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