Certainly! Let's consider the state space search tree for the Subset-Sum problem using the dynamic programming approach. The state space search tree visualizes the exploration of different states and the transitions between them. Here's an example of how the state space search tree would look for the Subset-Sum problem:

          S(0,0)
         /      \
   S(1,0)       S(1,3)
  /     \      /     \
S(2,0) S(2,3) S(2,2) S(2,6)
        /        \
     S(3,0)      S(3,6)

In the above state space search tree:

- Each state is represented by `(i, j)`, where `i` represents the current index of the set elements being considered, and `j` represents the remaining target sum.

- The root of the tree is the initial state `(0, 0)`, which means considering no elements from the set and having a target sum of 0.

- The left child of a state `(i, j)` represents the state where the current element `set[i]` is excluded from the subset, and the remaining target sum remains the same (`j`).

- The right child of a state `(i, j)` represents the state where the current element `set[i]` is included in the subset, and the remaining target sum is reduced by `set[i]` (`j - set[i]`).

- The leaf nodes of the tree represent the final states where either the target sum is achieved (`j = 0`), indicating a valid subset, or the target sum is not achieved (`j > 0`), indicating no valid subset.

Note that the state space search tree can grow exponentially with the input size, and the dynamic programming approach efficiently avoids redundant computations by utilizing the computed values from previous states. The state space search tree is a conceptual representation to understand the exploration of different states, but the actual dynamic programming implementation avoids explicit construction of the entire tree.

I hope this helps illustrate the state space search tree for the Subset-Sum problem! Let me know if you have any further questions.

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