From 9f3d527820f21cca5b71376724c5b4daef4b4122 Mon Sep 17 00:00:00 2001
From: Ahmad El-Melegy <ahmad.melegy@gmail.com>
Date: Wed, 28 Jan 2015 19:05:48 +0200
Subject: [PATCH 1/3] Add 1.10 exercise solution

---
 chapter-1/exercises/1.10.js | 132 ++++++++++++++++++++++++++++++++++++
 1 file changed, 132 insertions(+)

diff --git a/chapter-1/exercises/1.10.js b/chapter-1/exercises/1.10.js
index e69de29..d06c59d 100644
--- a/chapter-1/exercises/1.10.js
+++ b/chapter-1/exercises/1.10.js
@@ -0,0 +1,132 @@
+//Exercise 1.10. The following function computes a mathematical function called Ackermann’s function.
+
+function A(x,y) {
+   if (y === 0) 
+        return 0;
+   else if (x === 0) 
+        return 2 * y;
+   else if (y === 1)
+        return 2;
+   else return A(x - 1, A(x, y - 1));
+}
+
+/* What are the values of the following expressions?
+A(1, 10)
+A(2, 4)
+A(3, 3)
+*/
+
+//Solution
+
+/*
+A(1, 10)
+A(0, A(1, 9))
+A(0, A(0, A(1, 8)))
+A(0, A(0, A(0, A(1, 7))))
+A(0, A(0, A(0, A(0, A(1, 6)))))
+A(0, A(0, A(0, A(0, A(0, A(1, 5))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(1, 4)))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 3))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 2)))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 1)))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 2))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 4)))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, 8))))))
+A(0, A(0, A(0, A(0, A(0, A(0, 16)))))
+A(0, A(0, A(0, A(0, A(0, 32))))
+A(0, A(0, A(0, A(0, 64)))
+A(0, A(0, A(0, 128))
+A(0, A(0, 256)
+A(0, 512)
+1024
+
+---------------------------------------------------------------------
+
+A(2, 4)
+A(1, A(2, 3))
+A(1, A(1, A(2, 2)))
+A(1, A(1, A(1, A(2, 1))))
+A(1, A(1, A(1, 2)))
+A(1, A(1, A(0, A(1, 1))))
+A(1, A(1, A(0, 2)))
+A(1, A(1, 4))
+A(1, A(0, A(1, 3)))
+A(1, A(0, A(0, A(1, 2))))
+A(1, A(0, A(0, A(0, A(1, 1)))))
+A(1, A(0, A(0, A(0, 2)))))
+A(1, A(0, A(0, 4))))
+A(1, A(0, 8)))
+A(1, 16))
+A(0, A(1, 15)))
+A(0, A(0, A(1, 14))))
+A(0, A(0, A(0, A(1, 13)))))
+A(0, A(0, A(0, A(0, A(1, 12))))))
+A(0, A(0, A(0, A(0, A(0, A(1, 11)))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(1, 10))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 9)))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 8))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 7)))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 6))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 5)))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 4))))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 3)))))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 2))))))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 1))))))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 2)))))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 4))))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 8)))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 16))))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 32)))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 64))))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 128)))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 256))))))))
+A(0, A(0, A(0, A(0, A(0, A(0, A(0, 512)))))))
+A(0, A(0, A(0, A(0, A(0, A(0, 1024))))))
+A(0, A(0, A(0, A(0, A(0, 2048)))))
+A(0, A(0, A(0, A(0, 4096))))
+A(0, A(0, A(0, 8192)))
+A(0, A(0, A(0, 8192)))
+A(0, A(0, 16384))
+A(0, 32768)
+65536
+
+---------------------------------------------------------------------
+
+A(3, 3)
+A(2, A(3, 2))
+A(2, A(2, A(3, 1)))
+A(2, A(2, 2))
+A(2, A(1, A(2, 1)))
+A(2, A(1, 2))
+A(2, A(0, A(1, 1)))
+A(2, A(0, 2))
+A(2, 4)
+From previous substitution then ->
+65536
+*/
+
+//Consider the following functions, where A is the function defined above:
+
+function f(n) {
+   return A(0,n);
+}
+function g(n) {
+   return A(1,n);
+}
+function h(n) {
+   return A(2,n);
+}
+function k(n) {
+   return 5 * n * n;
+}
+
+//Give concise mathematical definitions for the functions computed by the functions f, g, and h for positive integer values of . For example, (k n) computes .
+
+//Solution
+
+/*
+f(n) --> 2 * n
+g(n) --> 2 ** n
+h(n) --> 2 ** 2 ** 2 .. n times
+k(n) --> 5 * (n ** 2)
+*/

From 2822950b6f84d290c468e11a3011dbea98fe596c Mon Sep 17 00:00:00 2001
From: Ahmad El-Melegy <ahmad.melegy@gmail.com>
Date: Thu, 29 Jan 2015 01:34:22 +0200
Subject: [PATCH 2/3] use A(1, 10) in 2nd problem, fix Indentation, add the
 term (Tetration)

---
 chapter-1/exercises/1.10.js | 44 ++++++++++++-------------------------
 1 file changed, 14 insertions(+), 30 deletions(-)

diff --git a/chapter-1/exercises/1.10.js b/chapter-1/exercises/1.10.js
index d06c59d..b32ae7f 100644
--- a/chapter-1/exercises/1.10.js
+++ b/chapter-1/exercises/1.10.js
@@ -1,13 +1,14 @@
 //Exercise 1.10. The following function computes a mathematical function called Ackermann’s function.
 
 function A(x,y) {
-   if (y === 0) 
-        return 0;
-   else if (x === 0) 
-        return 2 * y;
-   else if (y === 1)
-        return 2;
-   else return A(x - 1, A(x, y - 1));
+	if (y === 0) 
+		return 0;
+	else if (x === 0) 
+		return 2 * y;
+	else if (y === 1)
+		return 2;
+	else
+		return A(x - 1, A(x, y - 1));
 }
 
 /* What are the values of the following expressions?
@@ -63,24 +64,7 @@ A(0, A(0, A(0, A(1, 13)))))
 A(0, A(0, A(0, A(0, A(1, 12))))))
 A(0, A(0, A(0, A(0, A(0, A(1, 11)))))))
 A(0, A(0, A(0, A(0, A(0, A(0, A(1, 10))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 9)))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 8))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 7)))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 6))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 5)))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 4))))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 3)))))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 2))))))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(1, 1))))))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 2)))))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 4))))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 8)))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 16))))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 32)))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 64))))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 128)))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, A(0, 256))))))))
-A(0, A(0, A(0, A(0, A(0, A(0, A(0, 512)))))))
+From previous substitution then -> A(1, 10) = 1024
 A(0, A(0, A(0, A(0, A(0, A(0, 1024))))))
 A(0, A(0, A(0, A(0, A(0, 2048)))))
 A(0, A(0, A(0, A(0, 4096))))
@@ -108,16 +92,16 @@ From previous substitution then ->
 //Consider the following functions, where A is the function defined above:
 
 function f(n) {
-   return A(0,n);
+	return A(0,n);
 }
 function g(n) {
-   return A(1,n);
+	return A(1,n);
 }
 function h(n) {
-   return A(2,n);
+	return A(2,n);
 }
 function k(n) {
-   return 5 * n * n;
+	return 5 * n * n;
 }
 
 //Give concise mathematical definitions for the functions computed by the functions f, g, and h for positive integer values of . For example, (k n) computes .
@@ -127,6 +111,6 @@ function k(n) {
 /*
 f(n) --> 2 * n
 g(n) --> 2 ** n
-h(n) --> 2 ** 2 ** 2 .. n times
+h(n) --> 2 ** 2 ** 2 .. n times (Tetration)
 k(n) --> 5 * (n ** 2)
 */

From 6ca8fd6d47276867fa75df72b9edcdc6811f4164 Mon Sep 17 00:00:00 2001
From: Ahmad El-Melegy <ahmad.melegy@gmail.com>
Date: Thu, 29 Jan 2015 01:40:57 +0200
Subject: [PATCH 3/3] use A(2, 2) in 3rd problem

---
 chapter-1/exercises/1.10.js | 9 +++------
 1 file changed, 3 insertions(+), 6 deletions(-)

diff --git a/chapter-1/exercises/1.10.js b/chapter-1/exercises/1.10.js
index b32ae7f..75666ce 100644
--- a/chapter-1/exercises/1.10.js
+++ b/chapter-1/exercises/1.10.js
@@ -64,7 +64,7 @@ A(0, A(0, A(0, A(1, 13)))))
 A(0, A(0, A(0, A(0, A(1, 12))))))
 A(0, A(0, A(0, A(0, A(0, A(1, 11)))))))
 A(0, A(0, A(0, A(0, A(0, A(0, A(1, 10))))))))
-From previous substitution then -> A(1, 10) = 1024
+From previous substitution: A(1, 10) = 1024
 A(0, A(0, A(0, A(0, A(0, A(0, 1024))))))
 A(0, A(0, A(0, A(0, A(0, 2048)))))
 A(0, A(0, A(0, A(0, 4096))))
@@ -80,12 +80,9 @@ A(3, 3)
 A(2, A(3, 2))
 A(2, A(2, A(3, 1)))
 A(2, A(2, 2))
-A(2, A(1, A(2, 1)))
-A(2, A(1, 2))
-A(2, A(0, A(1, 1)))
-A(2, A(0, 2))
+From previous substitution: A(2, 2) = 4
 A(2, 4)
-From previous substitution then ->
+From previous substitution: A(2, 4) = 65536
 65536
 */