1. write a python code for this?
2. The class sample code on finding an LCS of two strings returns the leftmost LCS with respect to X. Modify the class code to return the leftmost LCS with respect to Y and the rightmost LCS with respect to X.
3. Let X = AABCCDIEEDSCYBA and Y = ABBCDDEFDHCNBAT. Return the leftmost LCS with respect to Y, and the rightmost LCS with respect to X.

Definition: Let L be an LCS of X and Y. Let L[0] denote the first symbol in L (assuming index starts from 0). Denote by X(L[0]) the index of L[0] in X and by Y[L[0]) the index of L[0] in Y.

• L is said to be the leftmost LCS with respect to X if for any other LCS H: X(H[0]) >= X(L[0]) and the index of each other symobl in L is as close as possible to the index of its proceeding symbol in X.
• L is said to be the leftmost LCS with respect to Y if for any other LCS H: Y(H[0]) >= Y(L[0]) and the index of each other symbol in L is as close as possible to the index of its proceeding symbol in Y.

For example, Let X = "abcd' and Y = 'badc'. There are 4 LCS's: 'ac', 'ad', 'bd', and 'bc'. Here 'ac' is the leftmost LCS with respect to X and 'bd' is the leftmost LCS with respect to Y.

The rightmost LCS with respect to X (or Y) is symmtrical. Let L[k-1] denote the last symbol in L with k = len(L). Denote by X(L[k-1]) the index of L[k-1] in X and by Y(L[k-1]) the index of L[k-1] in Y.

• L is said to be the rightmost LCS with respect to X if for any other LCS H: X(H[k-1])
• L is said to be the rightmost LCS with respect to Y if for any other LCS H: Y(H[k-1])

In the above example, 'bd' is the rightmost LCS with respect to X, and 'ac' is the rightmost LCS with respect to Y.

Note: Let L be a leftmost (rightmost) LCS for X and Y, then L^R is the rightmost (leftmost) LCS for X^R and Y^R, where X^R is the reversal of X. Your code should avoid directly using this trick. That is, your code should have a separatre function for each case without simply reversing the input for a previous function.

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