Edit Distance Transformation

This problem requires you to compute the minimum number of operations required to transform one string into another using three permitted operations: insertion, deletion, and substitution. This is a classic edit distance problem that can be solved using dynamic programming.

The state transition can be described using the formula:

\[ dp[i][j] = \begin{cases} j, & \text{if } i = 0 \\ i, & \text{if } j = 0 \\ dp[i-1][j-1], & \text{if } s_1[i-1]=s_2[j-1] \\ 1+\min\{dp[i-1][j],\, dp[i][j-1],\, dp[i-1][j-1]\}, & \text{otherwise} \end{cases} \]

inputFormat

The input is read from standard input (stdin) and consists of two lines:

• The first line contains the string s1.
• The second line contains the string s2.

Both strings may be empty.

outputFormat

Output to standard output (stdout) a single integer representing the minimum number of operations required to convert s1 into s2.

abcd
bcf

2