# Solution Alignment The prompt asks for an implementation-level answer. The safest way to present it is to define the state, maintain clear invariants, then walk through complexity and tests. ## Problem Restatement You're given a string S of length n consisting only of '(' , ')' , and digits '0'–'9'. For every digit at index i with numeric value v: ( 1) you must delete exactly v parentheses that occur at indices strictly less than i; ( 2) a given parenthesis can be deleted at most once across all digits; ( 3) digits themselves are not deleted and should be ignored when checking validity. After choosing deletions for all digits, consider the sequence of remaining parentheses (ignoring digits). Return true if there exists at least one choice of deletions such that the remaining parentheses form a valid parentheses string, otherwise return false. Also describe an efficient algorithm, its time and space co... ## Recommended Approach Use the string constraints to choose between two pointers, a stack, frequency counts, prefix/suffix state, or dynamic programming. Maintain the invariant that processed characters have already been normalized, counted, or matched according to the operation. ## Correctness The implementation should maintain an invariant after each loop or operation that directly matches the problem statement. At termination, that invariant implies the returned value has considered every valid candidate exactly once, or has preserved the required data-structure state after every API call. ## Complexity Most direct string scans are O(n) time. Space ranges from O(1) for two pointers to O(n) for stacks, maps, or DP tables. ## Edge Cases and Tests Empty string, length 1, repeated characters, invalid characters, case sensitivity, Unicode vs ASCII, and very long input.