translation: Add Python and Java code for EN version (#1345)

* Add the intial translation of code of all the languages

* test

* revert

* Remove

* Add Python and Java code for EN version

en/codes/python/chapter_dynamic_programming/edit_distance.py

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+"""
+File: edit_distancde.py
+Created Time: 2023-07-04
+Author: krahets (krahets@163.com)
+"""
+
+
+def edit_distance_dfs(s: str, t: str, i: int, j: int) -> int:
+    """Edit distance: Brute force search"""
+    # If both s and t are empty, return 0
+    if i == 0 and j == 0:
+        return 0
+    # If s is empty, return the length of t
+    if i == 0:
+        return j
+    # If t is empty, return the length of s
+    if j == 0:
+        return i
+    # If the two characters are equal, skip these two characters
+    if s[i - 1] == t[j - 1]:
+        return edit_distance_dfs(s, t, i - 1, j - 1)
+    # The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
+    insert = edit_distance_dfs(s, t, i, j - 1)
+    delete = edit_distance_dfs(s, t, i - 1, j)
+    replace = edit_distance_dfs(s, t, i - 1, j - 1)
+    # Return the minimum number of edits
+    return min(insert, delete, replace) + 1
+
+
+def edit_distance_dfs_mem(s: str, t: str, mem: list[list[int]], i: int, j: int) -> int:
+    """Edit distance: Memoized search"""
+    # If both s and t are empty, return 0
+    if i == 0 and j == 0:
+        return 0
+    # If s is empty, return the length of t
+    if i == 0:
+        return j
+    # If t is empty, return the length of s
+    if j == 0:
+        return i
+    # If there is a record, return it
+    if mem[i][j] != -1:
+        return mem[i][j]
+    # If the two characters are equal, skip these two characters
+    if s[i - 1] == t[j - 1]:
+        return edit_distance_dfs_mem(s, t, mem, i - 1, j - 1)
+    # The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
+    insert = edit_distance_dfs_mem(s, t, mem, i, j - 1)
+    delete = edit_distance_dfs_mem(s, t, mem, i - 1, j)
+    replace = edit_distance_dfs_mem(s, t, mem, i - 1, j - 1)
+    # Record and return the minimum number of edits
+    mem[i][j] = min(insert, delete, replace) + 1
+    return mem[i][j]
+
+
+def edit_distance_dp(s: str, t: str) -> int:
+    """Edit distance: Dynamic programming"""
+    n, m = len(s), len(t)
+    dp = [[0] * (m + 1) for _ in range(n + 1)]
+    # State transition: first row and first column
+    for i in range(1, n + 1):
+        dp[i][0] = i
+    for j in range(1, m + 1):
+        dp[0][j] = j
+    # State transition: the rest of the rows and columns
+    for i in range(1, n + 1):
+        for j in range(1, m + 1):
+            if s[i - 1] == t[j - 1]:
+                # If the two characters are equal, skip these two characters
+                dp[i][j] = dp[i - 1][j - 1]
+            else:
+                # The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
+                dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1
+    return dp[n][m]
+
+
+def edit_distance_dp_comp(s: str, t: str) -> int:
+    """Edit distance: Space-optimized dynamic programming"""
+    n, m = len(s), len(t)
+    dp = [0] * (m + 1)
+    # State transition: first row
+    for j in range(1, m + 1):
+        dp[j] = j
+    # State transition: the rest of the rows
+    for i in range(1, n + 1):
+        # State transition: first column
+        leftup = dp[0]  # Temporarily store dp[i-1, j-1]
+        dp[0] += 1
+        # State transition: the rest of the columns
+        for j in range(1, m + 1):
+            temp = dp[j]
+            if s[i - 1] == t[j - 1]:
+                # If the two characters are equal, skip these two characters
+                dp[j] = leftup
+            else:
+                # The minimum number of edits = the minimum number of edits from three operations (insert, remove, replace) + 1
+                dp[j] = min(dp[j - 1], dp[j], leftup) + 1
+            leftup = temp  # Update for the next round of dp[i-1, j-1]
+    return dp[m]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    s = "bag"
+    t = "pack"
+    n, m = len(s), len(t)
+
+    # Brute force search
+    res = edit_distance_dfs(s, t, n, m)
+    print(f"To change {s} to {t}, the minimum number of edits required is {res}")
+
+    # Memoized search
+    mem = [[-1] * (m + 1) for _ in range(n + 1)]
+    res = edit_distance_dfs_mem(s, t, mem, n, m)
+    print(f"To change {s} to {t}, the minimum number of edits required is {res}")
+
+    # Dynamic programming
+    res = edit_distance_dp(s, t)
+    print(f"To change {s} to {t}, the minimum number of edits required is {res}")
+
+    # Space-optimized dynamic programming
+    res = edit_distance_dp_comp(s, t)
+    print(f"To change {s} to {t}, the minimum number of edits required is {res}")