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35 lines
860 B
35 lines
860 B
/**
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* File: climbing_stairs_constraint_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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/* 带约束爬楼梯：动态规划 */
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fun climbingStairsConstraintDP(n: Int): Int {
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if (n == 1 || n == 2) {
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return 1
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}
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// 初始化 dp 表，用于存储子问题的解
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val dp = Array(n + 1) { IntArray(3) }
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// 初始状态：预设最小子问题的解
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dp[1][1] = 1
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dp[1][2] = 0
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dp[2][1] = 0
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dp[2][2] = 1
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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][1] = dp[i - 1][2]
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dp[i][2] = dp[i - 2][1] + dp[i - 2][2]
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}
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return dp[n][1] + dp[n][2]
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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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val res = climbingStairsConstraintDP(n)
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println("爬 $n 阶楼梯共有 $res 种方案")
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} |