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Longest Common Subsequence Length

A subsequence is formed by deleting zero or more elements while preserving the order of the remaining elements.

Problema

A subsequence is formed by deleting zero or more elements while preserving the order of the remaining elements. Find the longest length shared by two arrays. Matching elements need not be adjacent. Return only the length, since several equally long subsequences may exist.

Implement longest_common_subsequence_length(first, second).

Input

first: The first sequence.

second: The second sequence.

Output

Return the maximum common subsequence length. If either array is empty, return 0.

Restricciones

Each array has 0…1,000 integers between −1,000,000,000 and 1,000,000,000. Duplicates are allowed.

Ejemplos

Ejemplo 1
Entrada:
first = [1, 3, 2, 4]
second = [3, 1, 2, 4]

Salida esperada:
expected = 3
Entrada:
std::vector<long long> first = {1, 3, 2, 4};
std::vector<long long> second = {3, 1, 2, 4};

Salida esperada:
long long expected = 3;
Entrada:
long[] first = new long[] {1, 3, 2, 4};
long[] second = new long[] {3, 1, 2, 4};

Salida esperada:
long expected = 3;

Explicación

Both contain [1, 2, 4] in that order, after deleting one value. The original arrays differ, so a length-four match is impossible.

Ejemplo 2
Entrada:
first = [1, 2]
second = [3, 4]

Salida esperada:
expected = 0
Entrada:
std::vector<long long> first = {1, 2};
std::vector<long long> second = {3, 4};

Salida esperada:
long long expected = 0;
Entrada:
long[] first = new long[] {1, 2};
long[] second = new long[] {3, 4};

Salida esperada:
long expected = 0;

Explicación

The arrays have no shared value, so their only common subsequence is empty.

Referencias

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