2 Tromino Tiling (10 points) An I-ahaped tromieo in an object made op of three 11 wquarn, an abown in Figure 1 . A deficlent board in an nn board with one 11 qquare that is not tiled, where n=24 with k1. A tiling of a deficient hoard is an eact covering of the board with L-chapel trominoes without baving any of thin trominoee overlap ench cther at extend outside the board. Note that there could be multiple tilinge of a single deficient board. Figure 2 and Figure 3 thows an 88 deficket board and a tiling of it. Figure 1: An Lrehaped Tromino Figure 2: An 88 deficient bosed Figure 2 A tiling of an 88 de6. 2.1. (4 points) Design a divide and cosquer algorithin to find a tiling of an sn deficient beard. (a) ( 1 point) For a 22 grid, aceuming erientation, dencribe/draw the 4 wiss that you can tile it wing a tramino. (b) (3 points) Utilize your answe from 2.1(a) at your bece caie, dive a divile and cosper algarialin with a runtime of O(n2) for tiling an nn deficiest hoard. 2. (4 points) Justify the runtime of your algorithm. (a) (2 points) Write the recurrence relation in terms of side length n for your algorithm in Part a. Placing a single tromino takes constant, O(1), time. Remember to include your base case. (b) (2 points) Derive the asymptotic runtime based on the recurrence given in Part b. Do not use master theorem or master-masteruclear bomb theorem