mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-27 19:16:29 +08:00
1c0f350ad6
* Add the intial translation of code of all the languages * test * revert * Remove * Add Python and Java code for EN version
101 lines
3.6 KiB
Python
101 lines
3.6 KiB
Python
"""
|
|
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}")
|