36 lines
846 B
Go
36 lines
846 B
Go
// File: climbing_stairs_dp.go
|
|
// Created Time: 2023-07-18
|
|
// Author: Reanon (793584285@qq.com)
|
|
|
|
package chapter_dynamic_programming
|
|
|
|
/* Climbing stairs: Dynamic programming */
|
|
func climbingStairsDP(n int) int {
|
|
if n == 1 || n == 2 {
|
|
return n
|
|
}
|
|
// Initialize dp table, used to store subproblem solutions
|
|
dp := make([]int, n+1)
|
|
// Initial state: preset the smallest subproblem solution
|
|
dp[1] = 1
|
|
dp[2] = 2
|
|
// State transition: gradually solve larger subproblems from smaller ones
|
|
for i := 3; i <= n; i++ {
|
|
dp[i] = dp[i-1] + dp[i-2]
|
|
}
|
|
return dp[n]
|
|
}
|
|
|
|
/* Climbing stairs: Space-optimized dynamic programming */
|
|
func climbingStairsDPComp(n int) int {
|
|
if n == 1 || n == 2 {
|
|
return n
|
|
}
|
|
a, b := 1, 2
|
|
// State transition: gradually solve larger subproblems from smaller ones
|
|
for i := 3; i <= n; i++ {
|
|
a, b = b, a+b
|
|
}
|
|
return b
|
|
}
|