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>
2026-08-13 20:20:58 +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 +1,64 @@
+/*
+ * File: coin_change_ii.rs
+ * Created Time: 2023-07-09
+ * Author: sjinzh (sjinzh@gmail.com)
+ */
+
+/* 零钱兑换 II：动态规划 */
+fn coin_change_ii_dp(coins: &[i32], amt: usize) -> i32 {
+    let n = coins.len();
+    // 初始化 dp 表
+    let mut dp = vec![vec![0; amt + 1]; n + 1];
+    // 初始化首列
+    for i in 0..= n {
+        dp[i][0] = 1;
+    }
+    // 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[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] = dp[i - 1][a] + dp[i][a - coins[i - 1] as usize];
+            }
+        }
+    }
+    dp[n][amt]
+}
+
+/* 零钱兑换 II：状态压缩后的动态规划 */
+fn coin_change_dp_ii_comp(coins: &[i32], amt: usize) -> i32 {
+    let n = coins.len();
+    // 初始化 dp 表
+    let mut dp = vec![0; amt + 1];
+    dp[0] = 1;
+    // 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] = dp[a] + dp[a - coins[i - 1] as usize];
+            }
+        }
+    }
+    dp[amt]
+}
+
+/* Driver Code */
+pub fn main() {
+    let coins = [ 1, 2, 5 ];
+    let amt: usize = 5;
+
+    // 动态规划
+    let res = coin_change_ii_dp(&coins, amt);
+    println!("凑出目标金额的硬币组合数量为 {res}");
+
+    // 状态压缩后的动态规划
+    let res = coin_change_dp_ii_comp(&coins, amt);
+    println!("凑出目标金额的硬币组合数量为 {res}");
+}