Shell Programming - Write a program called collect users

#!/bin/bash
#This program runs in the background and counts the number of users logged in
#at the end of each interval and also the number of processes run during that
#interval.
if [ $# -eq 0 ]; then
        echo "usage: `basename $0` -t time | time" >&1; exit 2
elif [ "$1" = "-t" ]; then
        if [ $# -eq 2 ]; then
                time="$2"
        else
                time=600
        fi
else
        time="$1"
fi
if [ "$time" -lt 0 ]; then
    echo "Invalid argument: $time" >&2; exit 2
fi
function do_ps {
        ps -a | awk '$1 != "PID" && $1 != 1 { print $1 }' | sort -u >$1
}
newfile=/tmp/file1.$$
oldfile=/tmp/file2.$$
trap "rm -f $newfile $oldfile; exit 1" 2 3 15
let time=$((`date +%s`+$time))
do_ps $oldfile
back=$!
while [ `date +%s` -le ${time} ]; do
        do_ps $newfile
        #check for foreground processes
        if [ $((tmp=`diff $newfile $oldfile | grep -c "^<"`)) -ge 1 ]; then
                let count+=${tmp}
                tmp=$oldfile
                oldfile=$newfile
                newfile=$tmp
        fi
        #check for background processes
        if [ ${back} -ne $! ]; then
                let count+=1
                back=$!
        fi
        sleep 1
done
echo There were $count processes running
echo There were `who | uniq | wc -l` users on the system
rm $oldfile
rm $newfile