E. bits-Equalizer

Codeforces

IDCF10020E

Time2000ms

Memory64MB

Difficulty—

English · Original

Formal · Original

You are given two non-empty strings S and T of equal lengths. S contains the characters 0, 1 and ?, whereas T contains 0 and 1 only. Your task is to convert S into T in minimum number of moves. In each move, you can: 1. change a 0 in S to 1 2. change a ? in S to 0 or 1 3. swap any two characters in S As an example, suppose S = 01??00 and T = 001010. We can transform S into T in 3 moves: • Initially S = 01??00 • Move 1 – change S[2] to 1. S becomes 011?00 • Move 2 – change S[3] to 0. S becomes 011000 • Move 3 – swap S[1] with S[4]. S becomes 001010 • S is now equal to T The first line of input is an integer C (C ≤ 200) that indicates the number of test cases. Each case consists of two lines. The first line is the string S consisting of ‘0’, ‘1’ and ‘?’. The second line is the string T consisting of ‘0’ and ‘1’. The lengths of the strings won’t be larger than 100. For each case, output the case number first followed by the minimum number of moves required to convert S into T. If the transition is impossible, output - 1 instead. ## Input The first line of input is an integer C (C ≤ 200) that indicates the number of test cases. Each case consists of two lines. The first line is the string S consisting of ‘0’, ‘1’ and ‘?’. The second line is the string T consisting of ‘0’ and ‘1’. The lengths of the strings won’t be larger than 100. ## Output For each case, output the case number first followed by the minimum number of moves required to convert S into T. If the transition is impossible, output - 1 instead. [samples]

**Definitions** Let $ C \in \mathbb{Z} $ be the number of test cases. For each test case $ k \in \{1, \dots, C\} $: - Let $ S_k \in \{0, 1, ?\}^n $ be the source string of length $ n $. - Let $ T_k \in \{0, 1\}^n $ be the target string of length $ n $. **Constraints** 1. $ 1 \leq C \leq 200 $ 2. $ 1 \leq n \leq 100 $ 3. $ T_k $ contains only characters '0' and '1'. 4. $ S_k $ contains characters '0', '1', and '?'. **Objective** Find the minimum number of moves to transform $ S_k $ into $ T_k $, where each move is one of: - Change a '0' in $ S_k $ to '1' (cost 1). - Change a '?' in $ S_k $ to '0' or '1' (cost 1). - Swap any two characters in $ S_k $ (cost 1). If transformation is impossible, output $-1$. **Impossibility Condition** Let $ z_S $, $ o_S $, $ q_S $ denote the counts of '0', '1', '?' in $ S_k $, and $ z_T $, $ o_T $ the counts of '0', '1' in $ T_k $. Transformation is impossible if: $$ z_S + q_S < z_T \quad \text{or} \quad o_S + q_S < o_T $$ Otherwise, compute the minimum moves.

API Response (JSON)

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