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Science Fellows, Computer Science Lesson 1

Science Fellows, Computer Science Lesson 1. Fall 2010. Algorithm . Way to solve a problem (Write a program.) But, as computer SCIENTISTS we care about more than getting *a* solution. We want to know – how good a solution is it?. Example.

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Science Fellows, Computer Science Lesson 1

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  1. Science Fellows, Computer Science Lesson 1 Fall 2010

  2. Algorithm • Way to solve a problem (Write a program.) • But, as computer SCIENTISTS we care about more than getting *a* solution. We want to know – how good a solution is it?

  3. Example • Packs of word cards. Try to find the alphabetically first card in the pack. Count how many times you turn over a card. • Can’t memorize cards. • Usually keep the cards in numbered slots, but can switch them around or keep out a few “special” cards. • Only one card not in special slot can be turned over at a time. • With each step, the cards that aren’t in special slots have to get turned back over. • Can remember counts if you need to.

  4. Find alphabetically first card 1 5 2 6 3 • 7 8 4 Turn over count: 0

  5. Find alphabetically first card 1 Lane 5 2 6 3 • 7 8 4 Turn over count: 1

  6. Find alphabetically first card 1 5 Lane 2 6 3 • 7 8 4 Turn over count: 1

  7. Find alphabetically first card 1 5 Lane 2 6 Boy 3 • 7 8 4 Turn over count: 2

  8. Find alphabetically first card 1 5 Boy 2 6 3 • 7 8 4 Turn over count: 2

  9. Find alphabetically first card 1 5 Boy 2 6 3 • 7 Violin 8 4 Turn over count: 3

  10. Find alphabetically first card 1 5 Boy 2 6 3 • 7 8 4 Apple Turn over count: 4

  11. Find alphabetically first card 1 5 Apple 2 6 3 • 7 8 4 Turn over count: 4

  12. Examine Algorithm • How many times do I turn over a card? • What if I double the number of cards? • If there are n cards, how many times do I turn over a card?

  13. Your turn • Sort your cards alphabetically • We’ll see what algorithms we come up with and whose is best

  14. What if there are N cards? Some math you may want to know: 1+2+3+…+n = n(n-1)/2 Number of times I can cut the number n in half until I hit 1 = lg n

  15. Why do we care? exponential quadratic Num card turns (Time) linear logarithmic constant Number of cards ->

  16. 106 instructions/sec, runtimes

  17. So… • If my function is time = 2(n-1) all I really care about is that it is a LINEAR function. • What’s the best I can do for sorting, if I know NOTHING about my data? • What’s the best I can do for sorting if I do know something about my data?

  18. Searching • New problem: Find the card that has a given word on it. How long will it take? What could we do to make it fast?

  19. Back to the real world • Are these “real” problems? • Oh, yes! How does Google do such a good job? • They SORT (PageRank algorithm) better than the rest • They SEARCH quickly

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