Consider a table 𝑇, where the elements 𝑇[𝑖][𝑗], 0 ≤ 𝑖,𝑗 ≤ 𝑛, represent…

Consider a table 𝑇, where the elements 𝑇[𝑖][𝑗], 0 ≤ 𝑖,𝑗 ≤ 𝑛, represent the cost of the optimal solutions of different subproblems of a problem that is being solved using a dynamic programming algorithm. The recursive formulation to compute the table entries is as follows:
𝑇[0][𝑘] = 𝑇[𝑘][0] = 1 for 𝑘 = 0,1,2, … , 𝑛
𝑇[𝑖][𝑗] = 2𝑇[𝑖 − 1][𝑗] + 3𝑇[𝑖][𝑗 − 1] for 1 ≤ 𝑖,𝑗 ≤ n
Consider the following two algorithms to compute entries of 𝑇. Assume that for both the algorithms, for all 0 ≤ 𝑖,𝑗 ≤ 𝑛, 𝑇[𝑖][𝑗] has been initialized to 1.
Algorithm 𝐵1: For 𝑖 = 1, 2, … , 𝑛
For 𝑗 = 1, 2, … , 𝑛
𝑇[𝑖][𝑗] = 2𝑇[𝑖 − 1][𝑗] + 3𝑇[𝑖][𝑗 − 1]

Algorithm 𝐵2: For 𝑠 = 2, 3, … , 2𝑛
For 𝑖 = 1, 2, … , 𝑛
For 𝑗 = 1, 2, … , 𝑛
If (𝑖 + 𝑗 == 𝑠)
𝑇[𝑖][𝑗] = 2𝑇[𝑖 − 1][𝑗] + 3𝑇[𝑖][𝑗 − 1]

Algorithm 𝐵𝑘, 𝑘 ∈ {1,2} is said to be correct if and only if it calculates the correct values of 𝑇[𝑖][𝑗], for all 0 ≤ 𝑖,𝑗 ≤ 𝑛, (as per the recursive formulation) at the end of the execution of the algorithm 𝐵𝑘.
Which one of the following statements is true?