# Josephus Problem in Algol68

Published on 28 April 2022 (Updated: 02 February 2023) Welcome to the Josephus Problem in Algol68 page! Here, you’ll find the source code for this program as well as a description of how the program works.

## Current Solution

``````MODE PARSEINT_RESULT = STRUCT(BOOL valid, INT value, STRING leftover);
MODE PARSEINTLIST_RESULT = STRUCT(BOOL valid, REF []INT values);

PROC parse int = (REF STRING s) PARSEINT_RESULT:
(
BOOL valid := FALSE;
REAL r := 0.0;
INT n := 0;
STRING leftover;

# Associate string with a file #
FILE f;
associate(f, s);

# On end of input, exit if valid number not seen. Otherwise ignore it #
on logical file end(f, (REF FILE dummy) BOOL:
(
IF NOT valid THEN done FI;
TRUE
)
);

# Exit if value error #
on value error(f, (REF FILE dummy) BOOL: done);

# Convert string to real number #
get(f, r);

# If real number is in range of an integer, convert to integer. Indicate integer is valid if same as real #
IF ABS r <= max int
THEN
n := ENTIER(r);
valid := (n = r)
FI;

# Get leftover string #
get(f, leftover);

done:
close(f);
PARSEINT_RESULT(valid, n, leftover)
);

PROC usage = VOID: printf((\$gl\$, "Usage: please input the total number of people and number of people to skip."));

COMMENT
Reference: https://en.wikipedia.org/wiki/Josephus_problem#The_general_case

Use zero-based index algorithm:

g(1, k) = 0
g(m, k) = [g(m - 1, k) + k] MOD m, for m = 2, 3, ..., n

Final answer is g(n, k) + 1 to get back to one-based index
COMMENT
PROC josephus = (INT n, INT k) INT:
(
INT g := 0;
FOR m FROM 2 TO n
DO
g := (g + k) MOD m
OD;

g + 1
);

# Parse 1st and 2nd command-line arguments #
INT values;
FOR m TO 2
DO
STRING s := argv(m + 3);
PARSEINT_RESULT result := parse int(s);

# If invalid, extra characters, exit #
values[m] := value OF result;
IF NOT (valid OF result) OR (leftover OF result) /= ""
THEN
usage;
stop
FI
OD;

INT n := values;
INT k := values;
INT g := josephus(n, k);
printf((\$gl\$, whole(g, 0)))
``````

Josephus Problem in Algol68 was written by:

• rzuckerm

If you see anything you’d like to change or update, please consider contributing.

Note: The solution shown above is the current solution in the Sample Programs repository as of Jan 31 2023 21:55:33. The solution was first committed on Jan 24 2023 19:58:12. As a result, documentation below may be outdated.

## How to Implement the Solution

No ‘How to Implement the Solution’ section available. Please consider contributing.

## How to Run the Solution

No ‘How to Run the Solution’ section available. Please consider contributing.