88 lines
2.0 KiB
C++
88 lines
2.0 KiB
C++
/*
|
|
Printing longest common subseqeunce from 2 subsequences using dp bottom-up approach
|
|
*/
|
|
|
|
#include<bits/stdc++.h>
|
|
|
|
using namespace std;
|
|
|
|
void longestCommonSubsequence(vector < int > a, vector < int > b) {
|
|
int n = a.size();
|
|
int m = b.size();
|
|
int i, j;
|
|
vector < vector < int >> dp(n + 1, vector < int > (m + 1, 0)); //creating lookup table to keep track of subsequnces
|
|
vector < int > result; //result vector
|
|
for (i = 1; i <= n; i++) {
|
|
for (j = 1; j <= m; j++) //iterating through all subsequences, if common then increment value of dp[i][j] else consider max from previous
|
|
{
|
|
if (a[i - 1] == b[j - 1]) {
|
|
dp[i][j] = dp[i - 1][j - 1] + 1;
|
|
} else {
|
|
dp[i][j] = max(dp[i][j - 1], dp[i - 1][j]);
|
|
}
|
|
}
|
|
}
|
|
i = n, j = m;
|
|
|
|
while (i > 0 && j > 0) { //traversing dp vector and finding the same elements in both to print result
|
|
if (a[i - 1] == b[j - 1]) {
|
|
result.push_back(a[i - 1]);
|
|
i--;
|
|
j--;
|
|
} else if (dp[i][j - 1] > dp[i - 1][j]) {
|
|
j--;
|
|
} else
|
|
i--;
|
|
|
|
}
|
|
|
|
cout << "Length of lcs " << result.size() << '\n';
|
|
reverse(result.begin(), result.end()); //reversing to get correct order
|
|
cout << "\nLongest common subsequence ";
|
|
for (auto it: result) {
|
|
cout << it;
|
|
}
|
|
cout << "\n";
|
|
}
|
|
|
|
int main() {
|
|
|
|
int n, m;
|
|
cout << "\nEnter no of elements in first sequence"; //Input and output
|
|
cin >> n;
|
|
cout << "\nEnter no of elements in second sequence";
|
|
cin >> m;
|
|
vector < int > a(n);
|
|
vector < int > b(m);
|
|
cout << "\nEnter elements in first sequence\n";
|
|
for (int i = 0; i < n; i++) {
|
|
cin >> a[i];
|
|
}
|
|
cout << "\nEnter elements in second sequence\n";
|
|
for (int i = 0; i < m; i++) {
|
|
cin >> b[i];
|
|
}
|
|
|
|
longestCommonSubsequence(a, b);
|
|
|
|
return 0;
|
|
}
|
|
|
|
/*
|
|
Time and space complexity for subsequence-O(m*n)
|
|
|
|
SAMPLE INPUT-
|
|
Enter no of elements in first sequence5
|
|
|
|
Enter no of elements in second sequence3
|
|
|
|
Enter elements in first sequence
|
|
1 2 3 4 5
|
|
|
|
Enter elements in second sequence
|
|
1 3 4
|
|
Length of lcs 3
|
|
|
|
Longest common subsequence 134
|
|
|
|
*/ |