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A shuffle of two strings X and Y is formed by interspersing the characters into a new string, keeping the characters of X and Y in the same order. For example, the string BANANA ANANAS is a shue of the strings BANANA and ANANAS in several different ways.

BANANAANANAS BANANAANANAS BANANANANA

Similarly, the strings PRODGYRNAMAMMIINCG and DYPRONGARMAMMICING are both shuffles of DYNAMIC and PROGRAMMING:

PROGRAMMING PROGRAMMING

Describe and analyze an efficient algorithm to determine, given throe strings A1 [1...m], B [1...n] and C[1...m+n], whether C is a shuffle of A and B.

Respuesta :

Shuffle (A[1..m], B[1..n], C[1..m+n]):

Shuf[0, 0] ← True

for j ← 1 to n

Shuf[0, j] ← Shuf[0, j − 1] ∧ (B[j] = C[j])

for i ← 1 to n

Shuf[i, 0] ← Shuf[i − 1, 0] ∧ (A[i] = B[i])

for j ← 1 to n

Shuf[i, j] ← False

if A[i] = C[i + j]

Shuf[i, j] ← Shuf[i, j] ∨ Shuf[i − 1, j]

if B[i] = C[i + j]

Shuf[i, j] ← Shuf[i, j] ∨ Shuf[i, j − 1]

return Shuf[m, n]

The algorithm runs in O(mn) time.

The shuffle of the X and Y strings is formed by the intersection of the characters into the new string and keeps the characters Y and X in same order.

  • Shuffle (A[1..m], B[1..n], C[1..m+n]):
  • Shuf[0, 0] ← True
  • for j ← 1 to n
  • Shuf[0, j] ← Shuf[0, j − 1] ∧ (B[j] = C[j])
  • for i ← 1 to n

Learn more about the strings X and Y is formed by interspersing  

brainly.com/subject/mathematics

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