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The tree is expanded breadth-first. After the root's children are created, the instructor treats that whole level as completed and then expands nodes from left to right across the current frontier.

Conditions: The tree is explored level by level.; At each node, only jobs not already used on the path from the root are appended.; The clip shows structural expansion only, not pruning by bounds.

The tree is expanded breadth-first. After the root's children are created, the instructor treats that whole level as completed and then expands nodes from left to right across the current frontier.

Conditions: The tree is explored level by level.; At each node, only jobs not already used on the path from the root are appended.; The clip shows structural expansion only, not pruning by bounds.

A solution can be represented in two main ways: as a variable-size subset of selected jobs (e.g., $S1 = {J_1, J_4}$), or as a fixed-size binary vector where each position corresponds to a job and the value indicates whether the job is done (1) or not (0) (e.g., $S2 = {1, 0, 0, 1}$).

Conditions: The problem involves selecting a subset of jobs from a given set.; The representation must clearly indicate which jobs are included in the solution.

A solution can be represented in two main ways: as a variable-size subset of selected jobs (e.g., $S1 = {J_1, J_4}$), or as a fixed-size binary vector where each position corresponds to a job and the value indicates whether the job is done (1) or not (0) (e.g., $S2 = {1, 0, 0, 1}$).

Conditions: The problem involves selecting a subset of jobs from a given set.; The representation must clearly indicate which jobs are included in the solution.

In this lecture segment, backtracking is described as depth-first search, while branch and bound is described as breadth-first search. Backtracking goes down one branch to the next level before considering siblings, whereas branch and bound considers all alternatives at the current level first.

Conditions: Applied to a state-space tree for job sequencing.; The comparison is about exploration order, not about bounding rules or cost evaluation.

In this lecture segment, backtracking is described as depth-first search, while branch and bound is described as breadth-first search. Backtracking goes down one branch to the next level before considering siblings, whereas branch and bound considers all alternatives at the current level first.

Conditions: Applied to a state-space tree for job sequencing.; The comparison is about exploration order, not about bounding rules or cost evaluation.

A path from the root records the ordered partial sequence of chosen jobs. Following a route in the drawn tree corresponds to selecting the jobs along that route in order; for example, the route using $J_1$ then $J_4$ means doing job 1 and job 4 and not taking jobs 2 and 3 along that partial path.

Conditions: The tree is the job-sequencing state-space tree drawn on the board.; Each edge label indicates appending one job to the current partial sequence.

A path from the root records the ordered partial sequence of chosen jobs. Following a route in the drawn tree corresponds to selecting the jobs along that route in order; for example, the route using $J_1$ then $J_4$ means doing job 1 and job 4 and not taking jobs 2 and 3 along that partial path.

Conditions: The tree is the job-sequencing state-space tree drawn on the board.; Each edge label indicates appending one job to the current partial sequence.