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| '''problem1
0-1背包
输出受限背包容量的最优价值
'''
def knapsack(w, n, wt, val):
dp = [[0] * (w + 1) for _ in range(n+1)]
for i in range(1, n+1):
for j in range(1, w+1):
if j - wt[i-1] < 0:
dp[i][j] = dp[i-1][j]
else:
dp[i][j] = max(dp[i-1][j-wt[i-1]] + val[i-1], dp[i-1][j])
return dp[n][w]
def knapsack(w, n, wt, val):
dp = [0] * (w+1)
for i in range(n):
for j in range(w, 0, -1):
if wt[i] <= j:
dp[j] = max(dp[j], dp[j - wt[i]] + val[i])
return dp[-1]
n = 3
w = 4
wt = [2, 1, 3]
val = [4, 2, 3]
print(knapsack(w, n, wt, val))
'''problem2
0-1背包变体
leetcode416
输出能否凑出具体背包容量
'''
class Solution:
def canPartition(self, nums: List[int]) -> bool:
nums_sum = sum(nums)
if nums_sum % 2 != 0: return False
nums_sum //= 2
nums_len = len(nums)
dp = [[False] * (nums_sum + 1) for _ in range(nums_len + 1)]
for i in range(nums_len + 1): dp[i][0] = True
for i in range(nums_len + 1):
for j in range(nums_sum + 1):
if j - nums[i-1] < 0: dp[i][j] = dp[i-1][j]
else: dp[i][j] = dp[i-1][j] or dp[i-1][j-nums[i-1]]
return dp[nums_len][nums_sum]
class Solution:
def canPartition(self, nums: List[int]) -> bool:
nums_len = len(nums)
nums_sum = sum(nums)
if nums_sum % 2 != 0: return False
nums_sum //= 2
dp = [False] * (nums_sum + 1)
dp[0] = True
for i in range(nums_len):
for j in range(nums_sum, -1, -1):
if j - nums[i] >= 0:
dp[j] = dp[j] or dp[j - nums[i]]
return dp[nums_sum]
''' problem3
完全背包
输出可能的组合总数
'''
def combinationSum(candidates, target):
n = len(candidates)
dp = [[0] * (target + 1) for _ in range(n + 1)]
for i in range(n + 1):
dp[i][0] = 1
for i in range(1, n + 1):
for j in range(1, target + 1):
if j - candidates[i - 1] < 0: dp[i][j] = dp[i - 1][j]
else: dp[i][j] = dp[i - 1][j] + dp[i][j - candidates[i - 1]]
print(dp)
return dp[-1][-1]
def combinationSum(candidates, target):
n = len(candidates)
dp = [0] * (target + 1)
dp[0] = 1
for i in range(n):
for j in range(1, target + 1):
if j - candidates[i] >= 0: dp[j] += dp[j - candidates[i]]
return dp[-1]
candidates = [2,3,6,7]
target = 7
print(combinationSum(candidates, target))
'''problem4
完全背包变体
leetcode39
输出具体组合情况
'''
class Solution:
def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]:
dp = {i:[] for i in range(target+1)}
dp[0] = [[]]
for num in candidates:
for i in range(num, target+1):
if dp[i-num]:
for a in dp[i-num]:
dp[i].append([num]+a)
return dp[target]
|