49 lines
1.2 KiB
Rust
49 lines
1.2 KiB
Rust
/*
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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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/* Climbing stairs: Dynamic programming */
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fn climbing_stairs_dp(n: usize) -> i32 {
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// Known dp[1] and dp[2], return them
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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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// Initialize dp table, used to store subproblem solutions
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let mut dp = vec![-1; n + 1];
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// Initial state: preset the smallest subproblem solution
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dp[1] = 1;
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dp[2] = 2;
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// State transition: gradually solve larger subproblems from smaller ones
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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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/* Climbing stairs: Space-optimized dynamic programming */
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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!("Climb {n} steps, there are {res} solutions in total");
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let res = climbing_stairs_dp_comp(n);
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println!("Climb {n} steps, there are {res} solutions in total");
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}
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