Last saturday, Tomiwa (BlackDev) and I had a joint session. Well, I was conducting a mock interview for him, but it ended up a joint discussion at the end. It was fascinating as we got to discuss and solve questions - in the course of that, the longest sequence question was solved.

In the mock interview, he solved a simple calculation question, then a backtracking question gotten from the Andela crack the code challenge. He also solved Codility's frog jump question and then we discussed optimisations on both time and space.

Here is the link to a GitHub gist that houses the dicsussion - Click me.

## Longest Sequence

This question is a combination of both the longest increasing and decreasing sequence. I thought of the question whilst interviewing him, there's a similar stock question ( I don't know the name ). However, here's the problem statement I wrote on it and the code written by Tomiwa, and I.

Real credit goes to Tomiwa! - Baba went from not knowing dynamic programming to solving it, fear blockchain boys.

#### Problem statement

Given an array of integers, return the length of the longest sequence. This sequence can be in ascending or descending order. Example:

Examples
``````Input: [1,2,3,0,6,5,4,3,2,1]
Output: 6. [6,5,4,3,2,1] is the longest sequence

Input: [1,2,3,4,2,1]
Output:  4. [1,2,3,4] is the longest sequence

Input: [1,2,2,1]
Output:  2. [1,2] or [2,1] is the longest sequence``````

Since this question is from the longest * family, it's a dynamic programming question. This question can be solved in many other ways, however, the optimal solution is the dynamic programming approach.

### Solution

As stated earlier, to find the longest sequence, we find both the longest increasing and decreasing then return the maximum length. We'll create a 2D array to store our result as we calculate the length of the sequence as we walk through the original array. ( I might try to sketch something if it's needed - for now, no)

In JavaScript (Credits to Tomiwa) :

LongestSequence.js
``````function sequence(arr){
// Create a 2D array and fill it with 1s => [[1,1], [1,1], [1,1]]
var dp = new Array(arr.length);

for(var i = 0; i < dp.length; i++){
dp[i] = new Array(2)
dp[i].fill(1)
}

// Loop through the array.
for(var i = 0; i < arr.length; i++){
for(var j = i-1; j >= 0; j--){
// Perform the longest Increasing sequence and store the result
// in the first part of the array.

if(arr[j] < arr[i]){
dp[i] = Math.max(dp[j]+1, dp[i]);
}

// Perform the longst decreasing sequence and store the result
// in the second part of the array.

if(arr[j] > arr[i]){
dp[i] = Math.max(dp[j]+1, dp[i]);
}
}
}

// Return the max value from both arrays.

var maxRow = dp.map(function(row){ return Math.max.apply(null, row); });
return Math.max.apply(null, maxRow)
}``````

Whew. That's a lot of code lol. In Python, we have it as:

LongestSequence.py
``````def longestSequence(array):
dp = [[1 for _ in range(len(array))] for _ in range(2)]
for i in range(len(array)):
for j in range(i - 1, len(array)):
if array[j] < array[i]:
dp[i] = max(dp[j] + 1, dp[i])
if array[j] > array[i]:
dp[i] = max(dp[j] + 1, dp[i])

return max(max(dp), max(dp))``````

The code runs in O(n^2) time and O(n) space.

## Conclusion

Tomiwa & I had a very good time discussing questions and stuff. We had a joint session yesterday (6th of July) again, I'll find time to write on what we did - mostly talks, whines and solving.

The longest sequence is a very interesting question, and I'll be publishing my backtracking solution ( didn't pass all test cases because well, it's slow ) for the second question in the Andela challenge soon.