rust and zig : add codes for chapter_dynamic_programming (#606)

* rust : add codes for chapter_dynamic_programming * zig : add codes for chapter_dynamic_programming * rust : add codes for chapter_backtracking * Update n_queens.rs --------- Co-authored-by: Yudong Jin <krahets@163.com>
2026-07-26 13:06:07 +00:00 · 2023-07-15 23:16:02 +08:00
parent 5c09add1ec
commit b1f8857212
27 changed files with 1654 additions and 6 deletions
@@ -0,0 +1,67 @@
+/*
+ * File: coin_change.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 零钱兑换：动态规划 */
+fn coin_change_dp(coins: &[i32], amt: usize) -> i32 {
+    let n = coins.len();
+    let max = amt + 1;
+    // 初始化 dp 表
+    let mut dp = vec![vec![0; amt + 1]; n + 1];
+    // 状态转移：首行首列
+    for a in 1..= amt {
+        dp[0][a] = max;
+    }
+    // 状态转移：其余行列
+    for i in 1..=n {
+        for a in 1..=amt {
+            if coins[i - 1] > a as i32 {
+                // 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 这两种方案的较小值
+                dp[i][a] = std::cmp::min(dp[i - 1][a], dp[i][a - coins[i - 1] as usize] + 1);
+            }
+        }
+    }
+    if dp[n][amt] != max { return dp[n][amt] as i32; } else { -1 }
+}
+
+/* 零钱兑换：状态压缩后的动态规划 */
+fn coin_change_dp_comp(coins: &[i32], amt: usize) -> i32 {
+    let n = coins.len();
+    let max = amt + 1;
+    // 初始化 dp 表
+    let mut dp = vec![0; amt + 1];
+    dp.fill(max);
+    dp[0] = 0;
+    // 状态转移
+    for i in 1..=n {
+        for a in 1..=amt {
+            if coins[i - 1] > a as i32 {
+                // 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 这两种方案的较小值
+                dp[a] = std::cmp::min(dp[a], dp[a - coins[i - 1] as usize] + 1);
+            }
+        }
+    }
+    if dp[amt] != max { return dp[amt] as i32; } else { -1 }
+}
+
+/* Driver Code */
+pub fn main() {
+    let coins = [ 1, 2, 5 ];
+    let amt: usize = 4;
+
+    // 动态规划
+    let res = coin_change_dp(&coins, amt);
+    println!("凑到目标金额所需的最少硬币数量为 {res}");
+
+    // 状态压缩后的动态规划
+    let res = coin_change_dp_comp(&coins, amt);
+    println!("凑到目标金额所需的最少硬币数量为 {res}");
+}