# Longest subsequence with different adjacent characters

Given string **str**. The task is to find the longest subsequence of **str** such that all the characters adjacent to each other in the subsequence are different.

**Examples:**

Input:str = “ababa”

Output:5

Explanation:

“ababa” is the subsequence satisfying the condition

Input:str = “xxxxy”

Output:2

Explanation:

“xy” is the subsequence satisfying the condition

**Method 1: Greedy Approach**

It can be observed that choosing the first character which is not similar to the previously chosen character given the longest subsequence of the given string with different adjacent characters.

The idea is to keep track of previously picked character while iterating through the string and if the current character is different than the previous character then count the current character to find the longest subsequence.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the longest Subsequence ` `// with different adjacent character ` `int` `longestSubsequence(string s) ` `{ ` ` ` `// Length of the string s ` ` ` `int` `n = s.length(); ` ` ` `int` `answer = 0; ` ` ` ` ` `// Previously picked character ` ` ` `char` `prev = ` `'-'` `; ` ` ` ` ` `for` `(` `int` `i = 0; i < n; i++) { ` ` ` `// If the current character is ` ` ` `// different from the previous ` ` ` `// then include this character ` ` ` `// and update previous character ` ` ` `if` `(prev != s[i]) { ` ` ` `prev = s[i]; ` ` ` `answer++; ` ` ` `} ` ` ` `} ` ` ` ` ` `return` `answer; ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `string str = ` `"ababa"` `; ` ` ` ` ` `// Function call ` ` ` `cout << longestSubsequence(str); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for the above approach ` `import` `java.util.*; ` ` ` `class` `GFG{ ` ` ` `// Function to find the longest subsequence ` `// with different adjacent character ` `static` `int` `longestSubsequence(String s) ` `{ ` ` ` ` ` `// Length of the String s ` ` ` `int` `n = s.length(); ` ` ` `int` `answer = ` `0` `; ` ` ` ` ` `// Previously picked character ` ` ` `char` `prev = ` `'-'` `; ` ` ` ` ` `for` `(` `int` `i = ` `0` `; i < n; i++) ` ` ` `{ ` ` ` ` ` `// If the current character is ` ` ` `// different from the previous ` ` ` `// then include this character ` ` ` `// and update previous character ` ` ` `if` `(prev != s.charAt(i)) ` ` ` `{ ` ` ` `prev = s.charAt(i); ` ` ` `answer++; ` ` ` `} ` ` ` `} ` ` ` ` ` `return` `answer; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `String str = ` `"ababa"` `; ` ` ` ` ` `// Function call ` ` ` `System.out.print(longestSubsequence(str)); ` `} ` `} ` ` ` `// This code is contributed by sapnasingh4991 ` |

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## Python3

`# Python3 program for the above approach ` ` ` `# Function to find the longest Subsequence ` `# with different adjacent character ` `def` `longestSubsequence(s): ` ` ` ` ` `# Length of the string s ` ` ` `n ` `=` `len` `(s); ` ` ` `answer ` `=` `0` `; ` ` ` ` ` `# Previously picked character ` ` ` `prev ` `=` `'-'` `; ` ` ` ` ` `for` `i ` `in` `range` `(` `0` `, n): ` ` ` ` ` `# If the current character is ` ` ` `# different from the previous ` ` ` `# then include this character ` ` ` `# and update previous character ` ` ` `if` `(prev !` `=` `s[i]): ` ` ` `prev ` `=` `s[i]; ` ` ` `answer ` `+` `=` `1` `; ` ` ` ` ` `return` `answer; ` ` ` `# Driver Code ` `str` `=` `"ababa"` `; ` ` ` `# Function call ` `print` `(longestSubsequence(` `str` `)); ` ` ` `# This code is contributed by Code_Mech ` |

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## C#

`// C# program for the above approach ` `using` `System; ` ` ` `class` `GFG{ ` ` ` `// Function to find the longest subsequence ` `// with different adjacent character ` `static` `int` `longestSubsequence(String s) ` `{ ` ` ` ` ` `// Length of the String s ` ` ` `int` `n = s.Length; ` ` ` `int` `answer = 0; ` ` ` ` ` `// Previously picked character ` ` ` `char` `prev = ` `'-'` `; ` ` ` ` ` `for` `(` `int` `i = 0; i < n; i++) ` ` ` `{ ` ` ` ` ` `// If the current character is ` ` ` `// different from the previous ` ` ` `// then include this character ` ` ` `// and update previous character ` ` ` `if` `(prev != s[i]) ` ` ` `{ ` ` ` `prev = s[i]; ` ` ` `answer++; ` ` ` `} ` ` ` `} ` ` ` `return` `answer; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `String str = ` `"ababa"` `; ` ` ` ` ` `// Function call ` ` ` `Console.Write(longestSubsequence(str)); ` `} ` `} ` ` ` `// This code is contributed by amal kumar choubey ` |

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**Output:**

5

**Time Complexity:** O(N), where N is the length of the given string.

**Method 2: Dynamic Programming**

- For each characters in the given string str, do the following:
- Choose the current characters in the string for the resultant subsequence and recurr for the remaining string to find the next possible characters for the resultant subsequence.
- Omit the current characters and recurr for the the remaining string to find the next possible characters for the resultant subsequence.

- The maximum value in the above recursive call will be the longest subsequence with different adjacent element.
- The recurrence relation is given by:
Let

**dp[pos][prev]**be the length of longest subsequence till index pos such that alphabet prev was picked previously. dp[pos][prev] = max(1 + function(pos+1, s[pos] - 'a' + 1, s), function(pos+1, prev, s));

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// dp table ` `int` `dp[100005][27]; ` ` ` `// A recursive function to find the ` `// update the dp[][] table ` `int` `calculate(` `int` `pos, ` `int` `prev, string& s) ` `{ ` ` ` ` ` `// If we reach end of the string ` ` ` `if` `(pos == s.length()) { ` ` ` `return` `0; ` ` ` `} ` ` ` ` ` `// If subproblem has been computed ` ` ` `if` `(dp[pos][prev] != -1) ` ` ` `return` `dp[pos][prev]; ` ` ` ` ` `// Initialise variable to find the ` ` ` `// maximum length ` ` ` `int` `val = 0; ` ` ` ` ` `// Choose the current character ` ` ` `if` `(s[pos] - ` `'a'` `+ 1 != prev) { ` ` ` `val = max(val, ` ` ` `1 + calculate(pos + 1, ` ` ` `s[pos] - ` `'a'` `+ 1, ` ` ` `s)); ` ` ` `} ` ` ` ` ` `// Omit the current character ` ` ` `val = max(val, calculate(pos + 1, prev, s)); ` ` ` ` ` `// Return the store answer to the ` ` ` `// current subproblem ` ` ` `return` `dp[pos][prev] = val; ` `} ` ` ` `// Function to find the longest Subsequence ` `// with different adjacent character ` `int` `longestSubsequence(string s) ` `{ ` ` ` ` ` `// Length of the string s ` ` ` `int` `n = s.length(); ` ` ` ` ` `// Initialise the memoisation table ` ` ` `memset` `(dp, -1, ` `sizeof` `(dp)); ` ` ` ` ` `// Return the final ans after every ` ` ` `// recursive call ` ` ` `return` `calculate(0, 0, s); ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `string str = ` `"ababa"` `; ` ` ` ` ` `// Function call ` ` ` `cout << longestSubsequence(str); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for the above approach ` `class` `GFG{ ` ` ` `// dp table ` `static` `int` `dp[][] = ` `new` `int` `[` `100005` `][` `27` `]; ` ` ` `// A recursive function to find the ` `// update the dp[][] table ` `static` `int` `calculate(` `int` `pos, ` `int` `prev, String s) ` `{ ` ` ` ` ` `// If we reach end of the String ` ` ` `if` `(pos == s.length()) ` ` ` `{ ` ` ` `return` `0` `; ` ` ` `} ` ` ` ` ` `// If subproblem has been computed ` ` ` `if` `(dp[pos][prev] != -` `1` `) ` ` ` `return` `dp[pos][prev]; ` ` ` ` ` `// Initialise variable to find the ` ` ` `// maximum length ` ` ` `int` `val = ` `0` `; ` ` ` ` ` `// Choose the current character ` ` ` `if` `(s.charAt(pos) - ` `'a'` `+ ` `1` `!= prev) ` ` ` `{ ` ` ` `val = Math.max(val, ` `1` `+ calculate(pos + ` `1` `, ` ` ` `s.charAt(pos) - ` `'a'` `+ ` `1` `, ` ` ` `s)); ` ` ` `} ` ` ` ` ` `// Omit the current character ` ` ` `val = Math.max(val, calculate(pos + ` `1` `, prev, s)); ` ` ` ` ` `// Return the store answer to the ` ` ` `// current subproblem ` ` ` `return` `dp[pos][prev] = val; ` `} ` ` ` `// Function to find the longest Subsequence ` `// with different adjacent character ` `static` `int` `longestSubsequence(String s) ` `{ ` ` ` ` ` `// Length of the String s ` ` ` `int` `n = s.length(); ` ` ` ` ` `// Initialise the memoisation table ` ` ` `for` `(` `int` `i = ` `0` `; i < ` `100005` `; i++) ` ` ` `{ ` ` ` `for` `(` `int` `j = ` `0` `; j < ` `27` `; j++) ` ` ` `{ ` ` ` `dp[i][j] = -` `1` `; ` ` ` `} ` ` ` `} ` ` ` ` ` `// Return the final ans after every ` ` ` `// recursive call ` ` ` `return` `calculate(` `0` `, ` `0` `, s); ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `String str = ` `"ababa"` `; ` ` ` ` ` `// Function call ` ` ` `System.out.print(longestSubsequence(str)); ` `} ` `} ` ` ` `// This code is contributed by Rohit_ranjan ` |

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**Output:**

5

**Time Complexity:** O(N), where N is the length of the given string.

**Auxilliary Space:** O(26*N) where N is the length of the given string.

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