# HG changeset patch
# User Robert McIntyre <rlm@mit.edu>
# Date 1326889137 25200
# Node ID c8e35134bf8e40e98a5fe7df481626b5598c02a9
# Parent  c7df1ea6fd7187c328e23990a5d21f2ba58c570d
working on qotd.

diff -r c7df1ea6fd71 -r c8e35134bf8e src/rlm/function_utils.clj
--- a/src/rlm/function_utils.clj	Tue Dec 27 23:27:22 2011 -0700
+++ b/src/rlm/function_utils.clj	Wed Jan 18 05:18:57 2012 -0700
@@ -80,6 +80,22 @@
 	 (dorun (map future-cancel futures))
 	 answer))))
 
+(defn mix-pred
+  "Takes any number of mathematically equal functions with
+   possibly different run-times and returns a function that
+   runs each in a separate thread, returns the result from
+   the first thread which finishes, and cancels the other threads."
+  {:author "Robert McIntyre"}
+  ([pred & functions]
+     (fn [& args]
+       (let [result (promise)
+	     futures (doall (for [fun functions]
+                              (let [answer (apply fun args)]
+                                (if (pred answer)
+                                  (future (deliver result (apply fun args)))))))
+	     answer @result]
+	 (dorun (map future-cancel futures))
+	 answer))))
 
 
 
diff -r c7df1ea6fd71 -r c8e35134bf8e src/rlm/qotd.clj
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/rlm/qotd.clj	Wed Jan 18 05:18:57 2012 -0700
@@ -0,0 +1,80 @@
+(ns rlm.qotd)
+(rlm.rlm-commands/help)
+
+;;;There is a pair of integers, 1 < m < n, whose sum is less
+;;;than 100.
+
+(def pos (fn [a]
+           (filter (fn [[a b]] (< a b))
+                   (map #(vector % a) (range 1 (- 100 a))))))
+
+(def p0 (reduce concat (map pos (range 2 99))))
+
+;;; Person S knows their sum, but nothing else about them.
+;;; Person P knows their product, but nothing else about
+;;; them.
+
+;;; Now, Persons S and P know the above information, and each
+;;; one knows that the other one knows it. They have the
+;;; following conversation:
+
+;;; P: I can't figure out what the numbers are.
+
+
+
+;; Eliminate pairs with a unique product.
+
+(defn group-by
+  "Split coll into groups where the f maps each element in a
+  group to the same value in O(n*log(n)) time."
+  [f coll]
+  (partition-by f (sort-by f coll)))
+
+(defn unique-by
+  "Remove all elements a,b of coll that for which
+   (= (f a) (f b)) in O(n*log(n)) time."
+  [f coll]
+  (reduce
+    concat
+    (filter #(= (count %) 1) (group-by f coll))))
+  
+(defn multiple-by
+  "Keep all elements a,b, a!=b of coll for which
+   (= (f a) (f b)) in O(n*log(n)) time."
+  [f coll]
+  (reduce
+    concat
+    (filter #(> (count %) 1) (group-by f coll))))
+
+(defn prod [[a b]] (* a b))
+
+(def p1 (multiple-by prod p0))
+
+;;; S: I was sure you couldn't.
+
+;; Each possible sum s has a set of possible pairs [a b]
+;; where (= s (+ a b)). Partition p0 (since he *was* sure)
+;; by sum, and keep those pairs that belong in partitions
+;; where each pair in that partition is in p1.
+
+(defn sum [[a b]] (+ a b))
+
+(def p2
+  (reduce
+   concat
+   (filter
+    (partial every? (set p1))
+    (group-by sum p0))))
+
+
+;;; P: Then I have.
+
+;; Keep those pairs that have a unique product out of the
+;; ones that are left.
+
+(def p3
+  (unique-by prod p2))
+
+
+;;; S: Then I have, too.
+
diff -r c7df1ea6fd71 -r c8e35134bf8e src/rlm/rlm_commands.clj
--- a/src/rlm/rlm_commands.clj	Tue Dec 27 23:27:22 2011 -0700
+++ b/src/rlm/rlm_commands.clj	Wed Jan 18 05:18:57 2012 -0700
@@ -124,7 +124,9 @@
    "/home/r/java/jdk6u30-docs/jdk/api")
   (clojure.java.javadoc/add-local-javadoc
    "/home/r/java/jdk6u30-docs/jre/api")
-  
+  (clojure.java.javadoc/add-local-javadoc
+   "/home/r/proj/jmeCapture/docs")
+
   nil)