n = 2 3 (b) Answer the following questions in your script file. It will be handgraded. For the puzzle defined below (which turns out to be a relatively easy-to-solve Sudoku puzzle for people) begin code NaN; P1 = [2 n 8 4 5 6 n 79; n 5 6 9 7 nn 4 1; nnnnnn 6nn; n2 n n 9 4nnn; 6 nnnnnnn 8; nnn 7 8 n n 6 n; nn 4 nnnnnn; 18 nn 4 5 7 9 n; 7 6 n 3 1 9 4 n 5] ; end code 4 5 6 7 00 9 10 how many leaf nodes are in the associated tree? If you can examine the arrays at the leaf nodes for valid Sudoku solutions (since these are completely filled in puzzles) at 1 billion/ second, approximately how many centuries will it take to look at all leaf nodes? Clearly, there are an enormous number of leaf nodes in a typical Sudoku puzzle, and there is not enough time to individually look at all leaf nodes. If the puzzle-array at any node (even only partially filled) violates the row/column/array rules, what can you say about all of its descendent puzzle arrays? For example, the puzzle below is a child of P1 begin code C1 = [2 n 8 4 5 6 n 7 9; 2.5 6 9 7 n n 4 1; nnnnnn 6nn; n 2 nn 9 4 nnn; 6 nnnnnnn 8; 2 3 5 6 7 nnn 7 8 nn 6 n; nn 4 nnnnnn; 18 n n 4 5 7 9 n; 76 n 31 9 4 n 5] ; 8 9 end code Note that it differs from P1 only in the (2,1) entry. Can any of its descendants ever be a solution? n = 2 3 (b) Answer the following questions in your script file. It will be handgraded. For the puzzle defined below (which turns out to be a relatively easy-to-solve Sudoku puzzle for people) begin code NaN; P1 = [2 n 8 4 5 6 n 79; n 5 6 9 7 nn 4 1; nnnnnn 6nn; n2 n n 9 4nnn; 6 nnnnnnn 8; nnn 7 8 n n 6 n; nn 4 nnnnnn; 18 nn 4 5 7 9 n; 7 6 n 3 1 9 4 n 5] ; end code 4 5 6 7 00 9 10 how many leaf nodes are in the associated tree? If you can examine the arrays at the leaf nodes for valid Sudoku solutions (since these are completely filled in puzzles) at 1 billion/ second, approximately how many centuries will it take to look at all leaf nodes? Clearly, there are an enormous number of leaf nodes in a typical Sudoku puzzle, and there is not enough time to individually look at all leaf nodes. If the puzzle-array at any node (even only partially filled) violates the row/column/array rules, what can you say about all of its descendent puzzle arrays? For example, the puzzle below is a child of P1 begin code C1 = [2 n 8 4 5 6 n 7 9; 2.5 6 9 7 n n 4 1; nnnnnn 6nn; n 2 nn 9 4 nnn; 6 nnnnnnn 8; 2 3 5 6 7 nnn 7 8 nn 6 n; nn 4 nnnnnn; 18 n n 4 5 7 9 n; 76 n 31 9 4 n 5] ; 8 9 end code Note that it differs from P1 only in the (2,1) entry. Can any of its descendants ever be a solution