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Shortest Common Super Sequence
Shortest common super-sequence is a sequence where each element of both of the given sequences is present. In other words, we can say that the given two strings, both are sub-sequence of Shortest Common Super-Sequence.
When there are no common characters in two strings, then we can simply concatenate them to get Super-sequence. But when they have some common characters, then firstly we have to find the longest string, then add extra characters of the other string.
Input and Output
Input: Two strings. “ABCDEF” and “XYDEF” Output: The length of the shortest common super-sequence. Here the super-sequence is “ABCDEFXY”. So the length is 8.
Algorithm
superSeq(str1, str2)
Input: Two strings str1 and str2.
Output: Find length of super sequence.
Begin m := length of str1 n := length of str2 define table named seqTab of size (m+1 x n+1) for i := 0 to m, do for j := 0 to n, do if i = 0, then seqTab[i, j] := j else if j = 0, then seqTab[i, j] := i else if str1[i-1] = str2[j-1], then seqTab[i, j] := 1 + seqTab[i-1, j-1] else seqTab[i, j] := 1 + minimum of seqTab[i-1, j] and seqTab[i, j-1] done done return seqTab[m, n] End
Example
#include<iostream>
using namespace std;
int min(int a, int b) {
return (a<b)?a:b;
}
int superSeq(string str1, string str2) {
int m = str1.size();
int n = str2.size();
int supSeqTable[m+1][n+1];
for (int i = 0; i <= m; i++) {
for (int j = 0; j <= n; j++) {
if (!i)
supSeqTable[i][j] = j; //shortest supersequence length is j
else if (!j)
supSeqTable[i][j] = i; //shortest supersequence length is i
else if (str1[i-1] == str2[j-1])
supSeqTable[i][j] = 1 + supSeqTable[i-1][j-1];
else
supSeqTable[i][j] = 1 + min(supSeqTable[i-1][j], supSeqTable[i][j-1]);
}
}
return supSeqTable[m][n];
}
int main() {
string first = "ABCDEF";
string second = "XYDEF";
cout << "Length of the shortest supersequence is " << superSeq(first, second);
}Output
Length of the shortest supersequence is 8
Updated on: 17-Jun-2020
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