KGP13I - Editorial

dynamic-programming
easy-medium
editorial
kgp13acm

#1

PROBLEM LINK:

Practice
Contest

Editorialist: Jingbo Shang

DIFFICULTY:

Easy - Medium

PREREQUISITES:

Dynamic Programming

PROBLEM:

Given 3 types of operations, determine the minimum cost of transforming string S[1…n] to T[1…m].

EXPLANATION:

This problem is similar to the Edit Distance Problem. But here, due to the different cost plan, we need to slightly modify the classical dynamic programming.

Let’s use f*[j] to stand for the minimum cost of transform S[1…i] to T[1…j]. In this problem, the insert/delete cost is dependent on the length.

Consider the insert operation:

f*[j - k] + min{k + x, y} --update--> f*[j]

And the delete operation:

f[i - k][j] + k + x --update--> f*[j]

Replace/Directly match

f*[j] + (S[i + 1] != T[j + 1]) --update--> f[i + 1][j + 1]

Since we need to enumerate “k”, the time complexi will be O(n m^2 + n^2 m).