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Concept

Solution Space Trees

Nodes = partial solutions, edges = choices

The mental model behind every backtracking problem

time O(tree size) — pruning shrinks itspace O(depth)

step 1 / 14

nodes = partial solutions, edges = choices

{1}

{1,2}

take 1

{ }

{2}

skip 1

{ }

leaves reached

(none yet)

The mental model behind every backtracking problem


▸
1tree = solution space:
2    root      = empty solution
3    edge      = one decision
4    node      = partial solution
5    leaf      = complete solution (valid or dead)
6explore(node):
7    if rule already broken: prune subtree   // cut, do not recurse
8    else for each edge: explore(child)
9    collect valid leaves

state

examplesubsets of [1, 2]

line 1Every backtracking problem is secretly the SAME object: a solution-space tree. The root is the empty solution, each edge is one decision, internal nodes are partial solutions, and leaves are complete solutions — some valid, some dead.