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@@ -281,6 +281,53 @@ status: new
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[class]{}-[func]{fractionalKnapsack}
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```
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=== "Rust"
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```rust title="fractional_knapsack.rs"
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/* 物品 */
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struct Item {
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w: i32, // 物品重量
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v: i32, // 物品价值
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}
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impl Item {
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fn new(w: i32, v: i32) -> Self {
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Self { w, v }
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}
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}
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/* 分数背包:贪心 */
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fn fractional_knapsack(wgt: &[i32], val: &[i32], mut cap: i32) -> f64 {
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// 创建物品列表,包含两个属性:重量、价值
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let mut items = wgt
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.iter()
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.zip(val.iter())
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.map(|(&w, &v)| Item::new(w, v))
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.collect::<Vec<Item>>();
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// 按照单位价值 item.v / item.w 从高到低进行排序
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items.sort_by(|a, b| {
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(b.v as f64 / b.w as f64)
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.partial_cmp(&(a.v as f64 / a.w as f64))
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.unwrap()
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});
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// 循环贪心选择
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let mut res = 0.0;
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for item in &items {
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if item.w <= cap {
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// 若剩余容量充足,则将当前物品整个装进背包
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res += item.v as f64;
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cap -= item.w;
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} else {
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// 若剩余容量不足,则将当前物品的一部分装进背包
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res += item.v as f64 / item.w as f64 * cap as f64;
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// 已无剩余容量,因此跳出循环
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break;
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}
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}
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res
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}
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```
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最差情况下,需要遍历整个物品列表,**因此时间复杂度为 $O(n)$** ,其中 $n$ 为物品数量。
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由于初始化了一个 `Item` 对象列表,**因此空间复杂度为 $O(n)$** 。
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