Check if There is a Path With Equal Number of 0's And 1's

Given a binary-labeled structure (e.g., tree, grid, or graph), determine whether there exists a path (typically root-to-leaf or start-to-end) whose number of 0s equals its number of 1s. The core challenge is exploring paths while tracking the running balance between zeros and ones and pruning or memoizing states to avoid exponential search.