103 lines
2.2 KiB
Go
103 lines
2.2 KiB
Go
package backtracking
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import (
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"fmt"
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)
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const intMax = int(^uint(0) >> 1)
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var Cnt int
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// LeastCoins find least number of coins of which the total values are equals a given one
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func LeastCoins(targetTotal int, coinOptions []int) int {
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minNum := intMax
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memo := make([][]int, targetTotal+1)
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for i := range memo {
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memo[i] = make([]int, len(coinOptions))
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}
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fmt.Println("start")
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leastCoins(&minNum, 0, targetTotal, len(coinOptions)-1, coinOptions, memo)
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fmt.Println("end")
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return minNum
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}
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func leastCoins(minNum *int, cNum, totalValue, opIndex int, coinOptions []int, memo [][]int) {
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Cnt++
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if 0 == totalValue {
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if cNum < *minNum {
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*minNum = cNum
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}
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return
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}
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if opIndex < 0 {
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return
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}
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num4Option := 0
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remaining := totalValue - coinOptions[opIndex]*num4Option
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for remaining >= 0 {
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if opIndex != 0 {
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if shouldSkip(memo, remaining, opIndex-1, cNum+num4Option) {
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goto Next
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}
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}
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leastCoins(minNum, cNum+num4Option, remaining, opIndex-1, coinOptions, memo)
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Next:
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num4Option++
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remaining = totalValue - coinOptions[opIndex]*num4Option
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}
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}
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func shouldSkip(memo [][]int, totalValue, nextOpIdex, cNum int) bool {
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if memo[totalValue][nextOpIdex] > 0 && memo[totalValue][nextOpIdex] <= cNum {
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fmt.Printf("skip，%d, %d as %d <= %d \n", totalValue, nextOpIdex, memo[totalValue][nextOpIdex], cNum)
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return true
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}
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if memo[totalValue][nextOpIdex] == 0 || memo[totalValue][nextOpIdex] > cNum {
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memo[totalValue][nextOpIdex] = cNum
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}
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return false
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}
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func LeastCoins2(targetTotal int, coinOptions []int) int {
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minNum := intMax
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memo := make([][]bool, targetTotal)
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for i := range memo {
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memo[i] = make([]bool, targetTotal/coinOptions[0])
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}
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fmt.Println("start")
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leastCoins2(&minNum, targetTotal, coinOptions, 0, 0, memo)
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fmt.Println("end")
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return minNum
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}
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func leastCoins2(minNum *int, targetTotal int, coinOptions []int, cNum, cValue int, memo [][]bool) {
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Cnt++
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if cValue == targetTotal {
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if *minNum > cNum {
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*minNum = cNum
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}
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return
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}
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for _, coin := range coinOptions {
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if coin+cValue <= targetTotal && !memo[cValue+coin-1][cNum] {
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memo[cValue+coin-1][cNum] = true
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leastCoins2(minNum, targetTotal, coinOptions, cNum+1, cValue+coin, memo)
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}
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}
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}
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