3. (10 points) Let Al0..10 -1] be a two-dimensional array of non-negative integers. A sequence of entries in A is a monotone cut if the following conditions are satisfied: Each row of A contains exactly one entry in the sequence Successive entries in the sequence are either in the same column or in adjacent columns. Given a monotone cut ?, the cost of a row AI.0..n-1) is equal to the (X-Y)2, where X (resp. Y) is the sum of the entries in Alj, 0.. -1 that lies strictly to the left (resp. right) of the entry of ? in row ALi,0..n-1). The cost of ? is the sum of the cost of all rows. Design a dynamic programming algorithm to find a monotone cut with the minimum cost. Explain your design and the running time of your algorithm. 3. (10 points) Let Al0..10 -1] be a two-dimensional array of non-negative integers. A sequence of entries in A is a monotone cut if the following conditions are satisfied: Each row of A contains exactly one entry in the sequence Successive entries in the sequence are either in the same column or in adjacent columns. Given a monotone cut ?, the cost of a row AI.0..n-1) is equal to the (X-Y)2, where X (resp. Y) is the sum of the entries in Alj, 0.. -1 that lies strictly to the left (resp. right) of the entry of ? in row ALi,0..n-1). The cost of ? is the sum of the cost of all rows. Design a dynamic programming algorithm to find a monotone cut with the minimum cost. Explain your design and the running time of your algorithm