 0x42, 0x3E, 0x06, 0x47, 0xEC, 0xCB, 
0x04, 0xDD, 0x4C, 0x9D, 0x1E},
 
{0xBC, 0x75, 0x70, 0xBB, 0xBF, 0x1D, 0x46, 0xE8, 0x5A, 0xF9, 0xAA, 0x6C, 0x7A, 
0x9C, 0xEF, 0xA9, 0xE9, 0x82, 0x5C, 0xFD, 0x5E, 0x3A, 0x00, 0x47, 0xF7, 0xCD, 
0x00, 0x93, 0x05, 0xA7, 0x1E}
    };
 
// This outputs all possible candidates for each character of each ciphertext
    cout << "------------ Raw result: --------" << endl;
    char plaintext[7][31];
    for (int j = 0; j < 31; j++) {
        cout << dec << j + 1 << "---\n";
        int count = 0;
        for (int k = 0; k < 256; k++) {
            bool flag = true;
            for (int i = 0; i < 7; i++) {
// If the result is not in the desired ASCII range, break and move on to next key
                int check = (int) (ciphertext[i][j] ^ k);
                if ( (check < 65 && check != 32) ||
                     (check > 90 && check < 97) ||
                     (check > 122)) {
                        flag = false;
                        break;
                }
            }
 
// If this key produces a match, output the results (maybe wrong)
            if (flag) {
                cout << hex << k << ": ";
                for (int i = 0; i < 7; i++) {
                    cout << i + 1 << "." <<
                        (char) ((int) ciphertext[i][j] ^ k) << " ";
                    plaintext[i][j] = (char) ((int) ciphertext[i][j] ^ k);
                }
                cout << endl;
                count++;
            }
        }
        cout << endl;
// If there are more than one possibility, set that character of
// plaintext to (_) to denote unfilled blanks
        if (count > 1) {
            for (int i = 0; i < 7; i++) {
                plaintext[i][j] = '_';
            }
         }
    }
 
// Print out the partial results with some blanks unfilled in the plaintexts
    cout << "----------- Partial result: -----" << endl;
    for (int i = 0; i < 7; i++) {
        cout << i + 1 << ". ";
        for (int j = 0; j < 31; j++) {
            cout << plaintext[i][j];
        }
        cout << "\n \n";
    }
 
// This key is what I got after doing some manual fill-in-the-blanks
    cout << "----------- Full result: --------" << endl;
    unsigned char key[31] = {0xf2, 0x1a, 0x04, 0x9b, 0xd0, 0x73, 0x23, 0xc8, 0x39,
0x98, 0xce, 0x09, 0x0e, 0xbc, 0x86, 0xda, 0xc9, 0xe0,
0x39, 0x89, 0x2a, 0x5f, 0x72, 0x67, 0x83, 0xa5, 0x61,
0xfd, 0x25, 0xee, 0x30};
    for (int i = 0; i < 7; i++) {
        cout << i + 1 << ". ";
        for (int j = 0; j < 31; j++) {
            cout << (char) ((int) ciphertext[i][j] ^ key[j]);
        }
        cout << endl;
    }  
 
    return 0;
}

Leetcode #373: Find K Pairs with Smallest Sums

2016-07-23T03:41:19+00:00

Problem source: https://leetcode.com/problems/find-k-pairs-with-smallest-sums/

Problem Statement:

You are given two integer arrays nums1 and nums2 sorted in ascending order and an integer k. Define a pair (u,v) which consists of one element from the first array and one element from the second array. Find the k pairs (u₁,v₁),(u₂,v₂) …(u_k, v_k) with the smallest sums.

Example: Given nums1 = [1,7,11], nums2 = [2,4,6], k = 3. Return: [1,2],[1,4],[1,6]

Solution:

We know from mathematics that there will be n1 * n2 possible pairs where n1, n2 are the sizes of nums1 and nums2 respectively. As a human, we will naturally match each element in nums1 to all the elements in nums2 to create a list of all possible pairs, sort them, and then output the k pairs. This surely results in a correct solution, but performs too many unnecessary computations if k < n1 * n2. So the idea for a faster solution here is to keep track of how many elements of nums2 we have matched each element of nums1 with, then find the next smallest pair from all possible pairs of (u, v) where u is an element of nums1 and v is its next corresponding element in nums2 until we have found k pairs or exhausted all the possible pairs.

Here is the complete code in C++ with detailed comments and explanations:

vector<pair<int, int>> kSmallestPairs(vector<int>& nums1, vector<int>& nums2, 
                                      int k) {
    vector<pair<int, int>> result;
    int n1 = nums1.size(), n2 = nums2.size();
    if (n1 == 0 || n2 == 0) return result;
    //sort(nums1.begin(), nums1.end());  //the lists are already sorted
	//sort(nums2.begin(), nums2.end());
	int count = 0;
    /* this array tracks the index of the next element in nums2
	to match with each element in nums1 */
    int* other = new int[n1];          
    memset(other, 0, sizeof(int) * n1);  // set all indices in other[] to 0
    /* min is the index of the current smallest element in nums1 
	that hasn't finished matching with all elements in nums2. */
    int min = 0, first, second, index;
    /* 2 cases when the loop stops: (1) we find all k pairs; or
      (2) we find every possible pair that can be made from nums1 and nums2. */
    while (count < k && count < n1 * n2) {
        /* first, second form the next smallest pair. 
		index contains the index of first in nums1 */
        first = nums1[min];
        second = nums2[other[min]];
        index = min;
        /* this loop finds all the possible candidates to be the next 
		smallest pair and compares them to the current one */
        for (int i = min + 1; i < n1; i++) {
            if (nums1[i] + nums2[other[i]] < first + second) {
                first = nums1[i];
                second = nums2[other[i]];
                index = i;
            }
        }
        //cout << first << " ; " << second << endl;
        pair<int, int> tmp(first, second);
        result.push_back(tmp);
        other[index] += 1;
        count += 1;
        // Update min if nums1[min] has matched with all the elements of nums2
        if (other[min] == n2) {
            min += 1;
        }
    }
    delete [] other;
    return result;
}

What I’ve Learned After My Interview at Facebook

2016-03-30T22:41:19+00:00

Near the end of spring break of my sophomore year in college, I flew to California to be interviewed onsite for Facebook University for Analytics 2016. As a freshman I was rejected first round when applying for Facebook University for Engineering, so it was quite an excitement to actually make it to Facebook headquarters this year, even if it was only an interview trip and not an offer. I learned a lot, but this post will only contain the highlights.

Long story short: I didn’t get the job. But best thing: being physically inside the walls of Facebook and talking to the people behind it (very, very inspiring). Second best thing: I had a shot at putting my foot through the door, and met my peers from other colleges who had the same opportunity as me there. Third best thing: I didn’t have to pay for it.

As unhappy (for me) as I was for the last few hours since the decision email arrived, here are the three main pieces of wisdom I have learned from this experience:

1. Once I send in an application (or even before), I should start preparing for the interview.

I was on vacation with my best friend in New York City when I received the email from Facebook telling me to fly over to California for my interview. I was in panic mode because the last few weeks before spring break had been full of homework and midterms that I didn’t think about getting a mock interview with my college’s Career Planning office. It would be my first interview with a tech company as well. And the worst thing was that I actually didn’t expect to be selected for the interview at all. One week between receiving the email and getting on my flight was absolutely not enough for such a newbie inexperienced interviewee I was. I might know the technical things well, I might be able to write code and solve math problems, but right after the interview, I knew that I didn’t talk about everything that I felt the interviewers need to know to have a relatively complete picture of me. It could have been better if I had had a mock interview with someone more experienced, especially when most of the questions I got asked were quite general.

2. Facebook knows how to make prospective employees feel comfortable, but I should keep a level head with me at all times.

This might contain a little bias, because Facebook is currently the first and only company I have been interviewed at. But the impression they created was great. First they took care of your flights, hotel, transportation, meals, and other related costs. Once we were there, specifically for FBU for Analytics, we had a discussion with a panel of data scientists who gave us an overview of their job and their experiences, and answered some of our questions. At this point, I felt quite comfortable and excited already. Then the tour around Facebook campus really pointed out the openness and flexibility of their work environment, as well as all the perks of working at Facebook. Now I was sold, which was bad for two reasons. One, I would not be able to answer the question of what product(s) I think Facebook should improve as objectively and completely as I had thought about before. Two, it increased my nervousness before my interviews, because subconsciously, my brain switched from, “How do I show them my passion for solving problems with technology?” to, “How on Earth am I going to convince them to let me into this place?” Well, the second mindset was simply horrible. When I was sitting in the airport waiting for my flight back and my head was clear, I wished I had talked more about how I love doing math and solve problems, not tried to give the “right” answers.

3. Keep learning; and believe more in myself.

I enjoy learning and new knowledge. This opportunity has taught me many little things about myself, the tech industry, and the data analytics career that I would not have known by only sitting in lectures in college. Often, I blow up the first times I do things (especially if a large portion of it involves human factor), but I almost always improve on the second, the third, and so forth. Hopefully, this should apply to interviewing and getting internships/jobs as well! Also, I’m more confident in the path I’ve chosen. At least among those who were present on Facebook campus that day, I was the only kid from a small liberal arts college that is never on the recruiting radar of large tech companies. My school might be less well-known, and the probability that my interviewers graduated from the same place might be much lower than MIT or Stanford, but my resume can still pass the screening and land me interviews, as long as I keep adding interesting projects and experiences to it. After all, there is hope!

P/S: Big thanks to my parents, brother, best friends at NYU, Cornell University, Wooster, and everyone who’ve given me the greatest support throughout all of this from the beginning. It’s not the end yet :)