55 lines
1.3 KiB
Go
55 lines
1.3 KiB
Go
// File: coin_change_ii.go
|
|
// Created Time: 2023-07-23
|
|
// Author: Reanon (793584285@qq.com)
|
|
|
|
package chapter_dynamic_programming
|
|
|
|
/* Coin change II: Dynamic programming */
|
|
func coinChangeIIDP(coins []int, amt int) int {
|
|
n := len(coins)
|
|
// Initialize dp table
|
|
dp := make([][]int, n+1)
|
|
for i := 0; i <= n; i++ {
|
|
dp[i] = make([]int, amt+1)
|
|
}
|
|
// Initialize first column
|
|
for i := 0; i <= n; i++ {
|
|
dp[i][0] = 1
|
|
}
|
|
// State transition: the rest of the rows and columns
|
|
for i := 1; i <= n; i++ {
|
|
for a := 1; a <= amt; a++ {
|
|
if coins[i-1] > a {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[i][a] = dp[i-1][a]
|
|
} else {
|
|
// The sum of the two options of not choosing and choosing coin i
|
|
dp[i][a] = dp[i-1][a] + dp[i][a-coins[i-1]]
|
|
}
|
|
}
|
|
}
|
|
return dp[n][amt]
|
|
}
|
|
|
|
/* Coin change II: Space-optimized dynamic programming */
|
|
func coinChangeIIDPComp(coins []int, amt int) int {
|
|
n := len(coins)
|
|
// Initialize dp table
|
|
dp := make([]int, amt+1)
|
|
dp[0] = 1
|
|
// State transition
|
|
for i := 1; i <= n; i++ {
|
|
// Traverse in order
|
|
for a := 1; a <= amt; a++ {
|
|
if coins[i-1] > a {
|
|
// If exceeding the target amount, do not choose coin i
|
|
dp[a] = dp[a]
|
|
} else {
|
|
// The sum of the two options of not choosing and choosing coin i
|
|
dp[a] = dp[a] + dp[a-coins[i-1]]
|
|
}
|
|
}
|
|
}
|
|
return dp[amt]
|
|
}
|