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68 lines
1.8 KiB
68 lines
1.8 KiB
/**
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* File: unbounded_knapsack.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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import kotlin.math.max
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/* 完全背包：动态规划 */
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fun unboundedKnapsackDP(wgt: IntArray, _val: IntArray, cap: Int): Int {
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val n = wgt.size
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// 初始化 dp 表
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val dp = Array(n + 1) { IntArray(cap + 1) }
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// 状态转移
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for (i in 1..n) {
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for (c in 1..cap) {
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if (wgt[i - 1] > c) {
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// 若超过背包容量，则不选物品 i
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dp[i][c] = dp[i - 1][c]
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} else {
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// 不选和选物品 i 这两种方案的较大值
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dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + _val[i - 1])
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}
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}
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}
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return dp[n][cap]
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}
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/* 完全背包：空间优化后的动态规划 */
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fun unboundedKnapsackDPComp(
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wgt: IntArray,
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_val: IntArray,
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cap: Int
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): Int {
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val n = wgt.size
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// 初始化 dp 表
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val dp = IntArray(cap + 1)
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// 状态转移
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for (i in 1..n) {
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for (c in 1..cap) {
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if (wgt[i - 1] > c) {
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// 若超过背包容量，则不选物品 i
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dp[c] = dp[c]
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} else {
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// 不选和选物品 i 这两种方案的较大值
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dp[c] = max(dp[c], dp[c - wgt[i - 1]] + _val[i - 1])
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}
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}
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}
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return dp[cap]
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}
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/* Driver Code */
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fun main() {
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val wgt = intArrayOf(1, 2, 3)
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val _val = intArrayOf(5, 11, 15)
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val cap = 4
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// 动态规划
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var res = unboundedKnapsackDP(wgt, _val, cap)
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println("不超过背包容量的最大物品价值为 $res")
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// 空间优化后的动态规划
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res = unboundedKnapsackDPComp(wgt, _val, cap)
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println("不超过背包容量的最大物品价值为 $res")
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} |