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49 lines
1.1 KiB
49 lines
1.1 KiB
/*
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* File: climbing_stairs_dp.rs
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* Created Time: 2023-07-09
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* Author: codingonion (coderonion@gmail.com)
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*/
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/* 爬樓梯：動態規劃 */
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fn climbing_stairs_dp(n: usize) -> i32 {
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// 已知 dp[1] 和 dp[2] ，返回之
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if n == 1 || n == 2 {
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return n as i32;
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}
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// 初始化 dp 表，用於儲存子問題的解
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let mut dp = vec![-1; n + 1];
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// 初始狀態：預設最小子問題的解
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dp[1] = 1;
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dp[2] = 2;
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// 狀態轉移：從較小子問題逐步求解較大子問題
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for i in 3..=n {
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dp[i] = dp[i - 1] + dp[i - 2];
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}
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dp[n]
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}
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/* 爬樓梯：空間最佳化後的動態規劃 */
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fn climbing_stairs_dp_comp(n: usize) -> i32 {
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if n == 1 || n == 2 {
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return n as i32;
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}
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let (mut a, mut b) = (1, 2);
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for _ in 3..=n {
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let tmp = b;
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b = a + b;
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a = tmp;
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}
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b
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}
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/* Driver Code */
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pub fn main() {
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let n: usize = 9;
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let res = climbing_stairs_dp(n);
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println!("爬 {n} 階樓梯共有 {res} 種方案");
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let res = climbing_stairs_dp_comp(n);
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println!("爬 {n} 階樓梯共有 {res} 種方案");
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}
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