Printing longest Increasing consecutive subsequence

Given n elements, write a program that prints the longest increasing subsequence whose adjacent element difference is one.

Examples:

Input : a[] = {3, 10, 3, 11, 4, 5, 6, 7, 8, 12}
Output : 3 4 5 6 7 8
Explanation: 3, 4, 5, 6, 7, 8 is the longest increasing subsequence whose adjacent element differs by one.

Input : a[] = {6, 7, 8, 3, 4, 5, 9, 10}
Output : 6 7 8 9 10
Explanation: 6, 7, 8, 9, 10 is the longest increasing subsequence



We have discussed how to find length of Longest Increasing consecutive subsequence. To print the subsequence, we store index of last element. Then we print consecutive elements ending with last element.

Given below is the implementation of the above approach:

// CPP program to find length of the
// longest increasing subsequence
// whose adjacent element differ by 1
#include <bits/stdc++.h>
using namespace std;

// function that returns the length of the
// longest increasing subsequence
// whose adjacent element differ by 1
void longestSubsequence(int a[], int n)
{
    // stores the index of elements
    unordered_map<int, int> mp;

    // stores the length of the longest
    // subsequence that ends with a[i]
    int dp[n];
    memset(dp, 0, sizeof(dp));

    int maximum = INT_MIN;

    // iterate for all element
    int index = -1;
    for (int i = 0; i < n; i++) {

        // if a[i]-1 is present before i-th index
        if (mp.find(a[i] - 1) != mp.end()) {

            // last index of a[i]-1
            int lastIndex = mp[a[i] - 1] - 1;

            // relation
            dp[i] = 1 + dp[lastIndex];
        }
        else
            dp[i] = 1;

        // stores the index as 1-index as we need to
        // check for occurrence, hence 0-th index
        // will not be possible to check
        mp[a[i]] = i + 1;

        // stores the longest length
        if (maximum < dp[i]) {
            maximum = dp[i];
            index = i;
        }
    }

    // We know last element of sequence is
    // a[index]. We also know that length
    // of subsequence is "maximum". So We
    // print these many consecutive elements
    // starting from "a[index] - maximum + 1"
    // to a[index].
    for (int curr = a[index] - maximum + 1;
         curr <= a[index]; curr++)
        cout << curr << " ";
}

// Driver Code
int main()
{
    int a[] = { 3, 10, 3, 11, 4, 5, 6, 7, 8, 12 };
    int n = sizeof(a) / sizeof(a[0]);
    longestSubsequence(a, n);
    return 0;
}

Output:

3 4 5 6 7 8 

Time Complexity : O(n)
Auxiliary Space : O(n)





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