feat: add rust codes for chapter greedy (#646)

* feat: add rust codes for chapter greedy

* Update max_product_cutting.rs

---------

Co-authored-by: Yudong Jin <krahets@163.com>

codes/rust/Cargo.toml

@@ -349,5 +349,25 @@ path = "chapter_divide_and_conquer/hanota.rs"
 name = "build_tree"
 path = "chapter_divide_and_conquer/build_tree.rs"
 
+# Run Command: cargo run --bin coin_change_greedy
+[[bin]]
+name = "coin_change_greedy"
+path = "chapter_greedy/coin_change_greedy.rs"
+
+# Run Command: cargo run --bin fractional_knapsack
+[[bin]]
+name = "fractional_knapsack"
+path = "chapter_greedy/fractional_knapsack.rs"
+
+# Run Command: cargo run --bin max_capacity
+[[bin]]
+name = "max_capacity"
+path = "chapter_greedy/max_capacity.rs"
+
+# Run Command: cargo run --bin max_product_cutting
+[[bin]]
+name = "max_product_cutting"
+path = "chapter_greedy/max_product_cutting.rs"
+
 [dependencies]
 rand = "0.8.5"

codes/rust/chapter_greedy/coin_change_greedy.rs

@@ -0,0 +1,54 @@
+/*
+ * File: coin_change_greedy.rs
+ * Created Time: 2023-07-22
+ * Author: night-cruise (2586447362@qq.com)
+ */
+
+/* 零钱兑换：贪心 */
+fn coin_change_greedy(coins: &[i32], mut amt: i32) -> i32 {
+    // 假设 coins 列表有序
+    let mut i = coins.len() - 1;
+    let mut count = 0;
+    // 循环进行贪心选择，直到无剩余金额
+    while amt > 0 {
+        // 找到小于且最接近剩余金额的硬币
+        while coins[i] > amt {
+            i -= 1;
+        }
+        // 选择 coins[i]
+        amt -= coins[i];
+        count += 1;
+    }
+    // 若未找到可行方案，则返回 -1
+    if amt == 0 {
+        count
+    } else {
+        -1
+    }
+}
+
+/* Driver Code */
+fn main() {
+    // 贪心：能够保证找到全局最优解
+    let coins = [1, 5, 10, 20, 50, 100];
+    let amt = 186;
+    let res = coin_change_greedy(&coins, amt);
+    println!("\ncoins = {:?}, amt = {}", coins, amt);
+    println!("凑到 {} 所需的最少硬币数量为 {}", amt, res);
+
+    // 贪心：无法保证找到全局最优解
+    let coins = [1, 20, 50];
+    let amt = 60;
+    let res = coin_change_greedy(&coins, amt);
+    println!("\ncoins = {:?}, amt = {}", coins, amt);
+    println!("凑到 {} 所需的最少硬币数量为 {}", amt, res);
+    println!("实际上需要的最少数量为 3 ，即 20 + 20 + 20");
+
+    // 贪心：无法保证找到全局最优解
+    let coins = [1, 49, 50];
+    let amt = 98;
+    let res = coin_change_greedy(&coins, amt);
+    println!("\ncoins = {:?}, amt = {}", coins, amt);
+    println!("凑到 {} 所需的最少硬币数量为 {}", amt, res);
+    println!("实际上需要的最少数量为 2 ，即 49 + 49");
+}

codes/rust/chapter_greedy/fractional_knapsack.rs

@@ -0,0 +1,59 @@
+/*
+ * File: coin_change_greedy.rs
+ * Created Time: 2023-07-22
+ * Author: night-cruise (2586447362@qq.com)
+ */
+
+/* 物品 */
+struct Item {
+    w: i32, // 物品重量
+    v: i32, // 物品价值
+}
+
+impl Item {
+    fn new(w: i32, v: i32) -> Self {
+        Self { w, v }
+    }
+}
+
+/* 分数背包：贪心 */
+fn fractional_knapsack(wgt: &[i32], val: &[i32], mut cap: i32) -> f64 {
+    // 创建物品列表，包含两个属性：重量、价值
+    let mut items = wgt
+        .iter()
+        .zip(val.iter())
+        .map(|(&w, &v)| Item::new(w, v))
+        .collect::<Vec<Item>>();
+    // 按照单位价值 item.v / item.w 从高到低进行排序
+    items.sort_by(|a, b| {
+        (b.v as f64 / b.w as f64)
+            .partial_cmp(&(a.v as f64 / a.w as f64))
+            .unwrap()
+    });
+    // 循环贪心选择
+    let mut res = 0.0;
+    for item in &items {
+        if item.w <= cap {
+            // 若剩余容量充足，则将当前物品整个装进背包
+            res += item.v as f64;
+            cap -= item.w;
+        } else {
+            // 若剩余容量不足，则将当前物品的一部分装进背包
+            res += item.v as f64 / item.w as f64 * cap as f64;
+            // 已无剩余容量，因此跳出循环
+            break;
+        }
+    }
+    res
+}
+
+/* Driver Code */
+fn main() {
+    let wgt = [10, 20, 30, 40, 50];
+    let val = [50, 120, 150, 210, 240];
+    let cap = 50;
+
+    // 贪心算法
+    let res = fractional_knapsack(&wgt, &val, cap);
+    println!("不超过背包容量的最大物品价值为 {}", res);
+}

codes/rust/chapter_greedy/max_capacity.rs

@@ -0,0 +1,36 @@
+/*
+ * File: coin_change_greedy.rs
+ * Created Time: 2023-07-22
+ * Author: night-cruise (2586447362@qq.com)
+ */
+
+/* 最大容量：贪心 */
+fn max_capacity(ht: &[i32]) -> i32 {
+    // 初始化 i, j 分列数组两端
+    let mut i = 0;
+    let mut j = ht.len() - 1;
+    // 初始最大容量为 0
+    let mut res = 0;
+    // 循环贪心选择，直至两板相遇
+    while i < j {
+        // 更新最大容量
+        let cap = std::cmp::min(ht[i], ht[j]) * (j - i) as i32;
+        res = std::cmp::max(res, cap);
+        // 向内移动短板
+        if ht[i] < ht[j] {
+            i += 1;
+        } else {
+            j -= 1;
+        }
+    }
+    res
+}
+
+/* Driver Code */
+fn main() {
+    let ht = [3, 8, 5, 2, 7, 7, 3, 4];
+
+    // 贪心算法
+    let res = max_capacity(&ht);
+    println!("最大容量为 {}", res);
+}

codes/rust/chapter_greedy/max_product_cutting.rs

@@ -0,0 +1,35 @@
+/*
+ * File: coin_change_greedy.rs
+ * Created Time: 2023-07-22
+ * Author: night-cruise (2586447362@qq.com)
+ */
+
+/* 最大切分乘积：贪心 */
+fn max_product_cutting(n: i32) -> i32 {
+    // 当 n <= 3 时，必须切分出一个 1
+    if n <= 3 {
+        return 1 * (n - 1);
+    }
+    // 贪心地切分出 3 ，a 为 3 的个数，b 为余数
+    let a = n / 3;
+    let b = n % 3;
+    if b == 1 {
+        // 当余数为 1 时，将一对 1 * 3 转化为 2 * 2
+        3_i32.pow(a as u32 - 1) * 2 * 2
+    } else if b == 2 {
+        // 当余数为 2 时，不做处理
+        3_i32.pow(a as u32) * 2
+    } else {
+        // 当余数为 0 时，不做处理
+        3_i32.pow(a as u32)
+    }
+}
+
+/* Driver Code */
+fn main() {
+    let n = 58;
+
+    // 贪心算法
+    let res = max_product_cutting(n);
+    println!("最大切分乘积为 {}", res);
+}