Minimum Operations to Unbias Datasets

Problem Statement

Amazon developers aim to merge two binary classification datasets (data1 and data2, represented as binary strings where '0' and '1' denote classes) into an unbiased final dataset with equal counts of 0s and 1s. In one operation, remove the rightmost character from data1 or the leftmost from data2. Compute the minimum operations needed; datasets need not match in size post-operations, but the merged result must balance 0s and 1s (empty merge counts as balanced, with zero each).[1]

Function Signature

java int minOperationsToUnbias(int n, String data1, String data2)

• n: Initial size of each dataset (1 ≤ n ≤ 10).
• data1, data2: Binary strings of length n.
• Returns minimum operations (int).[1]

Constraints

• 1 ≤ n ≤ 10, so both strings are short (up to length 10), enabling brute-force or two-pointer/greedy approaches over suffixes/prefixes.[1]

Examples

Example 0

Input: n=2, data1="01", data2="11"
Output: 2
Explanation: Remove last '1' from data1 and first '1' from data2, leaving data1="0" (one 0), data2="1" (one 1); merged balances at 1 each. Alternatively, remove both from data2.[1]

Example 1

Input: n=6, data1="111001", data2="010110"
Output: 6
Explanation: Remove last '1' from data1 (now "11100", three 1s/two 0s), then first five from data2 (now "0", one 0); merged: three 1s/three 0s.[1]

Example 2

Input: n=1, data1="0", data2="1"
Output: 0
Explanation: Already balanced (one 0, one 1).[1]

Example 3

Input: n=3, data1="111", data2="11?" (likely "110" or similar, but all-1s case)
Output: 5
Explanation: No 0s exist; remove all (3 from data1 + 2 from data2) for empty balanced set.[1]

Example 4

Input: n=4, data1="0101", data2="0000"
Output: 2
Explanation: Remove two leading '0's from data2 (now "00"), enabling balance via data1's two 0s/two 1s + data2's two 0s (trim further if needed, but 2 suffices).[1]