# 9.4: Bubble Sort

- Page ID
- 27151

Sorting is the process of arranging data in an ascending or descending order. This example will introduce an algorithm, the Bubble Sort, for sorting integer data in a array. Consider for example the following array containing integer values.

The sort is carried out in two loops. The inner loop passes once through the data comparing elements in the array and swapping them if they are not in the correct order. For example, element 0 (55) is compared to element 1 (27), and they are swapped since 55 > 27

Next element 1 (now 55) is compared with element 2 (13), and they are swapped since 55 > 13.

This process continues until a complete pass has been made through the array. At the end of the inner loop the largest value of the array is at the end of the array, and in its correct position. The array would look as follows.

This process continues until a complete pass has been made through the array. At the end of the inner loop the largest value of the array is at the end of the array, and in its correct position. The array would look as follows.

Repeating this outer loop for all elements results in the array being sorted in ascending order.

Pseudo code for this algorithm follws.

for (int i = 0; i < size-1; i++) { for (int j = 0; j < ((size-1)-i); j++) { if (data[j] > data[j+1]) { swap(data, j, j+1) } } } swap(data, i, j) int tmp = data[i]; data[i] = data[j]; data[j] = tmp; }

## 9.3.1 Bubble Sort in MIPS assembly

The following assembly program implements the Bubble Sort matching the pseudo code algorithm in the previous section.

Program 9-4: Bubble Sort .text .globl main main: la $a0, array_base lw $a1, array_size jal PrintIntArray la $a0, array_base lw $a1, array_size jal BubbleSort jal PrintNewLine la $a0, array_base lw $a1, array_size jal PrintIntArray jal Exit .data array_size: .word 8 array_base: .word 55 .word 27 .word 13 .word 5 .word 44 .word 32 .word 17 .word 36 .text # Subproram: Bubble Sort # Purpose: Sort data using a Bubble Sort algorithm # Input Params: $a0 - array # $a1 - array size # Register conventions: # $s0 - array base # $s1 - array size # $s2 - outer loop counter # $s3 - inner loop counter BubbleSort: addi $sp, $sp -20 # save stack information sw $ra, 0($sp) sw $s0, 4($sp) # need to keep and restore save registers sw $s1, 8($sp) sw $s2, 12($sp) sw $s3, 16($sp) move $s0, $a0 move $s1, $a1 addi $s2, $zero, 0 #outer loop counter OuterLoop: addi $t1, $s1, -1 beqz $t0, EndOuterLoop addi $s3, $zero, 0 #inner loop counter InnerLoop: addi $t1, $s1, -1 sub $t1, $t1, $s2 slt $t0, $s3, $t1 beqz $t0, EndInnerLoop sll $t4, $s3, 2 # load data[j]. Note offset is 4 bytes add $t5, $s0, $t4 lw $t2, 0($t5) addi $t6, $t5, 4 # load data[j+1] lw $t3, 0($t6) sgt $t0, $t2, $t3 beqz $t0, NotGreater move $a0, $s0 move $a1, $s3 addi $t0, $s3, 1 move $a2, $t0 jal Swap # t5 is &data[j], t6 is &data[j=1] NotGreater: addi $s3, $s3, 1 b InnerLoop EndInnerLoop: addi $s2, $s2, 1 b OuterLoop EndOuterLoop: lw $ra, 0($sp) #restore stack information lw $s0, 4($sp) lw $s1, 8($sp) lw $s2, 12($sp lw $s3, 16($sp) addi $sp, $sp 20 jr $ra # Subprogram: swap # Purpose: to swap values in an array of integers # Input parameters: $a0 - the array containing elements to swap # $a1 - index of element 1 # $a2 - index of elelemnt 2 # Side Effects: Array is changed to swap element 1 and 2 Swap: sll $t0, $a1, 2 # calcualate address of element 1 add $t0, $a0, $t0 sll $t1, $a2, 2 # calculate address of element 2 add $t1, $a0, $t1 lw $t2, 0($t0) #swap elements lw $t3, 0($t1) sw $t2, 0($t1) sw $t3, 0($t0) jr $ra # Subprogram: PrintIntArray # Purpose: print an array of ints # inputs: $a0 - the base address of the array # $a1 - the size of the array # PrintIntArray: addi $sp, $sp, -16 # Stack record sw $ra, 0($sp) sw $s0, 4($sp) sw $s1, 8($sp) sw $s2, 12($sp) move $s0, $a0 # save the base of the array to $s0 # initialization for counter loop # $s1 is the ending index of the loop # $s2 is the loop counter move $s1, $a1 move $s2, $zero la $a0 open_bracket # print open bracket jal PrintString loop: # check ending condition sge $t0, $s2, $s1 bnez $t0, end_loop sll $t0, $s2, 2 # Multiply the loop counter by 4 to get offset (each element is 4 big). add $t0, $t0, $s0 # address of next array element lw $a1, 0($t0) # Next array element la $a0, comma jal PrintInt # print the integer from array addi $s2, $s2, 1 #increment $s0 b loop end_loop: li $v0, 4 # print close bracket la $a0, close_bracket syscall lw $ra, 0($sp) lw $s0, 4($sp) lw $s1, 8($sp) lw $s2, 12($sp) # restore stack and return addi $sp, $sp, 16 jr $ra .data open_bracket: .asciiz "[" close_bracket: .asciiz "]" comma: .asciiz "," .include "utils.asm"