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bash/difference-of-squares/README.md

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+# Difference Of Squares
+
+Find the difference between the square of the sum and the sum of the squares of the first N natural numbers.
+
+The square of the sum of the first ten natural numbers is
+(1 + 2 + ... + 10)² = 55² = 3025.
+
+The sum of the squares of the first ten natural numbers is
+1² + 2² + ... + 10² = 385.
+
+Hence the difference between the square of the sum of the first
+ten natural numbers and the sum of the squares of the first ten
+natural numbers is 3025 - 385 = 2640.
+
+You are not expected to discover an efficient solution to this yourself from
+first principles; research is allowed, indeed, encouraged. Finding the best
+algorithm for the problem is a key skill in software engineering.
+
+
+Run the tests with:
+
+```bash
+bats difference_of_squares_test.sh
+```
+
+After the first test(s) pass, continue by commenting out or removing the
+`[[ $BATS_RUN_SKIPPED == true ]] || skip` 
+annotations prepending other tests.
+
+To run all tests, including the ones with `skip` annotations, run:
+
+```bash
+BATS_RUN_SKIPPED=true bats difference_of_squares_test.sh
+```
+
+## Source
+
+Problem 6 at Project Euler [http://projecteuler.net/problem=6](http://projecteuler.net/problem=6)
+
+
+## External utilities
+`Bash` is a language to write "scripts" -- programs that can call
+external tools, such as
+[`sed`](https://www.gnu.org/software/sed/),
+[`awk`](https://www.gnu.org/software/gawk/),
+[`date`](https://www.gnu.org/software/coreutils/manual/html_node/date-invocation.html)
+and even programs written in other programming languages, 
+like [`Python`](https://www.python.org/).
+This track does not restrict the usage of these utilities, and as long
+as your solution is portable between systems and does not require
+installation of third party applications, feel free to use them to solve
+the exercise.
+
+For an extra challenge, if you would like to have a better understanding
+of the language, try to re-implement the solution in pure `Bash`,
+without using any external tools. Note that there are some types of
+problems that bash cannot solve, such as performing floating point
+arithmetic and manipulating dates: for those, you must call out to an
+external tool.
+
+## Submitting Incomplete Solutions
+It's possible to submit an incomplete solution so you can see how others
+have completed the exercise.

bash/difference-of-squares/difference_of_squares.sh

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+#!/usr/bin/env bash
+#
+# External tools: none.
+# subshell: none.
+#
+# V1: initial version
+
+shopt -s extglob
+
+# set to mask to enable logs. 0: none, 255: all
+(( debug=2#00000000 ))
+#(( debug=2#00001111 ))
+# $1: log level (mask), then strings to display.
+debug () {
+    (( debug & $1 )) && shift && echo Line ${BASH_LINENO[0]}: "${@}" >&2
+}
+
+die () {
+    echo "${@}" >&2
+    exit 1
+}
+usage() {
+    die "usage: difference_of_squares.sh command color"
+}
+
+debug 1 "#=$#" "arg=$1"
+(($# != 2)) || [[ $1 != @(square_of_sum|sum_of_squares|difference) ]] || \
+    [[ "$2" != +([[:digit:]]) ]] && usage
+
+# the 2 next functions will set $1 to the calculated value for $2
+sum_of_squares () {                     # set $1 to sum of squares ($2)
+    local -n res=$1
+    local val=$2
+
+    # the sum of 1st n integers squares is:
+    #  S = 1² + 2² + 3² ..... + (n-1)² + n²
+    #    = [ n * (n+1) * (2n+1) ] / 6
+    # demonstration on:
+    #   http://www.takayaiwamoto.com/Sums_and_Series/sumsqr_1.html
+    (( res = val * (val+1) * (2*val + 1) / 6 ))
+    debug 2 "sum_of_squares($val) = $res"
+}
+square_of_sum () {                      # set $1 to square of sum ($2)
+    local -n res=$1
+    local val=$2
+
+    # The sum of n 1st integers is:
+    #  S  = 1 + 2 + 3 ... + (n-1) + n
+    #     = [ n * (n+1) ] / 2
+    # demonstration is trivial for this one.
+    (( res = (val * (val+1) / 2 ) ** 2 ))
+    debug 2 "square_of_sum($val) = $res"
+}
+
+action="$1"
+(( num = $2 ))
+
+case "$action" in
+     square_of_sum)
+         square_of_sum result "$num"
+         debug 3 "result after calling square_of_sum: $result"
+         ;;
+     sum_of_squares)
+         sum_of_squares result "$num"
+         debug 3 "result after calling sum_of_squares: $result"
+         ;;
+     difference)
+         square_of_sum SqSum "$num"
+         sum_of_squares SumSq "$num"
+         ((result = SqSum - SumSq))
+         debug 3 "result after calling difference: $result"
+esac
+
+echo $result
+exit 0
+
+# emacs/vim settings.
+# Local Variables:
+# sh-basic-offset: 4
+# indent-tabs-mode: nil
+# comment-column: 40
+# fill-column: 80
+# End:
+# vim: set tabstop=4 expandtab: