I have been trying to get some kind of intiution in these kind of [problems](https://medium.com/@codingfreak/top-50-dynamic-programming-practice-problems-4208fed71aa3), while i can get the naive solutions done on my own, i cannot think up the solutions easily to the point where i can match the solutions given to these questions in each of those …

dynamic_naive.js

function catu(one, two) {
    var returnu = [];
    two.forEach(element => {
        returnu.push(one + element);
        returnu.push(element);
    });
    return returnu;
}
function main_fun(stringu) {
    if (stringu.length == 1) {
        return [stringu,''];
    } else {
        return catu(stringu[0], main_fun(stringu.slice(1,))); 
    }
}

// https://medium.freecodecamp.org/how-to-reverse-a-string-in-javascript-in-3-different-ways-75e4763c68cb
function reverseString(str) {
    if (str === "")
        return "";
    else
        return reverseString(str.substr(1)) + str.charAt(0);
}

function isPalindrome(inputString) {
    if (inputString.length > 2) {
        return inputString == reverseString(inputString);
    } else {
        return false;
    }
}
f = main_fun("ABBDCACB");
g = f.filter(isPalindrome);
g.sort((a, b) => { return b.length - a.length ; })
console.log("longest palindromic subsequence: ", g[0], " with length of ", g[0].length);

dynamic_optimised

function longestP(stringInput) {
    if (stringInput.length == 0) {
        return 0;
    }
    if (stringInput.length == 1) {
        return 1;
    }
    if (stringInput.slice(0, 1) == stringInput.slice(-1)) {
        //console.log(stringInput);
        return longestP(stringInput.slice(1, -1))+2;
    }
    return Math.max(longestP(stringInput.slice(0, -1)), longestP(stringInput.slice(1,))); 
}
console.log(longestP("ABBDCACB"));