Sorting Damian Gordon.

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Presentation transcript:

Sorting Damian Gordon

Sorting Let’s remember our integer array from before:

Sorting 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18 Age

Sorting 44 23 1 42 2 33 3 16 4 54 5 34 6 18 7 Age How do we sort the data, in other words, get it into this order:

Sorting 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18 Age How do we sort the data, in other words, get it into this order: 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting As humans, we can sort the array just by inspection (just be looking at it), but if the array was 100,000 elements long it would be more of a challenge for us.

Sorting: Bubble Sort The simplest algorithm for sort an array is called BUBBLE SORT.

Sorting: Bubble Sort The simplest algorithm for sort an array is called BUBBLE SORT. It works as follows:

Sorting: Bubble Sort The simplest algorithm for sort an array is called BUBBLE SORT. It works as follows for an array of size N: Look at the first and second element Are they in order? If so, do nothing If not, swap them around Look at the second and third element Do the same Keep doing this until you get to the end of the array Go back to the start again keep doing this whole process for N times.

Sorting: Bubble Sort Lets look at the swapping bit if I wanted to swap two values, the following won’t work: Age[0] <- Age[1]; Age[1] <- Age[0]; Why not?

Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is:

Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is: 23

Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is: 23 23

Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is: 23 23 23

Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is: 23 23 23 23

NOT a Successful swap Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is: NOT a Successful swap 23 23 23 23

NOT a Successful swap Age[0]=23 Age[1]=23 Sorting: Bubble Sort Lets assume Age[0]=44, and Age[1]=23, if we do the following: Age[0] <- Age[1]; Age[1] <- Age[0]; What happens is: NOT a Successful swap Age[0]=23 Age[1]=23 23 23 23 23

Sorting: Bubble Sort We need an extra variable to make this work:

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value.

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1];

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0];

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value;

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23 44

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23 44 44

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23 44 44 23

Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23 44 44 23 23

Successful swap Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23 Successful swap 44 44 23 23

Age[0]=23 Age[1]=44 Successful swap Sorting: Bubble Sort We need an extra variable to make this work: Lets call it Temp_Value. Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; 23 23 Age[0]=23 Age[1]=44 Successful swap 44 44 23 23

Sorting: Bubble Sort Let’s wrap an IF statement around this: IF (Age[1] < Age[0]) THEN Temp_Value <- Age[1]; Age[1] <- Age[0]; Age[0] <- Temp_Value; ENDIF;

Sorting: Bubble Sort And in general: IF (Age[N+1] < Age[N]) THEN Temp_Value <- Age[N+1]; Age[N+1] <- Age[N]; Age[N] <- Temp_Value; ENDIF;

Sorting: Bubble Sort Let’s replace “N” with “Index” IF (Age[Index+1] < Age[Index]) THEN Temp_Value <- Age[Index+1]; Age[Index+1] <- Age[Index]; Age[Index] <- Temp_Value; ENDIF;

Sorting: Bubble Sort To get from one end of the array to another: FOR Index IN 0 TO N-2 DO IF (Age[Index+1] < Age[Index]) THEN Temp_Value <- Age[Index+1]; Age[Index+1] <- Age[Index]; Age[Index] <- Temp_Value; ENDIF; ENDFOR;

Sorting: Bubble Sort Does this mean we have the array sorted?

Sorting: Bubble Sort Does this mean we have the array sorted? No

Sorting: Bubble Sort 44 23 1 42 2 33 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 44 1 42 2 33 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 44 2 33 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 44 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 44 3 16 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 54 5 6 34 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 54 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 54 7 18 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort Age 23 42 1 33 2 16 3 44 4 34 5 18 6 54 7 23 42 1 33 2 16 3 44 4 34 5 18 6 54 7 Age So what happened?

Sorting: Bubble Sort Age 23 42 1 33 2 16 3 44 4 34 5 18 6 54 7 23 42 1 33 2 16 3 44 4 34 5 18 6 54 7 Age So what happened? We have moved the largest value (54) into the correct position.

Sorting: Bubble Sort Let’s do it again:

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 42 1 33 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 42 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 42 2 16 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 44 4 34 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 44 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 44 5 6 18 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort Age 23 1 33 2 16 3 42 4 34 5 18 6 44 7 54 23 1 33 2 16 3 42 4 34 5 18 6 44 7 54 Age So what happened?

Sorting: Bubble Sort Age 23 1 33 2 16 3 42 4 34 5 18 6 44 7 54 23 1 33 2 16 3 42 4 34 5 18 6 44 7 54 Age So what happened? We have moved the second largest value (44) into the correct position.

Sorting: Bubble Sort Let’s do it again:

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 33 1 16 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 42 3 34 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 34 3 42 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 34 3 42 4 18 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort Age 23 16 1 33 2 34 3 18 4 42 5 44 6 54 7 23 16 1 33 2 34 3 18 4 42 5 44 6 54 7 Age So what happened? We have moved the third largest value (42) into the correct position.

Sorting: Bubble Sort Let’s do it again:

Sorting: Bubble Sort 23 16 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 34 3 18 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort Age 16 23 1 33 2 18 3 34 4 42 5 44 6 54 7 16 23 1 33 2 18 3 34 4 42 5 44 6 54 7 Age So what happened?

Sorting: Bubble Sort Age 16 23 1 33 2 18 3 34 4 42 5 44 6 54 7 16 23 1 33 2 18 3 34 4 42 5 44 6 54 7 Age So what happened? We have moved the fourth largest value (34) into the correct position.

Sorting: Bubble Sort Let’s do it again:

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 33 2 18 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort Age 16 23 1 18 2 33 3 34 4 42 5 44 6 54 7 16 23 1 18 2 33 3 34 4 42 5 44 6 54 7 Age So what happened? We have moved the fifth largest value (33) into the correct position.

Sorting: Bubble Sort Let’s do it again:

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 23 1 18 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort Age 16 18 1 23 2 33 3 34 4 42 5 44 6 54 7 16 18 1 23 2 33 3 34 4 42 5 44 6 54 7 Age So what happened?

Sorting: Bubble Sort Age 16 18 1 23 2 33 3 34 4 42 5 44 6 54 7 16 18 1 23 2 33 3 34 4 42 5 44 6 54 7 Age So what happened? We have moved the sixth largest value (23) into the correct position.

Sorting: Bubble Sort Let’s do it again:

Sorting: Bubble Sort Let’s do it again: Let’s not bother!

Sorting: Bubble Sort Let’s do it again: Let’s not bother! It’s sorted!

Sorting: Bubble Sort 16 18 1 23 2 33 3 34 4 42 5 6 44 7 54 Age

Sorting: Bubble Sort So we need two loops:

Sorting: Bubble Sort So we need two loops: FOR Outer-Index IN 0 TO N-1 DO FOR Index IN 0 TO N-2 DO IF (Age[Index+1] < Age[Index]) THEN Temp_Value <- Age[Index+1]; Age[Index+1] <- Age[Index]; Age[Index] <- Temp_Value; ENDIF; ENDFOR;

Sorting: Bubble Sort PROGRAM BubbleSort: Integer Age[8] <- {44,23,42,33,16,54,34,18}; FOR Outer-Index IN 0 TO N-1 DO FOR Index IN 0 TO N-2 DO IF (Age[Index+1] < Age[Index]) THEN Temp_Value <- Age[Index+1]; Age[Index+1] <- Age[Index]; Age[Index] <- Temp_Value; ENDIF; ENDFOR; END.

Sorting: Bubble Sort

etc.