问题

### Instructions: You are an expert Python programmer. You will be given a question (problem specification) and will generate a correct Python program that matches the specification and passes all tests. You will NOT return anything except for the program.
### Question:
You are given two 0-indexed strings source and target, both of length n and consisting of lowercase English letters. You are also given two 0-indexed character arrays original and changed, and an integer array cost, where cost[i] represents the cost of changing the character original[i] to the character changed[i].
You start with the string source. In one operation, you can pick a character x from the string and change it to the character y at a cost of z if there exists any index j such that cost[j] == z, original[j] == x, and changed[j] == y.
Return the minimum cost to convert the string source to the string target using any number of operations. If it is impossible to convert source to target, return -1.
Note that there may exist indices i, j such that original[j] == original[i] and changed[j] == changed[i].

Example 1:

Input: source = "abcd", target = "acbe", original = ["a","b","c","c","e","d"], changed = ["b","c","b","e","b","e"], cost = [2,5,5,1,2,20]
Output: 28
Explanation: To convert the string "abcd" to string "acbe":
- Change value at index 1 from 'b' to 'c' at a cost of 5.
- Change value at index 2 from 'c' to 'e' at a cost of 1.
- Change value at index 2 from 'e' to 'b' at a cost of 2.
- Change value at index 3 from 'd' to 'e' at a cost of 20.
The total cost incurred is 5 + 1 + 2 + 20 = 28.
It can be shown that this is the minimum possible cost.

Example 2:

Input: source = "aaaa", target = "bbbb", original = ["a","c"], changed = ["c","b"], cost = [1,2]
Output: 12
Explanation: To change the character 'a' to 'b' change the character 'a' to 'c' at a cost of 1, followed by changing the character 'c' to 'b' at a cost of 2, for a total cost of 1 + 2 = 3. To change all occurrences of 'a' to 'b', a total cost of 3 * 4 = 12 is incurred.

Example 3:

Input: source = "abcd", target = "abce", original = ["a"], changed = ["e"], cost = [10000]
Output: -1
Explanation: It is impossible to convert source to target because the value at index 3 cannot be changed from 'd' to 'e'.


Constraints:

1 <= source.length == target.length <= 10^5
source, target consist of lowercase English letters.
1 <= cost.length == original.length == changed.length <= 2000
original[i], changed[i] are lowercase English letters.
1 <= cost[i] <= 10^6
original[i] != changed[i]

### Format: You will use the following starter code to write the solution to the problem and enclose your code within delimiters.
```python
class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:

```

### Answer: (use the provided format with backticks)

答案

模型 模型答案 正确答案
金声玉亮2.0 ```python
from typing import List
from collections import defaultdict

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a dictionary to store the minimum cost to change from one character to another
min_cost = defaultdict(lambda: defaultdict(lambda: float('inf')))

# Populate the dictionary with the given costs
for o, c, co in zip(original, changed, cost):
min_cost[o][c] = min(min_cost[o][c], co)

# Function to find the minimum cost to change from one character to another using Floyd-Warshall algorithm
def floyd_warshall():
for k in min_cost:
for i in min_cost:
for j in min_cost:
if min_cost[i][k] != float('inf') and min_cost[k][j] != float('inf'):
min_cost[i][j] = min(min_cost[i][j], min_cost[i][k] + min_cost[k][j])

# Apply Floyd-Warshall algorithm to find the minimum cost between all pairs of characters
floyd_warshall()

# Calculate the total minimum cost to convert source to target
total_cost = 0
for s, t in zip(source, target):
if s != t:
if min_cost[s][t] == float('inf'):
return -1
total_cost += min_cost[s][t]

return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
deepseek-r1

```python
class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
INF = 1 << 60 # A very large number to represent infinity
dist = [[INF] * 26 for _ in range(26)]

# Initialize diagonal (same character) to 0 cost
for i in range(26):
dist[i][i] = 0

# Fill the distance matrix with direct edges
for o, c, co in zip(original, changed, cost):
u = ord(o) - ord('a')
v = ord(c) - ord('a')
if co < dist[u][v]:
dist[u][v] = co

# Floyd-Warshall algorithm to compute all pairs shortest paths
for k in range(26):
for i in range(26):
for j in range(26):
if dist[i][k] + dist[k][j] < dist[i][j]:
dist[i][j] = dist[i][k] + dist[k][j]

total = 0
for s, t in zip(source, target):
if s == t:
continue
u = ord(s) - ord('a')
v = ord(t) - ord('a')
if dist[u][v] == INF:
return -1
total += dist[u][v]

return total
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
gpto1 ```python
class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
INF = 1 << 60
n = len(source)
source = source
target = target

# Initialize cost matrix
cost_matrix = [[INF] * 26 for _ in range(26)]
for i in range(26):
cost_matrix[i][i] = 0 # Cost to convert a letter to itself is 0

# Build the direct transformation cost
for o, c, z in zip(original , changed, cost):
x = ord(o) - ord('a')
y = ord(c) - ord('a')
if cost_matrix[x][y] > z:
cost_matrix[x][y] = z # Keep minimal cost

# Floyd-Warshall algorithm to find minimal cost between all pairs
for k in range(26):
for i in range(26):
for j in range(26):
if cost_matrix[i][k] + cost_matrix[k][j] < cost_matrix[i][j]:
cost_matrix[i][j] = cost_matrix[i][k] + cost_matrix[k][j]

total_cost = 0
for s_char, t_char in zip(source, target):
x = ord(s_char) - ord('a')
y = ord(t_char) - ord('a')
if cost_matrix[x][y] == INF:
return -1 # Impossible to transform s_char to t_char
else:
total_cost += cost_matrix[x][y]
return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
gpt-4o-2024-08-06 ```python
from typing import List
from collections import defaultdict
import heapq

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a graph of transformations with costs
graph = defaultdict(list)
for o, c, z in zip(original, changed, cost):
graph[o].append((c, z))

# Function to find the minimum cost to transform a single character
def dijkstra(start, end):
if start == end:
return 0
# Priority queue for Dijkstra's algorithm
pq = [(0, start)]
# Visited set to keep track of minimum cost to reach each character
visited = {}

while pq:
current_cost, current_char = heapq.heappop(pq)

if current_char in visited and visited[current_char] <= current_cost:
continue

visited[current_char] = current_cost

if current_char == end:
return current_cost

for neighbor, edge_cost in graph[current_char]:
if neighbor not in visited or visited[neighbor] > current_cost + edge_cost:
heapq.heappush(pq, (current_cost + edge_cost, neighbor))

return float('inf')

total_cost = 0
for s_char, t_char in zip(source, target):
cost_to_transform = dijkstra(s_char, t_char)
if cost_to_transform == float('inf'):
return -1
total_cost += cost_to_transform

return total_cost
```
 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
DeepSeek-Coder-V2-Lite-Instruct ```python
class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a dictionary to map original and changed characters to their costs
cost_map = {}
for i in range(len(original)):
if original[i] not in cost_map:
cost_map[original[i]] = {}
cost_map[original[i]][changed[i]] = cost[i]

# Initialize the minimum cost to a large number
min_cost = float('inf')

# Use dynamic programming to find the minimum cost
n = len(source)
dp = [[float('inf')] * (n + 1) for _ in range(n + 1)]
dp[0][0] = 0

for i in range(n):
for j in range(n):
# If the characters match, no cost is added
if source[i] == target[j]:
dp[i + 1][j + 1] = min(dp[i + 1][j + 1], dp[i][j])

# Try to change the character in source to match the character in target
if source[i] in cost_map and target[j] in cost_map[source[i]]:
dp[i + 1][j + 1] = min(dp[i + 1][j + 1], dp[i][j] + cost_map[source[i]][target[j]])

# Skip the character in source
dp[i + 1][j + 1] = min(dp[i + 1][j + 1], dp[i + 1][j])

# Skip the character in target
dp[i + 1][j + 1] = min(dp[i + 1][j + 1], dp[i][j + 1])

# The result is the minimum cost to convert the entire source to target
min_cost = dp[n][n]
return min_cost if min_cost != float('inf') else -1
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
Meta-Llama-3.1-405B-Instruct-Turbo ```python
from typing import List
import heapq

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
graph = {}
for orig, ch, c in zip(original, changed, cost):
if orig not in graph:
graph[orig] = []
graph[orig].append((ch, c))

for char in 'abcdefghijklmnopqrstuvwxyz':
if char not in graph:
graph[char] = []

dist = {char: float('inf') for char in 'abcdefghijklmnopqrstuvwxyz'}
pq = [(0, source[0])]
dist[source[0]] = 0

while pq:
curr_dist, curr_char = heapq.heappop(pq)
if curr_dist > dist[curr_char]:
continue
for neighbor, weight in graph[curr_char]:
if curr_dist + weight < dist[neighbor]:
dist[neighbor] = curr_dist + weight
heapq.heappush(pq, (dist[neighbor], neighbor))

total_cost = 0
for s, t in zip(source, target):
if s == t:
continue
if dist[t] == float('inf'):
return -1
total_cost += dist[t]

return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
Meta-Llama-3.1-70B-Instruct-Turbo ```python
from collections import defaultdict, deque
from typing import List

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
graph = defaultdict(dict)
for orig, chg, cst in zip(original, changed, cost):
graph[orig][chg] = min(graph[orig].get(chg, float('inf')), cst)

def dijkstra(start):
dist = {start: 0}
queue = deque([start])
while queue:
node = queue.popleft()
for neighbor, weight in graph[node].items():
if neighbor not in dist or dist[neighbor] > dist[node] + weight:
dist[neighbor] = dist[node] + weight
queue.append(neighbor)
return dist

dist_from_source = {}
for char in set(source):
dist_from_source[char] = dijkstra(char)

total_cost = 0
for src, tgt in zip(source, target):
if src == tgt:
continue
if tgt not in dist_from_source[src]:
return -1
total_cost += dist_from_source[src][tgt]

return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
Qwen2-72B-Instruct ```python
from collections import defaultdict
import heapq

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
graph = defaultdict(lambda: defaultdict(lambda: float('inf')))
for o, c, co in zip(original, changed, cost):
graph[o][c] = min(graph[o][c], co)

# add direct conversion costs
for i in range(len(source)):
if source[i] != target[i]:
graph[source[i]][target[i]] = min(graph[source[i]][target[i]], abs(ord(source[i]) - ord(target[i])))

# Floyd-Warshall algorithm to find shortest paths between all pairs of characters
chars = set(original + changed)
dist = {c: {c2: graph[c][c2] for c2 in chars} for c in chars}
for k in chars:
for i in chars:
for j in chars:
if dist[i][j] > dist[i][k] + dist[k][j]:
dist[i][j] = dist[i][k] + dist[k][j]

ans = 0
for i in range(len(source)):
if source[i] != target[i]:
if dist[source[i]][target[i]] == float('inf'):
return -1
ans += dist[source[i]][target[i]]

return ans
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
baichuan4 ```python
from collections import defaultdict

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a mapping from each original character to its corresponding changed character and cost
char_map = {original[i]: (changed[i], cost[i]) for i in range(len(original))}

# Initialize the minimum cost to 0
min_cost = 0

# Iterate through the characters of the source string
for i in range(len(source)):
# Check if the current character in source needs to be changed
if source[i] != target[i]:
# Find the minimum cost to change the current character to the target character
min_change_cost = float('inf')
for orig, (chg, cst) in char_map.items():
if chg == target[i]:
min_change_cost = min(min_change_cost, cst)

# If it's impossible to change the character, return -1
if min_change_cost == float('inf'):
return -1

# Add the minimum cost to the total cost
min_cost += min_change_cost

return min_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
doubao ```python
class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
n = len(source)
dp = [float('inf')] * n
dp[0] = 0 if source[0] == target[0] else -1
for i in range(1, n):
if source[i] == target[i]:
dp[i] = dp[i - 1]
else:
for j in range(len(original)):
if original[j] == source[i] and changed[j] == target[i]:
if dp[i - 1]!= -1:
dp[i] = min(dp[i], dp[i - 1] + cost[j])
return dp[n - 1]
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
gpto1 ```python
class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
INF = 1 << 60
n = len(source)
source = source
target = target

# Initialize cost matrix
cost_matrix = [[INF] * 26 for _ in range(26)]
for i in range(26):
cost_matrix[i][i] = 0 # Cost to convert a letter to itself is 0

# Build the direct transformation cost
for o, c, z in zip(original , changed, cost):
x = ord(o) - ord('a')
y = ord(c) - ord('a')
if cost_matrix[x][y] > z:
cost_matrix[x][y] = z # Keep minimal cost

# Floyd-Warshall algorithm to find minimal cost between all pairs
for k in range(26):
for i in range(26):
for j in range(26):
if cost_matrix[i][k] + cost_matrix[k][j] < cost_matrix[i][j]:
cost_matrix[i][j] = cost_matrix[i][k] + cost_matrix[k][j]

total_cost = 0
for s_char, t_char in zip(source, target):
x = ord(s_char) - ord('a')
y = ord(t_char) - ord('a')
if cost_matrix[x][y] == INF:
return -1 # Impossible to transform s_char to t_char
else:
total_cost += cost_matrix[x][y]
return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
kimi ```python
from typing import List

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a dictionary to store the cost of changing a character to another character
change_cost = {}
for o, c, co in zip(original, changed, cost):
if o not in change_cost:
change_cost[o] = {}
change_cost[o][c] = co

# Initialize the total cost and the previous character
total_cost = 0
prev_char = None

# Iterate over the characters in the source and target strings
for s, t in zip(source, target):
# If the characters are the same, skip this iteration
if s == t:
prev_char = s
continue

# If the previous character is the same as the current character in the source string,
# it means we need to change the character back to the previous character before changing it to the target character
if prev_char == s:
# If there is no cost for changing the character to the previous character, return -1
if prev_char not in change_cost or t not in change_cost[prev_char]:
return -1
total_cost += change_cost[prev_char][t]
else:
# If there is no cost for changing the character to the target character, return -1
if s not in change_cost or t not in change_cost[s]:
return -1
total_cost += change_cost[s][t]
prev_char = s

return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
minimax ```python
from typing import List

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a dictionary to map each original character to its possible changes and costs
change_map = {}
for orig, chng, c in zip(original, changed, cost):
if orig not in change_map:
change_map[orig] = {}
change_map[orig][chng] = c

# Initialize the cost to 0
total_cost = 0

# Iterate through each character in source and target
for s, t in zip(source, target):
if s == t:
# If the characters are the same, no cost is incurred
continue
elif s in change_map and t in change_map[s]:
# If the character can be changed directly, add the cost
total_cost += change_map[s][t]
else:
# If the character cannot be changed to the target character, return -1
return -1

return total_cost

# Example usage:
# sol = Solution()
# print(sol.minimumCost("abcd", "ac		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
wenxinyiyan ```python
from typing import List
import sys

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
n = len(source)
INF = sys.maxsize

# Create a mapping from (original, changed) pairs to their costs
cost_map = {}
for orig, chg, cst in zip(original, changed, cost):
if (orig, chg) not in cost_map:
cost_map[(orig, chg)] = cst
# Keep the minimum cost if there are multiple entries for the same pair
cost_map[(orig, chg)] = min(cost_map[(orig, chg)], cst)

# Create a 2D array to store the minimum costs of converting source[0:i] to target[0:j]
dp = [[INF] * 26 for _ in range(n + 1)]

# Base case: converting an empty string to an empty string has a cost of 0
dp[0][ord(source[0]) - ord('a')] = 0

# Fill the dp array
for i in range(1, n + 1):
for j in range(26):
# Cost of not changing the character
if j == ord(source[i - 1]) - ord('a'):
dp[i][j] = dp[i - 1][j]

# Cost of changing the character
for k in range(26):
if k != j and dp[i - 1][k] != INF:
key = (chr(k + ord('a')), chr(j + ord('a')))
if key in cost_map:
dp[i][j] = min(dp[i][j], dp[i - 1][k] + cost_map[key])

# Check if it's possible to convert source to target
if dp[n][ord(target[-1]) - ord('a')] == INF:
return -1

return dp[n][ord(target[-1]) - ord('a')]

# Note: The provided solution has a time complexity of O(n * 26^2), which may not be efficient for the given constraints.
# However, due to the limited number of possible (original, changed) pairs (up to 2000), the solution should work in practice.
# For an optimal solution, consider using a graph-based approach with shortest path algorithms like Dijkstra or Bellman-Ford.
```
**Important Note**: The provided solution has a potentially high time complexity and may not be the most efficient approach for the given constraints. In practice, due to the limited number of possible `(original, changed)` pairs (up to 2000), the solution should work. However, for an optimal solution, you may need to consider a graph-based approach using shortest path algorithms like Dijkstra or Bellman-Ford.

The idea behind the graph-based approach is to represent each character in the `source` string as a node in the graph. Edges between nodes would represent the possible character transitions and their costs. You would then find the shortest path from the starting node (representing the first character in `source`) to the ending node (representing the last character in `target`). This approach can significantly reduce the time complexity, especially when dealing with large strings and many possible character transitions.		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
zhipu ```python
from typing import List
import sys

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a graph where each node is a character and edges represent the cost of changing one character to another
graph = {chr(i): {chr(i): 0 for i in range(ord('a'), ord('z') + 1)} for i in range(ord('a'), ord('z') + 1)}

# Populate the graph with the given transformations and costs
for o, c, co in zip(original, changed, cost):
if c in graph[o]:
graph[o][c] = min(graph[o][c], co)
else:
graph[o][c] = co

# Use Floyd-Warshall algorithm to find the minimum cost between any two characters
for k in graph:
for i in graph:
for j in graph:
if graph[i][j] > graph[i][k] + graph[k][j]:
graph[i][j] = graph[i][k] + graph[k][j]

# Calculate the minimum cost to convert source to target
total_cost = 0
for s_char, t_char in zip(source, target):
if s_char == t_char:
continue
if t_char not in graph[s_char]:
return -1
total_cost += graph[s_char][t_char]

return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]
deepseek-v3 ```python
import sys
from collections import defaultdict

class Solution:
def minimumCost(self, source: str, target: str, original: List[str], changed: List[str], cost: List[int]) -> int:
# Create a graph to store the minimum cost between any two characters
graph = defaultdict(lambda: defaultdict(lambda: sys.maxsize))

# Initialize the graph with direct costs
for o, c, cost_val in zip(original, changed, cost):
graph[o][c] = min(graph[o][c], cost_val)

# Floyd-Warshall algorithm to compute the shortest paths between all pairs
chars = set()
for o in original:
chars.add(o)
for c in changed:
chars.add(c)
chars = list(chars)

for k in chars:
for i in chars:
for j in chars:
if graph[i][k] + graph[k][j] < graph[i][j]:
graph[i][j] = graph[i][k] + graph[k][j]

total_cost = 0
for s, t in zip(source, target):
if s == t:
continue
if graph[s][t] == sys.maxsize:
return -1
total_cost += graph[s][t]

return total_cost
```		 [{"input": "\"abcd\"\n\"acbe\"\n[\"a\", \"b\", \"c\", \"c\", \"e\", \"d\"]\n[\"b\", \"c\", \"b\", \"e\", \"b\", \"e\"]\n[2, 5, 5, 1, 2, 20]", "output": "28", "testtype": "functional"}, {"input": "\"aaaa\"\n\"bbbb\"\n[\"a\", \"c\"]\n[\"c\", \"b\"]\n[1, 2]", "output": "12", "testtype": "functional"}, {"input": "\"abcd\"\n\"abce\"\n[\"a\"]\n[\"e\"]\n[10000]", "output": "-1", "testtype": "functional"}]