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/knapsack.py

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+"""
+File: knapsack.py
+Created Time: 2023-07-03
+Author: krahets (krahets@163.com)
+"""
+
+
+def knapsack_dfs(wgt: list[int], val: list[int], i: int, c: int) -> int:
+    """0-1 Knapsack: Brute force search"""
+    # If all items have been chosen or the knapsack has no remaining capacity, return value 0
+    if i == 0 or c == 0:
+        return 0
+    # If exceeding the knapsack capacity, can only choose not to put it in the knapsack
+    if wgt[i - 1] > c:
+        return knapsack_dfs(wgt, val, i - 1, c)
+    # Calculate the maximum value of not putting in and putting in item i
+    no = knapsack_dfs(wgt, val, i - 1, c)
+    yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]
+    # Return the greater value of the two options
+    return max(no, yes)
+
+
+def knapsack_dfs_mem(
+    wgt: list[int], val: list[int], mem: list[list[int]], i: int, c: int
+) -> int:
+    """0-1 Knapsack: Memoized search"""
+    # If all items have been chosen or the knapsack has no remaining capacity, return value 0
+    if i == 0 or c == 0:
+        return 0
+    # If there is a record, return it
+    if mem[i][c] != -1:
+        return mem[i][c]
+    # If exceeding the knapsack capacity, can only choose not to put it in the knapsack
+    if wgt[i - 1] > c:
+        return knapsack_dfs_mem(wgt, val, mem, i - 1, c)
+    # Calculate the maximum value of not putting in and putting in item i
+    no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)
+    yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]
+    # Record and return the greater value of the two options
+    mem[i][c] = max(no, yes)
+    return mem[i][c]
+
+
+def knapsack_dp(wgt: list[int], val: list[int], cap: int) -> int:
+    """0-1 Knapsack: Dynamic programming"""
+    n = len(wgt)
+    # Initialize dp table
+    dp = [[0] * (cap + 1) for _ in range(n + 1)]
+    # State transition
+    for i in range(1, n + 1):
+        for c in range(1, cap + 1):
+            if wgt[i - 1] > c:
+                # If exceeding the knapsack capacity, do not choose item i
+                dp[i][c] = dp[i - 1][c]
+            else:
+                # The greater value between not choosing and choosing item i
+                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])
+    return dp[n][cap]
+
+
+def knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -> int:
+    """0-1 Knapsack: Space-optimized dynamic programming"""
+    n = len(wgt)
+    # Initialize dp table
+    dp = [0] * (cap + 1)
+    # State transition
+    for i in range(1, n + 1):
+        # Traverse in reverse order
+        for c in range(cap, 0, -1):
+            if wgt[i - 1] > c:
+                # If exceeding the knapsack capacity, do not choose item i
+                dp[c] = dp[c]
+            else:
+                # The greater value between not choosing and choosing item i
+                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])
+    return dp[cap]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    wgt = [10, 20, 30, 40, 50]
+    val = [50, 120, 150, 210, 240]
+    cap = 50
+    n = len(wgt)
+
+    # Brute force search
+    res = knapsack_dfs(wgt, val, n, cap)
+    print(f"The maximum item value without exceeding knapsack capacity is {res}")
+
+    # Memoized search
+    mem = [[-1] * (cap + 1) for _ in range(n + 1)]
+    res = knapsack_dfs_mem(wgt, val, mem, n, cap)
+    print(f"The maximum item value without exceeding knapsack capacity is {res}")
+
+    # Dynamic programming
+    res = knapsack_dp(wgt, val, cap)
+    print(f"The maximum item value without exceeding knapsack capacity is {res}")
+
+    # Space-optimized dynamic programming
+    res = knapsack_dp_comp(wgt, val, cap)
+    print(f"The maximum item value without exceeding knapsack capacity is {res}")