SE103 - Week 9, Session 1

Transcript

1. Week 9 and 10:
   Dynamic Programming!
   

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2. What is Dynamic Programming
   

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3. 1. Break down into overlapping subproblems
   2. Cache results to avoid solving same subproblems
   What is Dynamic Programming
   

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4. 1. Break down into overlapping subproblems
   2. Cache results to avoid solving same subproblems
   What is Dynamic Programming
   “Dynamic Programming was basically a phrase
   made up to confuse the government about what
   RAND was doing.”
   - Richard Bellman, ‘father’ of dynamic
   programming
   

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5. Poll!
   

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6. Why is Dynamic Programming
   so difficult?
   

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7. Sounds easy in theory, but way harder in practice!
   Why is Dynamic Programming
   so difficult?
   

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8. Sounds easy in theory, but way harder in practice!
   Like all other problems, the key is to recognize
   common patterns
   Why is Dynamic Programming
   so difficult?
   

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9. Sounds easy in theory, but way harder in practice!
   Like all other problems, the key is to recognize
   common patterns
   Continuous practice is critical - you’re probably not
   going to master dynamic programming in 2 weeks.
   Why is Dynamic Programming
   so difficult?
   

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10. - Fibonacci
    - Knapsack
    - Unbounded knapsack
    - Palindromic Sequences
    - Common Substrings
    Common Patterns in DP
    

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11. - Fibonacci
    - Knapsack
    - Unbounded knapsack
    - Palindromic Sequences
    - Common Substrings
    Common Patterns in DP
    

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12. Fibonacci
    0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55…
    
    To get the nth fib number
    
    … add the previous two numbers
    

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13. Fibonacci
    Recursive:
    
    public int CalculateFibonacci(int n) {
    if(n < 2)
    return n;
    return CalculateFibonacci(n-1) + CalculateFibonacci(n-2);
    }
    Run time: ??
    

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14. Fibonacci
    Recursive:
    
    public int CalculateFibonacci(int n) {
    if(n < 2)
    return n;
    return CalculateFibonacci(n-1) + CalculateFibonacci(n-2);
    }
    Run time: 2^n
    

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15. Fibonacci
    What if we built up the fibonacci sequence first?
    

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16. Fibonacci
    0 1
    What if we built up the fibonacci sequence first?
    

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17. Fibonacci
    0 1 1
    What if we built up the fibonacci sequence first?
    

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18. Fibonacci
    What if we built up the fibonacci sequence first?
    0 1 1 2 3 5 8
    

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19. Fibonacci
    What if we built up the fibonacci sequence first?
    0 1 1 2 3 5 8
    int dp[] = new int[n + 1];
    dp[0] = 0;
    dp[1] = 1;
    for (int i = 2; i <= n; i++)
    dp[i] = dp[i - 1] + dp[i - 2];
    return dp[n];
    

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20. Fibonacci
    What if we built up the fibonacci sequence first?
    0 1 1 2 3 5 8
    int dp[] = new int[n + 1];
    dp[0] = 0;
    dp[1] = 1;
    for (int i = 2; i <= n; i++)
    dp[i] = dp[i - 1] + dp[i - 2];
    return dp[n];
    Run time: ??
    

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21. Fibonacci
    What if we built up the fibonacci sequence first?
    0 1 1 2 3 5 8
    int dp[] = new int[n + 1];
    dp[0] = 0;
    dp[1] = 1;
    for (int i = 2; i <= n; i++)
    dp[i] = dp[i - 1] + dp[i - 2];
    return dp[n];
    Run time: n
    

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22. Given an array representation of coin values and a
    value n, return the number of ways to make change
    for the target amount n
    
    Given: {1, 5}, n = 6
    
    Return: ??
    
    Number of Ways to Make Change
    

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23. Given an array representation of coin values and a
    value n, return the number of ways to make change
    for the target amount n
    
    Given: {1, 5}, n = 6
    
    Return: 2
    
    { {6 x 1}, {5 x 1, 1 x 1} }
    
    Number of Ways to Make Change
    

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24. Let’s start by building an array from 0 -> n 

    Given: {1, 5}, n = 6
    
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    

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25. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    In each box, we’ll see how many ways we can make ’n’
    with our coins 1, 5
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    

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26. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    In each box, we’ll see how many ways we can make ’n’
    with our coins 1, 5
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    1
    

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27. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    In each box, we’ll see how many ways we can make ’n’
    with our coins 1, 5
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    1 1
    

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28. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    In each box, we’ll see how many ways we can make ’n’
    with our coins 1, 5
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    1 1 1 1 1
    

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29. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    In each box, we’ll see how many ways we can make ’n’
    with our coins 1, 5
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    1 1 1 1 1 2 2
    

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30. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    Let’s build up our array one ‘coin’ at a time (one pass
    with 1, second pass with 5)
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    1 1 1 1 1 2 2
    

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31. Let’s start by building an array from 0 -> n
    
    Given: {1, 5}, n = 6
    
    if (coinValue <= amount) {

    ways[amount] =

    ways[amount] + ways[amount - coinValue];

    }
    Number of Ways to Make Change
    0 1 2 3 4 5 6
    1 1 1 1 1 2 2
    

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32. Number of Ways to Make Change
    General Pattern:
    
    - Create an array to store solutions to ‘subproblems’
    
    - what would be the solution up to ‘this’ point?
    
    

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33. Number of Ways to Make Change
    General Pattern:
    
    - Create an array to store solutions to ‘subproblems’
    
    - what would be the solution up to ‘this’ point?
    
    - Use stored solutions to populate future elements of
    the array
    
    

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34. Number of Ways to Make Change
    General Pattern:
    
    - Create an array to store solutions to ‘subproblems’
    
    - what would be the solution up to ‘this’ point?
    
    - Use stored solutions to populate future elements of
    the array
    
    - writing out the arrray and populating it by hand
    often helps you come up with the algorithm later
    

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35. Breakout Rooms
    - Half of group does one problem, other half does the
    other problem
    
    - 30 minutes, everybody tries to do their own problem
    
    - 10 minutes - group 1 explains their problem
    
    - 10 minutes - group 2 explains their problem
    
    - Last 10 minutes - everybody talks about the last
    problem and brainstorm what the dp array would look
    like
    

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36. How’d it go?
    

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37. Evaluating companies
    

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38. Evaluating companies
    Glassdoor reviews
    
    Researching current people who work at the company
    on LinkedIn
    
    

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39. Questions for me?
    

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40. Questions for me?
    Work Life Balance
    

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41. Questions for me?
    Work Life Balance
    - How does the team figure out what to work on in the
    next 3-6 months?
    
    - How does the team tackle tech debt?
    
    - What is a typical release process?
    
    - Weekly? Biweekly?
    
    - How does the team prepare for releases?
    
    - How is the release monitored afterwards?
    
    - Are there oncall schedules?
    

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42. Questions for me?
    Career Growth
    

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43. Questions for me?
    Career Growth
    - What do you see me working on in my first 3-6
    months on the job?
    
    - How do people on the team get feedback usually?
    
    

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44. Questions for me?
    General
    - What are some challenging projects you’ve worked
    on in the past 3-6 months?
    
    - What kind of meetings do you usually have in a
    week?
    
    

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45. Questions for me?
    Other questions?
    

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