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/* *
* F i l e : c l i m b i n g _ s t a i r s _ c o n s t r a i n t _ d p . s w i f t
* C r e a t e d T i m e : 2 0 2 3 - 0 7 - 1 5
* A u t h o r : n u o m i 1 ( n u o m i 1 @ q q . c o m )
*/
/* 带 约 束 爬 楼 梯 ： 动 态 规 划 */
func climbingStairsConstraintDP ( n : Int ) -> Int {
if n = = 1 || n = = 2 {
return 1
}
// 初 始 化 d p 表 ， 用 于 存 储 子 问 题 的 解
var dp = Array ( repeating : Array ( repeating : 0 , count : 3 ) , count : n + 1 )
// 初 始 状 态 ： 预 设 最 小 子 问 题 的 解
dp [ 1 ] [ 1 ] = 1
dp [ 1 ] [ 2 ] = 0
dp [ 2 ] [ 1 ] = 0
dp [ 2 ] [ 2 ] = 1
// 状 态 转 移 ： 从 较 小 子 问 题 逐 步 求 解 较 大 子 问 题
for i in stride ( from : 3 , through : n , by : 1 ) {
dp [ i ] [ 1 ] = dp [ i - 1 ] [ 2 ]
dp [ i ] [ 2 ] = dp [ i - 2 ] [ 1 ] + dp [ i - 2 ] [ 2 ]
}
return dp [ n ] [ 1 ] + dp [ n ] [ 2 ]
}
@ main
enum ClimbingStairsConstraintDP {
/* D r i v e r C o d e */
static func main ( ) {
let n = 9
let res = climbingStairsConstraintDP ( n : n )
print ( " 爬 \( n ) 阶楼梯共有 \( res ) 种方案 " )
}
}
