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* Fix Python code * Add the pythontutor blocks of the chapter tree, heap, graph, searching, sorting, divide and conquer, dynamic programming and greedy. Improve the pythontutor blocks of the chapter array and linkedlist and backtracking. Add the tutorial of pythontutor in how-to-read section. * Reduce the image's file size.
58 lines
1.6 KiB
Python
58 lines
1.6 KiB
Python
"""
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File: coin_change_ii.py
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Created Time: 2023-07-10
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Author: Krahets (krahets@163.com)
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"""
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def coin_change_ii_dp(coins: list[int], amt: int) -> int:
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"""零钱兑换 II：动态规划"""
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n = len(coins)
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# 初始化 dp 表
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dp = [[0] * (amt + 1) for _ in range(n + 1)]
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# 初始化首列
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for i in range(n + 1):
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dp[i][0] = 1
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# 状态转移
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for i in range(1, n + 1):
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for a in range(1, amt + 1):
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if coins[i - 1] > a:
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# 若超过目标金额，则不选硬币 i
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dp[i][a] = dp[i - 1][a]
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else:
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# 不选和选硬币 i 这两种方案之和
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dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]
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return dp[n][amt]
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def coin_change_ii_dp_comp(coins: list[int], amt: int) -> int:
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"""零钱兑换 II：空间优化后的动态规划"""
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n = len(coins)
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# 初始化 dp 表
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dp = [0] * (amt + 1)
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dp[0] = 1
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# 状态转移
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for i in range(1, n + 1):
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# 正序遍历
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for a in range(1, amt + 1):
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if coins[i - 1] > a:
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# 若超过目标金额，则不选硬币 i
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dp[a] = dp[a]
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else:
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# 不选和选硬币 i 这两种方案之和
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dp[a] = dp[a] + dp[a - coins[i - 1]]
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return dp[amt]
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"""Driver Code"""
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if __name__ == "__main__":
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coins = [1, 2, 5]
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amt = 5
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# 动态规划
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res = coin_change_ii_dp(coins, amt)
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print(f"凑出目标金额的硬币组合数量为 {res}")
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# 空间优化后的动态规划
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res = coin_change_ii_dp_comp(coins, amt)
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print(f"凑出目标金额的硬币组合数量为 {res}")
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