Chapter 3 - Section 3.1 - Algorithms - Exercises - Page 203: 30

procedure modelist $(a_1, a_2, a_3, ... a_n: $ non-decreasing sequence of integers) target $:=$ getnum $(a_1, a_2, a_3, ... a_n)$ {This will tell us the number of occurrences that a mode has} Initialize a set MODES to contain all the modes. It is initially empty index$:=1$ while index $\le n$ $\space\space\space$ curvalue $:= a_{index}$ $\space\space\space$ number $:= 0$ $\space\space\space$ while $a_{index} $ is equal to curvalue AND index $\le n$ $\space\space\space$$\space\space\space$ number $:= $number + $1$ $\space\space\space$$\space\space\space$ index $:= $ index + $1$ $\space\space\space$ if number $=$ target then add curvalue to MODES return MODES procedure getnum($a_1, a_2, a_3, ..., a_n:$ non-decreasing sequence of integers) count$:=0$ mode$:= -1$ index$:=1$ while index $\le n$ $\space\space\space$ curvalue $:= a_{index}$ $\space\space\space$ number $:= 0$ $\space\space\space$ while $a_{index} $ is equal to curvalue AND index $\le n$ $\space\space\space$$\space\space\space$ number $:= $number + $1$ $\space\space\space$$\space\space\space$ index $:= $ index + $1$ $\space\space\space$ if number $>$ count $\space\space\space$$\space\space\space$ count = number $\space\space\space$$\space\space\space$ mode = curvalue return number

This algorithm attempts to find the modes that a specific set has. It does this by getting the number of occurrences of a mode. The algorithm for this is the same as the one used in exercise $29$ but instead of returning the mode, it returns the number of occurrences of the mode. It then goes over the set again and calculates the occurrences of every value; if the occurrence of some value $\alpha$ is equal to target, then it must be a mode. It stores those values in a list called MODES and then returns this set.