给定一系列硬币面额coins和total，找出所有可能的组合，这些组合导致最小数量的硬币总和。在我的解决方案中，我保持table[i]总和为i的最小硬币数量的运行轨迹。我不确定如何修改它来存储总和为i的实际硬币，并确保包括这两种可能性。我已经查看了堆栈溢出的其他代码，但我只找到了可以打印任何一种最佳解决方案的代码。
输入：minimum_coins（10，[2,3,5,6,7,8]）
输出：[[5,5]，[2,8]]
INT_MAX = 2 ** 63 - 1
def minimum_coins(total, coins)
table = Array.new(total + 1)
table[0] = 0
(1..total).to_a.each do |i|
table[i] = INT_MAX
end
(1..total).to_a.each do |i|
(0..coins.length-1).to_a.each do |j|
if coins[j] <= i
sub_res = table[i-coins[j]]
if sub_res != INT_MAX && sub_res + 1 < table[i]
table[i] = sub_res + 1
end
end
end
end
puts table.inspect
end
minimum_coins(10, [2,3,5,6,7,8])
答案 0 :(得分：2)
我们的table条目包含(BestCount, LastCoinList)对。
如果sub_res + 1 < table[i].BestCount那么
将BestCount替换为sub_res + 1，并使LastCoinList包含coins[j]值
如果sub_res + 1 = table[i].BestCount那么
只需将coins[j]值添加到LastCoinList
所以最后table[10]将包含BestValue = 2和LastCoinList = (5,7,8)
现在递归地从table[10]条目展开到table[10-5]，再到table[10-7]，再到table[10-8]，分别包含5,3和2，然后所有递归分支停在第0次入场。
答案 1 :(得分：1)
令：
d[i] = minimum changes for i
因此，如果d[i] == d[i - c] + 1，我们可以说如果我们使用硬币c进行交换，我们仍然可以为i获得最小的硬币更改。
代码：
def find(n, result, d, coins, changes, index):
if n == 0:
changes.append(result)
return
for i in range(index, len(coins)):
if n - coins[i] >= 0 and d[n] == d[n - coins[i]] + 1:
find(n - coins[i], result + [coins[i]], d, coins, changes, i)
def all_coin_changes(n, coins):
d = [n + 1] * (n + 1)
d[0] = 0
for i in range(1, n + 1):
for c in coins:
if i - c >= 0:
d[i] = min(d[i], d[i - c] + 1)
changes = []
find(n, [], d, coins, changes, 0)
return changes
print all_coin_changes(10, [2, 3, 5, 6, 7, 8])
# [[2, 8], [3, 7], [5, 5]]
print all_coin_changes(100, [2, 3, 5, 6, 7, 8])
# [[5, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8], [7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8]]
如果您仍有疑问，请不要犹豫，在此发表评论。
答案 2 :(得分：-1)
我制作了一个迭代程序，该程序可以计算获得给定数量的美分所需的最小硬币数量（美元）。这是迭代的，但希望对您有所帮助！
import java.util.*;
public class CoinProblem
{
public static void main(String[] args)
{
System.out.println("----------------------------COIN PROBLEM--------------------------");
System.out.println("Denominations: \nCent - 1\nNickel - 5\nDime - 10\nQuarter - 25");
Map<Integer, Integer> map = new HashMap<Integer, Integer> ();
System.out.println("\nENTER TARGET NUMBER (CENTS): ");
Scanner sc = new Scanner(System.in);
int target = Integer.parseInt(sc.next());
int count = numCoins(target, map);
System.out.println("\nMINIMUM NUMBER OF COINS REQUIRED: " + count);
System.out.println( map.get(1) + " CENTS");
System.out.println( map.get(5) + " NICKELS");
System.out.println( map.get(10) + " DIMES");
System.out.println( map.get(25) + " QUARTERS");
System.out.println("------------------------------------------------------------------");
}
public static int numCoins(int target, Map<Integer, Integer> map)
{
int cent = 1;
int nickel = 5;
int dime = 10;
int quarter = 25;
map.put(cent, 0);
map.put(nickel, 0);
map.put(dime, 0);
map.put(quarter, 0);
int count = 0;
if (target >= 25)
{
if (target % 25 == 0)
{
count += target/25;
map.put(quarter, count);
return count;
}
else
{
count += target/25;
map.put(quarter, count);
int remtarget = target%25;
if (remtarget >= 10)
{
if (remtarget % 10 == 0)
{
count += remtarget/10;
map.put(dime, remtarget/10);
return count;
}
else
{
count += remtarget/10;
map.put(dime, remtarget/10);
int fivetarget = remtarget%10;
if (fivetarget >= 5)
{
if (fivetarget % 5 == 0)
{
count += fivetarget/5;
map.put(nickel, fivetarget/5);
}
else
{
count += fivetarget/5;
map.put(nickel, fivetarget/5);
int ones = fivetarget%5;
count+= ones;
map.put(cent, ones);
}
}
else
{
count += fivetarget;
map.put(cent, fivetarget);
return count;
}
}
}
else
{
if (remtarget >= 5)
{
if (remtarget % 5 == 0)
{
count += remtarget/5;
map.put(nickel, remtarget/5);
}
else
{
count += remtarget/5;
map.put(nickel, remtarget/5);
int ones = remtarget%5;
count+= ones;
map.put(cent, ones);
}
}
else
{
count += remtarget;
map.put(cent, remtarget);
return count;
}
}
}
}
else
{
if (target == 0)
{
return 0;
}
if (target >= 10)
{
if (target % 10 == 0)
{
count += target/10;
map.put(dime, target/10);
return count;
}
else
{
count += target/10;
map.put(dime, target/10);
int ftarget = target%10;
if (ftarget >= 5)
{
if (ftarget % 5 == 0)
{
count += ftarget/5;
map.put(nickel, ftarget/5);
}
else
{
count += ftarget/5;
map.put(nickel, ftarget/5);
int otarget = ftarget%5;
count+= otarget;
map.put(cent, otarget);
}
}
else
{
count += ftarget;
map.put(cent, ftarget);
return count;
}
}
}
else
{
if (target > 5)
{
if (target % 5 == 0)
{
count += target/5;
map.put(nickel, target/5);
}
else
{
count += target/5;
map.put(nickel, target/5);
int o = target%5;
count+= o;
map.put(cent, o);
}
}
else
{
count += target;
map.put(cent, target);
return count;
}
}
}
return count;
}
}