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Homework 3Prof. Wellingcs171due: Th, May 3April 26, 20071. Use the min-conflict (local search) method to solve the 4-Queen problem. Start withthe queens on the main diagonal. Break ties randomly.2. Exercise 5.2 (page 158)3. Exercise 5.3 (page 158)4. Exercise 5.5 (page 159)5. Compute the following gradients:• a)f(x, y, z, t) = (x − 1) ∗ (2 − y) ∗ z + z ∗ (t3− 1) ∗ x ∗ y• b)g(x, y) =11 + e−(ax+by+c)where a, b and c are some constants• c)h(x, y, z) = (x − 1)2ex+ (y − 2)3z3• d)c(x, y, z) = (x − z − 2y−2)bwhere b is some constant126. Implement a gradient descent algorithm to minimize the cost-function:C(x, y) = 2(x − 1)2+ 2(y − 2)2− 2(x − 1)(y − 2)What is the solution? What step-size did you
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