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Illustration of Algorithm 3 from paper:

Illustration of Algorithm 3 from paper:. Reconstructing a suffix array By F. Franek & B. Smyth. Slide 1. INDEX X. INDEX LSA LCP. Slide 2. The permutation of the alphabet for this example is defined by p[a]=a p[b]=c p[c]=d p[d]=b p[e]=e. Slide 3. stack. 0.

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Illustration of Algorithm 3 from paper:

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  1. Illustration of Algorithm 3 from paper: Reconstructing a suffix arrayBy F. Franek & B. Smyth Slide 1

  2. INDEX X INDEX LSA LCP Slide 2

  3. The permutation of the alphabet for this example is defined by p[a]=a p[b]=c p[c]=d p[d]=b p[e]=e Slide 3

  4. stack 0 (PREV of start) start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 1 9 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18 Slide 4 Next Slide

  5. stack 4 (PREV of 1) 0 (PREV of start) start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 1 9 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18 Slide 5 Next Slide

  6. stack 4 (PREV of 1) 0 (PREV of start) start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 1 9 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18 Slide 6 Next Slide

  7. stack 4 (PREV of 1) 0 (PREV of start) start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 1 9 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18 Slide 7 Next Slide

  8. stack 4 (PREV of 1) 0 (PREV of start) IDENTIFY AND EXTRACT FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 1 9 10 12 1 13 14 8 15 5 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18 Slide 8 Next Slide

  9. stack 4 (PREV of 1) 0 (PREV of start) IDENTIFY AND EXTRACT FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 2 1 0 3 3 2 1 1 2 1 0 0 0 0 1 9 10 12 1 0 14 8 15 5 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 9 5 13 16 2 10 6 14 17 3 12 11 7 8 15 18 9 1 5 3-family 3 3 2 Slide 9 Next Slide

  10. stack 4 (PREV of 1) 0 (PREV of start) SORT THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 5 9 13 16 2 10 6 14 17 3 12 11 7 8 15 18 9 1 5 3-family 5 1 9 3 3 2 3 3 2 LCP sort of t-family:preserve the last and every k>=tchange every k < t to t Slide 10 Next Slide

  11. stack 4 (PREV of 1) 0 (PREV of start) FLATTEN THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 19 4 1 5 9 13 16 2 10 6 14 17 3 12 11 7 8 15 18 Nothing to flatten, it is already flat Slide 11 Next Slide

  12. stack 4 (PREV of 1) 0 (PREV of start) 1 19 4 5 9 13 16 2 10 6 14 17 3 7 12 8 11 15 18 VERTICALIZE THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 13 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 4 5 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 next end Should we pop? NO Slide 12 Next Slide

  13. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 1 19 16 2 10 6 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 13 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 4 5 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 next end 13 Slide 13 Next Slide

  14. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 1 13 19 2 10 6 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 13 10 12 1 9 14 8 15 0 6 7 11 16 17 18 2 3 0 4 5 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 next end 16 Slide 14 Next Slide

  15. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 1 13 16 2 19 10 6 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY 1 13 16 2-family start=19 3 2 0 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 13 10 12 1 9 14 8 15 0 6 7 11 16 17 18 0 3 0 4 5 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 next end Slide 15 Next Slide

  16. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 13 1 16 2 19 10 6 14 17 3 7 12 8 11 15 18 SORT THE FAMILY 1 1 13 16 13 16 2-family start=19 3 3 2 0 2 0 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 16 10 12 13 9 14 8 15 0 6 7 11 1 17 18 0 3 0 4 5 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 next end Slide 16 Next Slide

  17. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 13 1 16 2 19 10 6 14 17 3 7 12 8 11 15 18 FLATTEN THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Slide 17 Next Slide

  18. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 13 1 16 2 19 10 6 14 17 3 7 12 8 11 15 18 FLATTEN THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Slide 18 Next Slide

  19. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 13 1 16 2 19 10 6 14 17 3 7 12 8 11 15 18 VERTICALIZE THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 2 17 18 0 3 0 4 16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 end next Slide 19 Next Slide

  20. 9 5 stack 4 (PREV of 1) 0 (PREV of start) 4 13 1 16 2 19 10 6 14 17 3 7 12 8 11 15 18 VERTICALIZE THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 2 17 18 2 3 0 4 16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 end next Should we pop? YES Slide 20 Next Slide

  21. 9 5 stack 0 (PREV of start) 1 16 2 10 6 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 2 17 18 0 3 0 4 16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 end next 19 4 13 Slide 21 Next Slide

  22. 9 5 stack 0 (PREV of start) 1 16 2 10 19 4 13 6 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY 19 4 13 1-family start=19 1 1 2 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 0 17 18 0 3 0 4 16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 end next Slide 2 Next Slide

  23. 9 5 stack 0 (PREV of start) 1 16 2 10 19 4 13 6 14 17 3 7 12 8 11 15 18 SORT THE FAMILY 19 4 13 1-family 19 4 13 start=19 1 1 2 1 1 2 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 0 17 18 0 3 0 4 16 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 end next Slide 23 Next Slide

  24. 9 5 stack 0 (PREV of start) 1 16 2 10 19 4 13 6 14 17 3 7 12 8 11 15 18 FLATTEN THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 2 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Slide 24 Next Slide

  25. 9 5 stack 0 (PREV of start) 1 16 2 10 19 4 13 6 14 17 3 7 12 8 11 15 18 FLATTEN THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Slide 25 Next Slide

  26. 9 5 stack 0 (PREV of start) 1 16 2 10 19 4 13 6 14 17 3 7 12 8 11 15 18 VERTICALIZE THE FAMILY start=19 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next Should we pop? YES Slide 26 Next Slide

  27. 9 5 stack 1 16 10 19 4 13 6 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next 2 Slide 27 Next Slide

  28. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 6 14 17 3 7 12 8 11 15 18 2 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next 10 Slide 28 Next Slide

  29. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 2 10 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next 6 Slide 29 Next Slide

  30. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 14 8 15 16 6 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next 2 10 6 Slide 30 Next Slide

  31. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 2 10 6 IDENTIFY AND EXTRACT FAMILY 2 10 6 2-family 2 2 1 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 1 0 3 2 2 1 1 2 1 0 0 0 0 1 5 10 12 13 9 0 8 15 16 6 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next Slide 31 Next Slide

  32. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 2 6 10 SORT THE FAMILY 2 10 6 2-family 2 6 10 2 2 1 2 2 1 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next Slide 32 Next Slide

  33. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 2 6 10 FLATTEN THE FAMILY Nothing to flatten, it is already flat INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 2 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next Slide 33 Next Slide

  34. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 2 6 10 VERTICALIZE THE FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 2 0 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4 next end end next Slide 34 Next Slide

  35. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 14 17 3 7 12 8 11 15 18 2 6 10 VERTICALIZE THE FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 2 0 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4 next end end next Should we pop? NO Slide 35 Next Slide

  36. 9 5 stack 19 (PREV of 2) 1 16 19 4 13 3 7 12 8 11 15 18 2 6 10 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 2 0 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4 next end end next 14 17 Slide 36 Next Slide

  37. 9 5 stack 19 (PREV of 2) 1 16 4 13 3 7 12 8 11 15 18 19 6 10 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 3 0 2 0 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4 next end end next 2 14 17 Slide 37 Next Slide

  38. 9 5 stack 19 (PREV of 2) 1 16 4 13 3 7 12 8 11 15 18 2 6 14 10 17 IDENTIFY AND EXTRACT FAMILY 2 14 17 2-family 2 1 0 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 14 12 13 9 10 8 15 16 0 7 11 1 17 18 0 0 0 2 0 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4 next end end next 19 Slide 38 Next Slide

  39. 9 5 stack 19 (PREV of 2) 1 16 4 13 3 7 12 8 11 15 18 2 6 14 10 17 SORT THE FAMILY 2 14 17 1-family 14 2 17 2 1 0 1 2 0 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 17 12 13 9 10 8 15 16 0 7 11 1 2 18 0 0 0 14 0 6 0 16 0 10 0 0 0 0 0 0 0 0 0 0 0 0 4 next end end next 19 Slide 39 Next Slide

  40. 9 5 stack 19 (PREV of 2) 1 16 4 13 3 7 12 8 11 15 18 2 6 14 10 17 FLATTEN THE FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 2 18 0 0 0 14 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next 19 Slide 40 Next Slide

  41. 9 5 stack 19 (PREV of 2) 1 16 4 13 3 7 12 8 11 15 18 2 6 14 10 17 FLATTEN THE FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 17 7 11 1 2 18 0 0 0 14 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 end next 19 Slide 41 Next Slide

  42. 9 5 stack 19 (PREV of 2) 1 16 4 13 3 7 12 8 11 15 18 2 6 14 10 17 VERTICALIZE THE FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next Should we pop? YES 19 Slide 42 Next Slide

  43. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 12 8 11 15 18 2 6 14 10 17 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 3 Slide 43 Next Slide

  44. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 3 14 10 17 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 12 Slide 44 Next Slide

  45. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 3 14 10 17 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 12 Slide 45 Next Slide

  46. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 14 10 17 IDENTIFY AND EXTRACT FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 11 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 3 12 Slide 46 Next Slide

  47. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 14 10 17 IDENTIFY AND EXTRACT FAMILY 3 12 2-family 2 1 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 3 12 Slide 47 Next Slide

  48. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 14 10 17 SORT FAMILY 3 12 2-family 3 12 2 1 2 1 INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 3 12 Slide 48 Next Slide

  49. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 14 10 17 FLATTEN THE FAMILY Nothing to flatten, it is already flat INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 12 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 14 0 17 0 16 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 end end next next 19 3 12 Slide 49 Next Slide

  50. 9 5 stack 14 (PREV of 3) 1 16 4 13 7 8 11 15 18 2 6 3 14 12 10 17 VERTICALIZE THE FAMILY INDEXmod LCPNEXTTAIL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 3 2 2 1 3 2 0 3 2 1 1 1 2 1 0 0 0 0 1 5 6 11 13 9 10 8 15 16 0 7 0 1 3 18 0 0 0 14 0 17 12 16 0 0 0 0 0 0 0 12 0 2 0 0 0 0 4 end end end next next next 19 Slide 50 Next Slide

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