![The “Bubble Up” Algorithm
index <- 1
last_compare_at <- n – 1
loopouter
exitif(index > last_compare_at)
Loopinner
to_do<-0
exitif(to_do > index)
if(A[to_do] > A[to_do + 1]) then
Swap(A[to_do], A[to_do + 1])
endif
to_do<- to_do + 1
endloopinner
index <- index - 1
endloopouter](https://image.slidesharecdn.com/sabqxbvssdwuzaziwiyu-140702212414-phpapp01/85/Bubble-sort-12-320.jpg)
![Bubble Sort Code
void bubble_sort( int data[ ], int size)
{
int outer, inner,temp;
for(outer = size-1; outer =>0; --outer)
{
for(inner = 0; inner < outer;++inner)
if(data[inner] > data[inner+1])
{
temp = data[inner];
data[inner] = data[inner+1];
data[inner+1] = temp;
}
}
}](https://image.slidesharecdn.com/sabqxbvssdwuzaziwiyu-140702212414-phpapp01/85/Bubble-sort-14-320.jpg)
Bubble sort
- 1. Bubble Sort Prepared By: Rao Muhammad Salman MCS The Islamia University BahawalPur(Pakistan)
- 2. Sorting • Sorting takes an unordered collection and makes it an ordered one. 1 2 3 4 5 6 7 8 674523 14 6 3398 42 1 2 3 4 5 6 7 8 452314 33 42 676 98
- 3. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping 1 2 3 4 5 6 7 8 674523 14 6 3398 42
- 4. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Swap 1 2 3 4 5 6 7 8 674598 14 6 3323 42 Value swapped
- 5. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Swap 1 2 3 4 5 6 7 8 679845 14 6 3323 42 Value swapped
- 6. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Swap 1 2 3 4 5 6 7 8 671445 98 6 3323 42 Value swapped
- 7. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Value swapped Swap 1 2 3 4 5 6 7 8 671445 6 98 3323 42
- 8. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Swap 1 2 3 4 5 6 7 8 981445 6 67 3323 42 Value swapped
- 9. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Swap 1 2 3 4 5 6 7 8 331445 6 67 9823 42 Value swapped
- 10. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Swap 1 2 3 4 5 6 7 8 331445 6 67 4223 98 Value swapped
- 11. "Bubbling Up" the Largest Element • Traverse a collection of elements – Move from the front to the end – “Bubble” the largest value to the end using pair-wise comparisons and swapping Largest value correctly placed 1 2 3 4 5 6 7 8 331445 6 67 4223 98
- 12. The “Bubble Up” Algorithm index <- 1 last_compare_at <- n – 1 loopouter exitif(index > last_compare_at) Loopinner to_do<-0 exitif(to_do > index) if(A[to_do] > A[to_do + 1]) then Swap(A[to_do], A[to_do + 1]) endif to_do<- to_do + 1 endloopinner index <- index - 1 endloopouter
- 13. No, Swap isn’t built in. Procedure Swap(a, b isoftype in/out Num) temp isoftype Num temp <- a a <- b b <- temp endprocedure // Swap
- 14. Bubble Sort Code void bubble_sort( int data[ ], int size) { int outer, inner,temp; for(outer = size-1; outer =>0; --outer) { for(inner = 0; inner < outer;++inner) if(data[inner] > data[inner+1]) { temp = data[inner]; data[inner] = data[inner+1]; data[inner+1] = temp; } } }
- 15. Items of Interest • Notice that only the largest value is correctly placed • All other values are still out of order • So we need to repeat this process Largest value correctly placed 1 2 3 4 5 6 7 8 331445 6 67 4223 98
- 16. Repeat “Bubble Up” How Many Times? • If we have N elements… • And if each time we bubble an element, we place it in its largest correct location… • Then we repeat InnerLoop the “bubble up” process OuterLoop – 1 times. • This guarantees we’ll correctly place all N elements.
- 17. Dry Run
- 18. 674523 14 6 3398 42 1 2 3 4 5 6 7 8 to_do index 7 N 8 did_swap true The First “Bubble Up”
- 19. 674523 14 6 3398 42 1 2 3 4 5 6 7 8 to_do index 7 1 N 8 did_swap false The First “Bubble Up”
- 20. The First “Bubble Up” 674523 14 6 3398 42 1 2 3 4 5 6 7 8 to_do index 7 1 N 8 Swap did_swap false
- 21. The First “Bubble Up” 674598 14 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 1 N 8 Swap did_swap true
- 22. The First “Bubble Up” 674598 14 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 2 N 8 did_swap true
- 23. The First “Bubble Up” 674598 14 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 2 N 8 Swap did_swap true
- 24. The First “Bubble Up” 679845 14 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 2 N 8 Swap did_swap true
- 25. The First “Bubble Up” 679845 14 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 3 N 8 did_swap true
- 26. The First “Bubble Up” 679845 14 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 3 N 8 Swap did_swap true
- 27. The First “Bubble Up” 671445 98 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 3 N 8 Swap did_swap true
- 28. The First “Bubble Up” 671445 98 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 4 N 8 did_swap true
- 29. The First “Bubble Up” 671445 98 6 3323 42 1 2 3 4 5 6 7 8 to_do index 7 4 N 8 Swap did_swap true
- 30. The First “Bubble Up” 671445 6 98 3323 42 1 2 3 4 5 6 7 8 to_do index 7 4 N 8 Swap did_swap true
- 31. The First “Bubble Up” 671445 6 98 3323 42 1 2 3 4 5 6 7 8 to_do index 7 5 N 8 did_swap true
- 32. The First “Bubble Up” 671445 6 98 3323 42 1 2 3 4 5 6 7 8 to_do index 7 5 N 8 Swap did_swap true
- 33. The First “Bubble Up” 981445 6 67 3323 42 1 2 3 4 5 6 7 8 to_do index 7 5 N 8 Swap did_swap true
- 34. The First “Bubble Up” 981445 6 67 3323 42 1 2 3 4 5 6 7 8 to_do index 7 6 N 8 did_swap true
- 35. The First “Bubble Up” 981445 6 67 3323 42 1 2 3 4 5 6 7 8 to_do index 7 6 N 8 Swap did_swap true
- 36. The First “Bubble Up” 331445 6 67 9823 42 1 2 3 4 5 6 7 8 to_do index 7 6 N 8 Swap did_swap true
- 37. The First “Bubble Up” 331445 6 67 9823 42 1 2 3 4 5 6 7 8 to_do index 7 7 N 8 did_swap true
- 38. The First “Bubble Up” 331445 6 67 9823 42 1 2 3 4 5 6 7 8 to_do index 7 7 N 8 Swap did_swap true
- 39. The First “Bubble Up” 331445 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 7 7 N 8 did_swap true Finished 1st “Bubble Up” No Swap
- 40. The Second “Bubble Up” 331445 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 1 N 8 did_swap false
- 41. The Second “Bubble Up” 331445 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 1 N 8 did_swap false No Swap
- 42. The Second “Bubble Up” 331445 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 2 N 8 did_swap false
- 43. The Second “Bubble Up” 331445 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 2 N 8 did_swap false Swap
- 44. The Second “Bubble Up” 334514 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 2 N 8 did_swap true Swap
- 45. The Second “Bubble Up” 334514 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 3 N 8 did_swap true
- 46. The Second “Bubble Up” 334514 6 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 3 N 8 did_swap true Swap
- 47. The Second “Bubble Up” 33614 45 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 3 N 8 did_swap true Swap
- 48. The Second “Bubble Up” 33614 45 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 4 N 8 did_swap true
- 49. The Second “Bubble Up” 33614 45 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 4 N 8 did_swap true No Swap
- 50. The Second “Bubble Up” 33614 45 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 5 N 8 did_swap true
- 51. The Second “Bubble Up” 33614 45 67 4223 98 1 2 3 4 5 6 7 8 to_do index 6 5 N 8 did_swap true Swap
- 52. The Second “Bubble Up” 67614 45 33 4223 98 1 2 3 4 5 6 7 8 to_do index 6 5 N 8 did_swap true Swap
- 53. The Second “Bubble Up” 67614 45 33 4223 98 1 2 3 4 5 6 7 8 to_do index 6 6 N 8 did_swap true
- 54. The Second “Bubble Up” 42614 45 33 6723 98 1 2 3 4 5 6 7 8 to_do index 6 6 N 8 did_swap true Swap
- 55. The Second “Bubble Up” 42614 45 33 6723 98 1 2 3 4 5 6 7 8 to_do index 6 6 N 8 did_swap true Swap Finished 2nd “Bubble Up”
- 56. The Third “Bubble Up” 42614 45 33 6723 98 1 2 3 4 5 6 7 8 to_do index 5 1 N 8 did_swap false
- 57. The Third “Bubble Up” 42614 45 33 6723 98 1 2 3 4 5 6 7 8 to_do index 5 1 N 8 did_swap false Swap
- 58. The Third “Bubble Up” 42623 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 1 N 8 did_swap true Swap
- 59. The Third “Bubble Up” 42623 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 2 N 8 did_swap true
- 60. The Third “Bubble Up” 42623 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 2 N 8 did_swap true Swap
- 61. The Third “Bubble Up” 42236 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 2 N 8 did_swap true Swap
- 62. The Third “Bubble Up” 42236 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 3 N 8 did_swap true
- 63. The Third “Bubble Up” 42236 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 3 N 8 did_swap true No Swap
- 64. The Third “Bubble Up” 42236 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 4 N 8 did_swap true
- 65. The Third “Bubble Up” 42236 45 33 6714 98 1 2 3 4 5 6 7 8 to_do index 5 4 N 8 did_swap true Swap
- 66. The Third “Bubble Up” 42236 33 45 6714 98 1 2 3 4 5 6 7 8 to_do index 5 4 N 8 did_swap true Swap
- 67. The Third “Bubble Up” 42236 33 45 6714 98 1 2 3 4 5 6 7 8 to_do index 5 5 N 8 did_swap true
- 68. The Third “Bubble Up” 42236 33 45 6714 98 1 2 3 4 5 6 7 8 to_do index 5 5 N 8 did_swap true Swap
- 69. The Third “Bubble Up” 45236 33 42 6714 98 1 2 3 4 5 6 7 8 to_do index 5 5 N 8 did_swap true Swap Finished 3rd “Bubble Up”
- 70. The Fourth “Bubble Up” 45236 33 42 6714 98 1 2 3 4 5 6 7 8 to_do index 4 1 N 8 did_swap false
- 71. The Fourth “Bubble Up” 45236 33 42 6714 98 1 2 3 4 5 6 7 8 to_do index 4 1 N 8 did_swap false Swap
- 72. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 1 N 8 did_swap true Swap
- 73. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 2 N 8 did_swap true
- 74. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 2 N 8 did_swap true No Swap
- 75. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 3 N 8 did_swap true
- 76. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 3 N 8 did_swap true No Swap
- 77. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 4 N 8 did_swap true
- 78. The Fourth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 4 4 N 8 did_swap true No Swap Finished 4th “Bubble Up”
- 79. The Fifth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 3 1 N 8 did_swap false
- 80. The Fifth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 3 1 N 8 did_swap false No Swap
- 81. The Fifth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 3 2 N 8 did_swap false
- 82. The Fifth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 3 2 N 8 did_swap false No Swap
- 83. The Fifth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 3 3 N 8 did_swap false
- 84. The Fifth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 3 3 N 8 did_swap false No Swap Finished 5th “Bubble Up”
- 85. The Sixth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 2 1 N 8 did_swap false
- 86. The Sixth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 2 1 N 8 did_swap false No Swap
- 87. The Sixth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 2 2 N 8 did_swap false
- 88. The Sixth “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 2 2 N 8 did_swap false No Swap Finished 6th “Bubble Up”
- 89. The Seventh “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 1 1 N 8 did_swap false
- 90. The Seventh “Bubble Up” 452314 33 42 676 98 1 2 3 4 5 6 7 8 to_do index 1 1 N 8 did_swap false No Swap Finished 7th “Bubble Up”
- 91. Sorted Elements 452314 33 42 676 98 1 2 3 4 5 6 7 8
- 92. Summary • “Bubble Up” algorithm will move largest value to its correct location (to the right) • Repeat “Bubble Up” until all elements are correctly placed: – Maximum of N-1 times – Can finish early if no swapping occurs • We reduce the number of elements we compare each time one is correctly placed