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Question
给定 \(n\) 种硬币,第 \(i\) 个硬币的面值为 \(coins[i - 1]\) ,目标金额为 \(amt\) ,每种硬币可以重复选取,问能够凑出目标金额的最少硬币个数。如果无法凑出目标金额则返回 \(-1\) 。
-贪心算法会迭代地做出一个又一个的贪心选择,每轮都将问题转化成一个规模更小的子问题,直到问题被解决。
这道题的贪心策略在生活中很常见:给定目标金额,我们贪心地选择不大于且最接近它的硬币,不断循环该步骤,直至凑出目标金额为止。

Fig. 零钱兑换的贪心策略
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15.1.2. 贪心算法特性
那么问题来了,什么样的问题适合用贪心算法求解呢?或者说,贪心算法在什么情况下可以保证找到最优解?
-相较于动态规划,贪心算法的使用条件更加苛刻,其主要关心问题的两个性质:
+相较于动态规划,贪心算法的使用条件更加苛刻,其主要关注问题的两个性质:
- 贪心选择性质:只有当局部最优选择始终可以导致全局最优解时,贪心算法才能保证得到最优解。
- 最优子结构:原问题的最优解包含子问题的最优解。值得注意的是,一些问题的最优子结构并不明显,但仍然可使用贪心算法解决。
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15.2 分数背包问题
15.3 最大容量问题
15.4 最大切分乘积问题
+15.5 小结
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