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54 lines
1.2 KiB
Go
54 lines
1.2 KiB
Go
// File: coin_change_ii.go
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// Created Time: 2023-07-23
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// Author: Reanon (793584285@qq.com)
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package chapter_dynamic_programming
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/* 零錢兌換 II：動態規劃 */
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func coinChangeIIDP(coins []int, amt int) int {
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n := len(coins)
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// 初始化 dp 表
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dp := make([][]int, n+1)
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for i := 0; i <= n; i++ {
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dp[i] = make([]int, amt+1)
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}
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// 初始化首列
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for i := 0; i <= n; i++ {
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dp[i][0] = 1
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}
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// 狀態轉移：其餘行和列
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for i := 1; i <= n; i++ {
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for a := 1; a <= amt; a++ {
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if coins[i-1] > a {
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// 若超過目標金額，則不選硬幣 i
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dp[i][a] = dp[i-1][a]
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} else {
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// 不選和選硬幣 i 這兩種方案之和
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dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]
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}
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}
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}
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return dp[n][amt]
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}
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/* 零錢兌換 II：空間最佳化後的動態規劃 */
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func coinChangeIIDPComp(coins []int, amt int) int {
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n := len(coins)
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// 初始化 dp 表
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dp := make([]int, amt+1)
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dp[0] = 1
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// 狀態轉移
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for i := 1; i <= n; i++ {
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// 正序走訪
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for a := 1; a <= amt; a++ {
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if coins[i-1] > a {
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// 若超過目標金額，則不選硬幣 i
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dp[a] = dp[a]
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} else {
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// 不選和選硬幣 i 這兩種方案之和
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dp[a] = dp[a] + dp[a-coins[i-1]]
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}
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}
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}
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return dp[amt]
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}
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