# Count distinct sequences obtained by replacing all elements of subarrays having equal first and last elements with the first element any number of times

• Last Updated : 24 Feb, 2022

Given an array arr[] consisting of N integers, the task is to find the number of different sequences that can be formed after performing the below operation on the given array arr[] any number of times.

Choose two indices i and j such that arr[i] is equal to arr[j] and update all the elements in the range [i, j] in the array to arr[i].

Examples:

Input: arr[] = {1, 2, 1, 2, 2}
Output: 3
Explanation:
There can be three possible sequences:

1. The initial array {1, 2, 1, 2, 2}.
2. Choose indices 0 and 2 and as arr(= 1) and arr(= 1) are equal and update the array elements arr[] over the range [0, 2] to arr(= 1). The new sequence obtained is {1, 1, 1, 2, 2}.
3. Choose indices 1 and 3 and as arr(= 2) and arr(= 2) are equal and update the array elements arr[] over the range [1, 3] to arr(= 2). The new sequence obtained is {1, 2, 2, 2, 2}.

Therefore, the total number of sequences formed is 3.

Input: arr[] = {4, 2, 5, 4, 2, 4}
Output: 5

Approach: This problem can be solved using Dynamic Programming. Follow the steps below to solve the problem:

• Initialize an auxiliary array dp[] where dp[i] stores the number of different sequences that are possible by first i elements of the given array arr[] and initialize dp as 1.
• Initialize an array lastOccur[] where lastOccur[i] stores the last occurrence of element arr[i] in the first i elements of the array arr[] and initialize lastOccur with -1.
• Iterate over the range [1, N] using the variable i and perform the following  steps:
• Update the value of dp[i] as dp[i – 1].
• If last occurrence of the current element is not equal to -1 and less than (i – 1), then add the value of dp[lastOccur[curEle]] to dp[i].
• Update the value of lastOccur[curEle] as i.
• After completing the above steps, print the value of dp[N] as the result.

Below is the implementation of the above approach:

## C++

 `// C++ program for the above approach` `#include ``using` `namespace` `std;` `// Function to count number of sequences``// satisfying the given criteria``void` `countPossiblities(``int` `arr[], ``int` `n)``{``    ``// Stores the index of the last``    ``// occurrence of the element``    ``int` `lastOccur;``    ``for` `(``int` `i = 0; i < n; i++) {``        ``lastOccur[i] = -1;``    ``}` `    ``// Initialize an array to store the``    ``// number of different sequences``    ``// that are possible of length i``    ``int` `dp[n + 1];` `    ``// Base Case``    ``dp = 1;` `    ``for` `(``int` `i = 1; i <= n; i++) {` `        ``int` `curEle = arr[i - 1];` `        ``// If no operation is applied``        ``// on ith element``        ``dp[i] = dp[i - 1];` `        ``// If operation is applied on``        ``// ith element``        ``if` `(lastOccur[curEle] != -1``            ``& lastOccur[curEle] < i - 1) {``            ``dp[i] += dp[lastOccur[curEle]];``        ``}` `        ``// Update the last occurrence``        ``// of curEle``        ``lastOccur[curEle] = i;``    ``}` `    ``// Finally, print the answer``    ``cout << dp[n] << endl;``}` `// Driver Code``int` `main()``{``    ``int` `arr[] = { 1, 2, 1, 2, 2 };``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);``    ``countPossiblities(arr, N);` `    ``return` `0;``}`

## Java

 `// Java Program for the above approach``import` `java.io.*;` `class` `GFG {` `    ``// Function to count number of sequences``    ``// satisfying the given criteria``    ``static` `void` `countPossiblities(``int` `arr[], ``int` `n)``    ``{``        ``// Stores the index of the last``        ``// occurrence of the element``        ``int``[] lastOccur = ``new` `int``[``100000``];``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``lastOccur[i] = -``1``;``        ``}` `        ``// Initialize an array to store the``        ``// number of different sequences``        ``// that are possible of length i``        ``int``[] dp = ``new` `int``[n + ``1``];` `        ``// Base Case``        ``dp[``0``] = ``1``;` `        ``for` `(``int` `i = ``1``; i <= n; i++) {` `            ``int` `curEle = arr[i - ``1``];` `            ``// If no operation is applied``            ``// on ith element``            ``dp[i] = dp[i - ``1``];` `            ``// If operation is applied on``            ``// ith element``            ``if` `(lastOccur[curEle] != -``1``                ``& lastOccur[curEle] < i - ``1``) {``                ``dp[i] += dp[lastOccur[curEle]];``            ``}` `            ``// Update the last occurrence``            ``// of curEle``            ``lastOccur[curEle] = i;``        ``}` `        ``// Finally, print the answer``        ``System.out.println(dp[n]);``    ``}` `    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `arr[] = { ``1``, ``2``, ``1``, ``2``, ``2` `};``        ``int` `N = arr.length;``        ``countPossiblities(arr, N);` `    ``}``}` `    ``// This code is contributed by Potta Lokesh`

## Python3

 `# Python3 program for the above approach` `# Function to count number of sequences``# satisfying the given criteria``def` `countPossiblities(arr, n):``    ` `    ``# Stores the index of the last``    ``# occurrence of the element``    ``lastOccur ``=` `[``-``1``] ``*` `100000` `    ``# Initialize an array to store the``    ``# number of different sequences``    ``# that are possible of length i``    ``dp ``=` `[``0``] ``*` `(n ``+` `1``)` `    ``# Base Case``    ``dp[``0``] ``=` `1` `    ``for` `i ``in` `range``(``1``, n ``+` `1``):``        ``curEle ``=` `arr[i ``-` `1``]` `        ``# If no operation is applied``        ``# on ith element``        ``dp[i] ``=` `dp[i ``-` `1``]` `        ``# If operation is applied on``        ``# ith element``        ``if` `(lastOccur[curEle] !``=` `-``1` `and``            ``lastOccur[curEle] < i ``-` `1``):``            ``dp[i] ``+``=` `dp[lastOccur[curEle]]` `        ``# Update the last occurrence``        ``# of curEle``        ``lastOccur[curEle] ``=` `i` `    ``# Finally, print the answer``    ``print``(dp[n])` `# Driver Code``if` `__name__ ``=``=` `'__main__'``:``    ` `    ``arr ``=` `[ ``1``, ``2``, ``1``, ``2``, ``2` `]``    ``N ``=` `len``(arr)``    ` `    ``countPossiblities(arr, N)` `# This code is contributed by mohit kumar 29`

## C#

 `// C# Program for the above approach``using` `System;` `class` `GFG {` `    ``// Function to count number of sequences``    ``// satisfying the given criteria``    ``static` `void` `countPossiblities(``int``[] arr, ``int` `n)``    ``{``        ``// Stores the index of the last``        ``// occurrence of the element``        ``int``[] lastOccur = ``new` `int``;``        ``for` `(``int` `i = 0; i < n; i++) {``            ``lastOccur[i] = -1;``        ``}` `        ``// Initialize an array to store the``        ``// number of different sequences``        ``// that are possible of length i``        ``int``[] dp = ``new` `int``[n + 1];` `        ``// Base Case``        ``dp = 1;` `        ``for` `(``int` `i = 1; i <= n; i++) {` `            ``int` `curEle = arr[i - 1];` `            ``// If no operation is applied``            ``// on ith element``            ``dp[i] = dp[i - 1];` `            ``// If operation is applied on``            ``// ith element``            ``if` `(lastOccur[curEle] != -1``                ``& lastOccur[curEle] < i - 1) {``                ``dp[i] += dp[lastOccur[curEle]];``            ``}` `            ``// Update the last occurrence``            ``// of curEle``            ``lastOccur[curEle] = i;``        ``}` `        ``// Finally, print the answer``        ``Console.WriteLine(dp[n]);``    ``}` `    ``public` `static` `void` `Main()``    ``{``        ``int``[] arr = { 1, 2, 1, 2, 2 };``        ``int` `N = arr.Length;``        ``countPossiblities(arr, N);``    ``}``}` `// This code is contributed by subham348.`

## Javascript

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Output:

`3`

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

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