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/climbing_stairs_backtrack.py

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+"""
+File: climbing_stairs_backtrack.py
+Created Time: 2023-06-30
+Author: krahets (krahets@163.com)
+"""
+
+
+def backtrack(choices: list[int], state: int, n: int, res: list[int]) -> int:
+    """Backtracking"""
+    # When climbing to the nth step, add 1 to the number of solutions
+    if state == n:
+        res[0] += 1
+    # Traverse all choices
+    for choice in choices:
+        # Pruning: do not allow climbing beyond the nth step
+        if state + choice > n:
+            continue
+        # Attempt: make a choice, update the state
+        backtrack(choices, state + choice, n, res)
+        # Retract
+
+
+def climbing_stairs_backtrack(n: int) -> int:
+    """Climbing stairs: Backtracking"""
+    choices = [1, 2]  # Can choose to climb up 1 step or 2 steps
+    state = 0  # Start climbing from the 0th step
+    res = [0]  # Use res[0] to record the number of solutions
+    backtrack(choices, state, n, res)
+    return res[0]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_backtrack(n)
+    print(f"Climb {n} steps, there are {res} solutions in total")

en/codes/python/chapter_dynamic_programming/climbing_stairs_constraint_dp.py

@@ -0,0 +1,29 @@
+"""
+File: climbing_stairs_constraint_dp.py
+Created Time: 2023-06-30
+Author: krahets (krahets@163.com)
+"""
+
+
+def climbing_stairs_constraint_dp(n: int) -> int:
+    """Constrained climbing stairs: Dynamic programming"""
+    if n == 1 or n == 2:
+        return 1
+    # Initialize dp table, used to store subproblem solutions
+    dp = [[0] * 3 for _ in range(n + 1)]
+    # Initial state: preset the smallest subproblem solution
+    dp[1][1], dp[1][2] = 1, 0
+    dp[2][1], dp[2][2] = 0, 1
+    # State transition: gradually solve larger subproblems from smaller ones
+    for i in range(3, n + 1):
+        dp[i][1] = dp[i - 1][2]
+        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]
+    return dp[n][1] + dp[n][2]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_constraint_dp(n)
+    print(f"Climb {n} steps, there are {res} solutions in total")

en/codes/python/chapter_dynamic_programming/climbing_stairs_dfs.py

@@ -0,0 +1,28 @@
+"""
+File: climbing_stairs_dfs.py
+Created Time: 2023-06-30
+Author: krahets (krahets@163.com)
+"""
+
+
+def dfs(i: int) -> int:
+    """Search"""
+    # Known dp[1] and dp[2], return them
+    if i == 1 or i == 2:
+        return i
+    # dp[i] = dp[i-1] + dp[i-2]
+    count = dfs(i - 1) + dfs(i - 2)
+    return count
+
+
+def climbing_stairs_dfs(n: int) -> int:
+    """Climbing stairs: Search"""
+    return dfs(n)
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_dfs(n)
+    print(f"Climb {n} steps, there are {res} solutions in total")

en/codes/python/chapter_dynamic_programming/climbing_stairs_dfs_mem.py

@@ -0,0 +1,35 @@
+"""
+File: climbing_stairs_dfs_mem.py
+Created Time: 2023-06-30
+Author: krahets (krahets@163.com)
+"""
+
+
+def dfs(i: int, mem: list[int]) -> int:
+    """Memoized search"""
+    # Known dp[1] and dp[2], return them
+    if i == 1 or i == 2:
+        return i
+    # If there is a record for dp[i], return it
+    if mem[i] != -1:
+        return mem[i]
+    # dp[i] = dp[i-1] + dp[i-2]
+    count = dfs(i - 1, mem) + dfs(i - 2, mem)
+    # Record dp[i]
+    mem[i] = count
+    return count
+
+
+def climbing_stairs_dfs_mem(n: int) -> int:
+    """Climbing stairs: Memoized search"""
+    # mem[i] records the total number of solutions for climbing to the ith step, -1 means no record
+    mem = [-1] * (n + 1)
+    return dfs(n, mem)
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_dfs_mem(n)
+    print(f"Climb {n} steps, there are {res} solutions in total")

en/codes/python/chapter_dynamic_programming/climbing_stairs_dp.py

@@ -0,0 +1,40 @@
+"""
+File: climbing_stairs_dp.py
+Created Time: 2023-06-30
+Author: krahets (krahets@163.com)
+"""
+
+
+def climbing_stairs_dp(n: int) -> int:
+    """Climbing stairs: Dynamic programming"""
+    if n == 1 or n == 2:
+        return n
+    # Initialize dp table, used to store subproblem solutions
+    dp = [0] * (n + 1)
+    # Initial state: preset the smallest subproblem solution
+    dp[1], dp[2] = 1, 2
+    # State transition: gradually solve larger subproblems from smaller ones
+    for i in range(3, n + 1):
+        dp[i] = dp[i - 1] + dp[i - 2]
+    return dp[n]
+
+
+def climbing_stairs_dp_comp(n: int) -> int:
+    """Climbing stairs: Space-optimized dynamic programming"""
+    if n == 1 or n == 2:
+        return n
+    a, b = 1, 2
+    for _ in range(3, n + 1):
+        a, b = b, a + b
+    return b
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    n = 9
+
+    res = climbing_stairs_dp(n)
+    print(f"Climb {n} steps, there are {res} solutions in total")
+
+    res = climbing_stairs_dp_comp(n)
+    print(f"Climb {n} steps, there are {res} solutions in total")

en/codes/python/chapter_dynamic_programming/coin_change.py

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+"""
+File: coin_change.py
+Created Time: 2023-07-10
+Author: krahets (krahets@163.com)
+"""
+
+
+def coin_change_dp(coins: list[int], amt: int) -> int:
+    """Coin change: Dynamic programming"""
+    n = len(coins)
+    MAX = amt + 1
+    # Initialize dp table
+    dp = [[0] * (amt + 1) for _ in range(n + 1)]
+    # State transition: first row and first column
+    for a in range(1, amt + 1):
+        dp[0][a] = MAX
+    # State transition: the rest of the rows and columns
+    for i in range(1, n + 1):
+        for a in range(1, amt + 1):
+            if coins[i - 1] > a:
+                # If exceeding the target amount, do not choose coin i
+                dp[i][a] = dp[i - 1][a]
+            else:
+                # The smaller value between not choosing and choosing coin i
+                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)
+    return dp[n][amt] if dp[n][amt] != MAX else -1
+
+
+def coin_change_dp_comp(coins: list[int], amt: int) -> int:
+    """Coin change: Space-optimized dynamic programming"""
+    n = len(coins)
+    MAX = amt + 1
+    # Initialize dp table
+    dp = [MAX] * (amt + 1)
+    dp[0] = 0
+    # State transition
+    for i in range(1, n + 1):
+        # Traverse in order
+        for a in range(1, amt + 1):
+            if coins[i - 1] > a:
+                # If exceeding the target amount, do not choose coin i
+                dp[a] = dp[a]
+            else:
+                # The smaller value between not choosing and choosing coin i
+                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)
+    return dp[amt] if dp[amt] != MAX else -1
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    coins = [1, 2, 5]
+    amt = 4
+
+    # Dynamic programming
+    res = coin_change_dp(coins, amt)
+    print(f"Minimum number of coins required to reach the target amount = {res}")
+
+    # Space-optimized dynamic programming
+    res = coin_change_dp_comp(coins, amt)
+    print(f"Minimum number of coins required to reach the target amount = {res}")

en/codes/python/chapter_dynamic_programming/coin_change_ii.py

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+"""
+File: coin_change_ii.py
+Created Time: 2023-07-10
+Author: krahets (krahets@163.com)
+"""
+
+
+def coin_change_ii_dp(coins: list[int], amt: int) -> int:
+    """Coin change II: Dynamic programming"""
+    n = len(coins)
+    # Initialize dp table
+    dp = [[0] * (amt + 1) for _ in range(n + 1)]
+    # Initialize first column
+    for i in range(n + 1):
+        dp[i][0] = 1
+    # State transition
+    for i in range(1, n + 1):
+        for a in range(1, amt + 1):
+            if coins[i - 1] > a:
+                # If exceeding the target amount, do not choose coin i
+                dp[i][a] = dp[i - 1][a]
+            else:
+                # The sum of the two options of not choosing and choosing coin i
+                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]
+    return dp[n][amt]
+
+
+def coin_change_ii_dp_comp(coins: list[int], amt: int) -> int:
+    """Coin change II: Space-optimized dynamic programming"""
+    n = len(coins)
+    # Initialize dp table
+    dp = [0] * (amt + 1)
+    dp[0] = 1
+    # State transition
+    for i in range(1, n + 1):
+        # Traverse in order
+        for a in range(1, amt + 1):
+            if coins[i - 1] > a:
+                # If exceeding the target amount, do not choose coin i
+                dp[a] = dp[a]
+            else:
+                # The sum of the two options of not choosing and choosing coin i
+                dp[a] = dp[a] + dp[a - coins[i - 1]]
+    return dp[amt]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    coins = [1, 2, 5]
+    amt = 5
+
+    # Dynamic programming
+    res = coin_change_ii_dp(coins, amt)
+    print(f"The number of coin combinations to make up the target amount is {res}")
+
+    # Space-optimized dynamic programming
+    res = coin_change_ii_dp_comp(coins, amt)
+    print(f"The number of coin combinations to make up the target amount is {res}")

en/codes/python/chapter_dynamic_programming/edit_distance.py

@@ -0,0 +1,123 @@
+"""
+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}")

en/codes/python/chapter_dynamic_programming/knapsack.py

@@ -0,0 +1,101 @@
+"""
+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}")

en/codes/python/chapter_dynamic_programming/min_cost_climbing_stairs_dp.py

@@ -0,0 +1,43 @@
+"""
+File: min_cost_climbing_stairs_dp.py
+Created Time: 2023-06-30
+Author: krahets (krahets@163.com)
+"""
+
+
+def min_cost_climbing_stairs_dp(cost: list[int]) -> int:
+    """Climbing stairs with minimum cost: Dynamic programming"""
+    n = len(cost) - 1
+    if n == 1 or n == 2:
+        return cost[n]
+    # Initialize dp table, used to store subproblem solutions
+    dp = [0] * (n + 1)
+    # Initial state: preset the smallest subproblem solution
+    dp[1], dp[2] = cost[1], cost[2]
+    # State transition: gradually solve larger subproblems from smaller ones
+    for i in range(3, n + 1):
+        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]
+    return dp[n]
+
+
+def min_cost_climbing_stairs_dp_comp(cost: list[int]) -> int:
+    """Climbing stairs with minimum cost: Space-optimized dynamic programming"""
+    n = len(cost) - 1
+    if n == 1 or n == 2:
+        return cost[n]
+    a, b = cost[1], cost[2]
+    for i in range(3, n + 1):
+        a, b = b, min(a, b) + cost[i]
+    return b
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    cost = [0, 1, 10, 1, 1, 1, 10, 1, 1, 10, 1]
+    print(f"Enter the list of stair costs as {cost}")
+
+    res = min_cost_climbing_stairs_dp(cost)
+    print(f"Minimum cost to climb the stairs {res}")
+
+    res = min_cost_climbing_stairs_dp_comp(cost)
+    print(f"Minimum cost to climb the stairs {res}")

en/codes/python/chapter_dynamic_programming/min_path_sum.py

@@ -0,0 +1,104 @@
+"""
+File: min_path_sum.py
+Created Time: 2023-07-04
+Author: krahets (krahets@163.com)
+"""
+
+from math import inf
+
+
+def min_path_sum_dfs(grid: list[list[int]], i: int, j: int) -> int:
+    """Minimum path sum: Brute force search"""
+    # If it's the top-left cell, terminate the search
+    if i == 0 and j == 0:
+        return grid[0][0]
+    # If the row or column index is out of bounds, return a +∞ cost
+    if i < 0 or j < 0:
+        return inf
+    # Calculate the minimum path cost from the top-left to (i-1, j) and (i, j-1)
+    up = min_path_sum_dfs(grid, i - 1, j)
+    left = min_path_sum_dfs(grid, i, j - 1)
+    # Return the minimum path cost from the top-left to (i, j)
+    return min(left, up) + grid[i][j]
+
+
+def min_path_sum_dfs_mem(
+    grid: list[list[int]], mem: list[list[int]], i: int, j: int
+) -> int:
+    """Minimum path sum: Memoized search"""
+    # If it's the top-left cell, terminate the search
+    if i == 0 and j == 0:
+        return grid[0][0]
+    # If the row or column index is out of bounds, return a +∞ cost
+    if i < 0 or j < 0:
+        return inf
+    # If there is a record, return it
+    if mem[i][j] != -1:
+        return mem[i][j]
+    # The minimum path cost from the left and top cells
+    up = min_path_sum_dfs_mem(grid, mem, i - 1, j)
+    left = min_path_sum_dfs_mem(grid, mem, i, j - 1)
+    # Record and return the minimum path cost from the top-left to (i, j)
+    mem[i][j] = min(left, up) + grid[i][j]
+    return mem[i][j]
+
+
+def min_path_sum_dp(grid: list[list[int]]) -> int:
+    """Minimum path sum: Dynamic programming"""
+    n, m = len(grid), len(grid[0])
+    # Initialize dp table
+    dp = [[0] * m for _ in range(n)]
+    dp[0][0] = grid[0][0]
+    # State transition: first row
+    for j in range(1, m):
+        dp[0][j] = dp[0][j - 1] + grid[0][j]
+    # State transition: first column
+    for i in range(1, n):
+        dp[i][0] = dp[i - 1][0] + grid[i][0]
+    # State transition: the rest of the rows and columns
+    for i in range(1, n):
+        for j in range(1, m):
+            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]
+    return dp[n - 1][m - 1]
+
+
+def min_path_sum_dp_comp(grid: list[list[int]]) -> int:
+    """Minimum path sum: Space-optimized dynamic programming"""
+    n, m = len(grid), len(grid[0])
+    # Initialize dp table
+    dp = [0] * m
+    # State transition: first row
+    dp[0] = grid[0][0]
+    for j in range(1, m):
+        dp[j] = dp[j - 1] + grid[0][j]
+    # State transition: the rest of the rows
+    for i in range(1, n):
+        # State transition: first column
+        dp[0] = dp[0] + grid[i][0]
+        # State transition: the rest of the columns
+        for j in range(1, m):
+            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]
+    return dp[m - 1]
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    grid = [[1, 3, 1, 5], [2, 2, 4, 2], [5, 3, 2, 1], [4, 3, 5, 2]]
+    n, m = len(grid), len(grid[0])
+
+    # Brute force search
+    res = min_path_sum_dfs(grid, n - 1, m - 1)
+    print(f"The minimum path sum from the top-left to the bottom-right corner is {res}")
+
+    # Memoized search
+    mem = [[-1] * m for _ in range(n)]
+    res = min_path_sum_dfs_mem(grid, mem, n - 1, m - 1)
+    print(f"The minimum path sum from the top-left to the bottom-right corner is {res}")
+
+    # Dynamic programming
+    res = min_path_sum_dp(grid)
+    print(f"The minimum path sum from the top-left to the bottom-right corner is {res}")
+
+    # Space-optimized dynamic programming
+    res = min_path_sum_dp_comp(grid)
+    print(f"The minimum path sum from the top-left to the bottom-right corner is {res}")

en/codes/python/chapter_dynamic_programming/unbounded_knapsack.py

@@ -0,0 +1,55 @@
+"""
+File: unbounded_knapsack.py
+Created Time: 2023-07-10
+Author: krahets (krahets@163.com)
+"""
+
+
+def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -> int:
+    """Complete 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][c - wgt[i - 1]] + val[i - 1])
+    return dp[n][cap]
+
+
+def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -> int:
+    """Complete 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 order
+        for c in range(1, cap + 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 = [1, 2, 3]
+    val = [5, 11, 15]
+    cap = 4
+
+    # Dynamic programming
+    res = unbounded_knapsack_dp(wgt, val, cap)
+    print(f"The maximum item value without exceeding knapsack capacity is {res}")
+
+    # Space-optimized dynamic programming
+    res = unbounded_knapsack_dp_comp(wgt, val, cap)
+    print(f"The maximum item value without exceeding knapsack capacity is {res}")