You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
36 lines
783 B
36 lines
783 B
// File: climbing_stairs_dp.go
|
|
// Created Time: 2023-07-18
|
|
// Author: Reanon (793584285@qq.com)
|
|
|
|
package chapter_dynamic_programming
|
|
|
|
/* 爬楼梯：动态规划 */
|
|
func climbingStairsDP(n int) int {
|
|
if n == 1 || n == 2 {
|
|
return n
|
|
}
|
|
// 初始化 dp 表，用于存储子问题的解
|
|
dp := make([]int, n+1)
|
|
// 初始状态：预设最小子问题的解
|
|
dp[1] = 1
|
|
dp[2] = 2
|
|
// 状态转移：从较小子问题逐步求解较大子问题
|
|
for i := 3; i <= n; i++ {
|
|
dp[i] = dp[i-1] + dp[i-2]
|
|
}
|
|
return dp[n]
|
|
}
|
|
|
|
/* 爬楼梯：空间优化后的动态规划 */
|
|
func climbingStairsDPComp(n int) int {
|
|
if n == 1 || n == 2 {
|
|
return n
|
|
}
|
|
a, b := 1, 2
|
|
// 状态转移：从较小子问题逐步求解较大子问题
|
|
for i := 3; i <= n; i++ {
|
|
a, b = b, a+b
|
|
}
|
|
return b
|
|
}
|