Problem Set 2 Solutions

Problem 1. this needs to be fleshed out We will use 3 arrays A, B, and C. A will represent that actual array and hold the stored items in their stored positions. Arrays B and C will act as “checks” for which entries of A are truly initialized. B will contain a list, built up sequentially from position 0, of all entries of A that have been filled. We use a “length” variable i to keep track of the number of entries in B. Each time we fill a new position k in A, we store the value k at B[i], then increment i. Array C will “index” Array 2. When we store k at B[i], we store i at C[k]. Now, when we want to check whether position k is full, we look at C[k] to find out where in B the value k should be stored. If C[k] ≥ i then it must be garbage meaning k is empty. If C[k] < i then we check if B[C[k]] = k, in which case we have proof that position k is full; if B[C[k]] has any other value then C[k] is garbage meaning position k is empty.