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46 lines
1.0 KiB
46 lines
1.0 KiB
/**
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* File: climbing_stairs_dp.kt
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* Created Time: 2024-01-25
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* Author: curtishd (1023632660@qq.com)
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*/
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package chapter_dynamic_programming
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/* 爬楼梯：动态规划 */
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fun climbingStairsDP(n: Int): Int {
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if (n == 1 || n == 2) return n
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// 初始化 dp 表，用于存储子问题的解
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val dp = IntArray(n + 1)
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// 初始状态：预设最小子问题的解
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dp[1] = 1
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dp[2] = 2
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// 状态转移：从较小子问题逐步求解较大子问题
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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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return dp[n]
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}
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/* 爬楼梯：空间优化后的动态规划 */
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fun climbingStairsDPComp(n: Int): Int {
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if (n == 1 || n == 2) return n
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var a = 1
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var b = 2
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for (i in 3..n) {
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val tmp = b
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b += a
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a = tmp
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}
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return b
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}
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/* Driver Code */
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fun main() {
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val n = 9
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var res = climbingStairsDP(n)
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println("爬 $n 阶楼梯共有 $res 种方案")
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res = climbingStairsDPComp(n)
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println("爬 $n 阶楼梯共有 $res 种方案")
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} |