Add ex 1.10 sol

chapter-1/exercises/1.10.js

@@ -0,0 +1,113 @@
+//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))))))))
+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))))
+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))
+From previous substitution: A(2, 2) = 4
+A(2, 4)
+From previous substitution: A(2, 4) = 65536
+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 (Tetration)
+k(n) --> 5 * (n ** 2)
+*/