import sys

import math

def read$\_$timestamps$($file$\_$path$)$:

with open$($file$\_$path, $\text{'}$r$\text{'})$ as file:

data $=$ file.read$().$strip$()$

timestamps $=$ list$($map$($float$,$ data.split$()))$

return timestamps

def calculate$\_$intervals$($timestamps$)$:

intervals $=[$timestamps$[$i $+1]-$ timestamps$[$i$]$ for i in range$($len$($timestamps$)-1)]$

return intervals

def viterbi$\_$algorithm$($timestamps$,$ debug$=$False$)$:

intervals $=$ calculate$\_$intervals$($timestamps$)$

n $=$ len$($intervals$)$

k $=3$ # Number of states: $0,1,$ and $2$

# Initialize C and P matrices

C $=[[$float$(\text{'}$inf$\text{'})]*$ k for $\_$ in range$($n $+1)]$

P $=[[0]*($n $+1)$ for $\_$ in range$($k$)]$

C$[0][0]=0$

def tau$($l$,$ s$)$:

return $2\mathrm{.}20$ if l $!=$ s else $0$

def f$\_$s$($interval$,$ state$)$:

if state $==0$:

return $1\mathrm{.}0$ if interval $>=10$ else $0\mathrm{.}01$

elif state $==1$:

return $1\mathrm{.}0$ if $5<=$ interval $<10$ else $0\mathrm{.}01$

elif state $==2$:

return $1\mathrm{.}0$ if interval $<5$ else $0\mathrm{.}01$

if debug:

print$("$Initial C matrix:"$)$

for row in C:

print$([$round$($x$,2)$ if x $!=$ float$(\text{'}$inf$\text{'})$ else float$(\text{'}$inf$\text{'})$ for x in row$])$

print$("")$

for t in range$(1,$ n $+1)$:

for s in range$($k$)$:

lmin $=0$

cmin $=$ C$[$t $-1][0]+$ tau$(0,$ s$)$

for l in range$(1,$ k$)$:

c $=$ C$[$t $-1][$l$]+$ tau$($l$,$ s$)$

if c $<$ cmin:

cmin $=$ c

lmin $=$ l

C$[$t$][$s$]=$ cmin $-$ math.log$($f$\_$s$($intervals$[$t $-1],$ s$))$

P$[$s$][$:t$]=$ P$[$lmin$][$:t$]$

P$[$s$][$t$]=$ s

if debug:

print$($f$"$Iteration $\{$t$\}")$

print$($f$"$Intervals: $\{$intervals$[$t $-1]\}")$

print$($f$"$C matrix after iteration $\{$t$\}$:$")$

for row in C:

print$([$round$($x$,2)$ if x $!=$ float$(\text{'}$inf$\text{'})$ else float$(\text{'}$inf$\text{'})$ for x in row$])$

print$("$P matrix:"$)$

for row in P:

print$($row$)$

print$("")$

cmin $=$ C$[$n$][0]$

smin $=0$

for s in range$(1,$ k$)$:

if C$[$n$][$s$]<$ cmin:

cmin $=$ C$[$n$][$s$]$

smin $=$ s

if debug:

print$($f$"$Final cmin$=\{$round$($cmin$,2)\},$ smin$=\{$smin$\}")$

print$("")$

return P$[$smin$][$:n $+1]$

def merge$\_$intervals$($timestamps$,$ states$)$:

merged$\_$intervals $=[]$

start$\_$time $=$ timestamps$[0]$

current$\_$state $=$ states$[0]$

for i in range$(1,$ len$($states$))$:

if states$[$i$]!=$ current$\_$state:

merged$\_$intervals.append$(($current$\_$state, start$\_$time, timestamps$[$i$]))$

start$\_$time $=$ timestamps$[$i$]$

current$\_$state $=$ states$[$i$]$

merged$\_$intervals.append$(($current$\_$state, start$\_$time, timestamps$[-1]))$

return merged$\_$intervals

def print$\_$viterbi$\_$output$($merged$\_$intervals$)$:

for state, start$\_$time, end$\_$time in merged$\_$intervals:

print$($f$"\{$state$\}[\{$start$\_$time$\}\{$end$\_$time$\})")$

if $\_\_$name$\_\_=="\_\_$main$\_\_"$:

if len$($sys$.$argv$)<3$:

print$("$Usage: python bursts.py $[-$d$]")$

sys$.$exit$(1)$

algorithm $=$ sys$.$argv$[1]$

file$\_$path $=$ sys$.$argv$[2]$

debug $=$ len$($sys$.$argv$)>3$ and sys$.$argv$[3]==\text{'}-$d$\text{'}$

timestamps $=$ read$\_$timestamps$($file$\_$path$)$

if algorithm $==$ "viterbi":

states $=$ viterbi$\_$algorithm$($timestamps$,$ debug$)$

merged$\_$intervals $=$ merge$\_$intervals$($timestamps$,$ states$)$

print$\_$viterbi$\_$output$($merged$\_$intervals$)$

else:

print$("$Invalid algorithm. Use 'viterbi'."$)$ for python bursts.py viterbi three$\_$states$\_1.$txt i get $0[0\mathrm{.}0415\mathrm{.}0)$

$1[415\mathrm{.}0451\mathrm{.}0)$

$2[451\mathrm{.}0480\mathrm{.}0)$

$0[480\mathrm{.}0485\mathrm{.}0)$

$1[485\mathrm{.}0700\mathrm{.}0)$

$0[700\mathrm{.}0715\mathrm{.}0)$

$1[715\mathrm{.}0900\mathrm{.}0)$

$0[900\mathrm{.}01000\mathrm{.}0)$ where as i should be getting as a result $0[0\mathrm{.}0410\mathrm{.}0)$

$1[410\mathrm{.}0450\mathrm{.}0)$

$2[450\mathrm{.}0469\mathrm{.}0)$

$1[469\mathrm{.}0600\mathrm{.}0)$

$0[600\mathrm{.}0710\mathrm{.}0)$

$1[710\mathrm{.}0800\mathrm{.}0)$

$0[800\mathrm{.}01000\mathrm{.}0)$ what is wrong and how can it be fixed $?$