Problem 3. (40 points) Answer the following problems. For each problem, start with the B+-tree in Figure 1. 0 12 15 16 HB 1001 H18|27| H22 || 39| 14 | 152 ||58| H23 | 80 Figure 1: B+-Tree Example (a) (10 points) Show the tree that would result from inserting 7 into the tree in Figure 1. You may omit the parts of the tree that do not change. (b) (10 points) Show the tree that would result from deleting 10 from the tree in Figure 1. You may omit the parts of the tree that do not change. (c) (10 points) Show the tree that would result from deleting 73 from the tree in Figure 1. You may omit the parts of the tree that do not change. (d) (10 points) Show the tree that would result from deleting 32, 39, 41, 45, and 73 from the tree in Figure 1 (no need to show the tree for each deletion). You may omit the parts of the tree that do not change. Problem 3. (40 points) Answer the following problems. For each problem, start with the B+-tree in Figure 1. 0 12 15 16 HB 1001 H18|27| H22 || 39| 14 | 152 ||58| H23 | 80 Figure 1: B+-Tree Example (a) (10 points) Show the tree that would result from inserting 7 into the tree in Figure 1. You may omit the parts of the tree that do not change. (b) (10 points) Show the tree that would result from deleting 10 from the tree in Figure 1. You may omit the parts of the tree that do not change. (c) (10 points) Show the tree that would result from deleting 73 from the tree in Figure 1. You may omit the parts of the tree that do not change. (d) (10 points) Show the tree that would result from deleting 32, 39, 41, 45, and 73 from the tree in Figure 1 (no need to show the tree for each deletion). You may omit the parts of the tree that do not change