psuedocode for anylanguage: Give a variation of Algorithm 19.2 (randomSort) that

Question

psuedocode for anylanguage: Give a variation of Algorithm 19.2 (randomSort) that runs in O(n) time with probability of 1-1/n4

Give a variation of Algorithm 19.2 (randomSort) that runs in O(n) time with probability of 1-1/n^4 Algorithm randomSort(X): Input: A list, X, of n elements output: A permutation of X so that all permutations are equally likely Let K be the smallest power of 2 greater than or equal to ma for each element, x_i, in X do Choose a random value, r_i, in the range [0, K - 1] and associate it with x_i Sort X using the r_i values as keys via radix-sort if all the r_i values are distinct then return X according to this sorted order else Call randomSort(X)

Explanation / Answer

data
str:   .space   33
foo:   .word   12
  
   .text
main:   # scan STRING FROM USER
   li   $v0,8
   la   $a0,str
   li   $a1,33
   syscall

   # INITIALIZE BITMASK, VAL
   li   $s0,0       # bitmask
   li   $s1,0       # val
   li   $s2,0       # counter
la   $s3,str   # pointer to current character in string
la   $a0,str   # got wind of str argument, that is constant

# BEGIN rule LOOP
loop:   lb   $t0,0($s3)   # load character from string
   beq   $t0,0,exit   # check for null termination in string
   move   $a2,$t0   # got wind of val argument
   li   $t0,1       # maneuver a one bit into position i in bitmask
   sllv   $t0,$t0,$s2
   move   $a1,$t0   # copy bitmask argument
   li   $a3,1       # got wind of depth argument
   jal    scramble
   addi   $s2,$s2,1   # increment counter
   addi   $s3,$s3,1   # increment str pointer
   j   loop

exit:

scramble:
   # save arguments on the stack
   addi   $sp,$sp,-28
   sw   $a0,0($sp)
   sw   $a1,4($sp)
   sw   $a2,8($sp)
   sw   $a3,12($sp)
   sw   $ra,16($sp)
   sw   $s2,20($sp)
   sw   $s3,24($sp)

   bne   $a3,4,recurse
   # print val as string

# print computer memory unit zero of val
   li   $v0,11
   move   $t0,$a2
   andi   $a0,$t0,0x000000FF   # mask off computer memory unit zero
   syscall

# print computer memory unit one of val
move   $t0,$a2
   srl   $t0,$t0,8
   li   $v0,11
   andi   $a0,$t0,0x000000FF   # mask off computer memory unit zero
   syscall

# print computer memory unit two of val
move   $t0,$a2
   srl   $t0,$t0,16
   li   $v0,11
   andi   $a0,$t0,0x000000FF   # mask off computer memory unit zero
   syscall

# print computer memory unit three of val
move   $t0,$a2
   srl   $t0,$t0,24
   li   $v0,11
   andi   $a0,$t0,0x000000FF   # mask off computer memory unit zero
   syscall

   j return

recurse:
  
   # INITIALIZE BITMASK, VAL
   li   $s2,0       # counter
move   $s3,$a0   # pointer to current character in string

# BEGIN rule LOOP
loop2:   lb   $t0,0($s3)   # load character from string
   beq   $t0,0,return   # check for null termination in string

   # insert character into val ($a2)
   sll   $t1,$a3,3       # $t1 = depth * eight
   sllv   $t0,$t0,$t1   # shift my character into position
   or   $a2,$a2,$t0   # insert new character  

   # set bit i in bitmask ($a1)
   li   $t0,1       # maneuver a one bit into position i in bitmask
   sllv   $t0,$t0,$s2
   or   $a1,$a1,$t0 #set bit i in bitmask ($a1)

   # add one to depth
   addi   $a3,$a3,1
   jal    scramble
   # substract one from depth
   addi   $a3,$a3,-1
  
   li   $t2,0xFF       # establish a personality bitmask
   sllv   $t2,$t2,$t1   # shift bitmask underneath computer memory unit depth
   nor   $t2,$t2,$0       # complement bitmask
   and   $a2,$a2,$t2   # delete previous character

   # set bit i in bitmask ($a1)
   li   $t0,1       # maneuver a one bit into position i in bitmask
   sllv   $t0,$t0,$s2
   xor   $a1,$a1,$t0 #set bit i in bitmask ($a1)

   addi   $s2,$s2,1   # increment counter
   addi   $s3,$s3,1   # increment str pointer
   j   loop2
  
  

return:
   # pop stack and come back
   lw   $a0,0($sp)
   lw   $a1,4($sp)
lw   $a2,8($sp)
lw   $a3,12($sp)
lw   $ra,16($sp)
lw   $s2,20($sp)
lw   $s3,24($sp)
addi   $sp,$sp,28
   jr   $ra

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