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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 :
""" 零钱兑换 II： """
n = len ( coins )
# 初始化 dp 表
dp = [ [ 0 ] * ( amt + 1 ) for _ in range ( n + 1 ) ]
# 初始化首列
for i in range ( n + 1 ) :
dp [ i ] [ 0 ] = 1
# 状态转移
for i in range ( 1 , n + 1 ) :
for a in range ( 1 , amt + 1 ) :
if coins [ i - 1 ] > a :
# 若超过背包容量，则不选硬币 i
dp [ i ] [ a ] = dp [ i - 1 ] [ a ]
else :
# 不选和选硬币 i 这两种方案之和
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 :
""" 零钱兑换 II： """
n = len ( coins )
# 初始化 dp 表
dp = [ 0 ] * ( amt + 1 )
dp [ 0 ] = 1
# 状态转移
for i in range ( 1 , n + 1 ) :
# 正序遍历
for a in range ( 1 , amt + 1 ) :
if coins [ i - 1 ] > a :
# 若超过背包容量，则不选硬币 i
dp [ a ] = dp [ a ]
else :
# 不选和选硬币 i 这两种方案之和
dp [ a ] = dp [ a ] + dp [ a - coins [ i - 1 ] ]
return dp [ amt ]
""" Driver Code """
if __name__ == " __main__ " :
coins = [ 1 , 2 , 5 ]
amt = 5
n = len ( coins )
# 动态规划
res = coin_change_ii_dp ( coins , amt )
print ( f " 凑出目标金额的硬币组合数量为 { res } " )
# 状态压缩后的动态规划
res = coin_change_ii_dp_comp ( coins , amt )
print ( f " 凑出目标金额的硬币组合数量为 { res } " )
