构造一个整数数组以实现特定的序列
本文关键字:实现 数组 整数 一个 | 更新日期: 2023-09-27 18:32:46
构造以 A 结尾的尽可能短的整数序列, 使用以下规则:
序列的第一个元素是 1,每个连续的 元素是前面任意两个元素的总和(添加一个 元素本身也是允许的),每个元素都大于 上述所有要素;也就是说,序列正在增加。
例如,对于 A = 42,可能的解为 [1, 2, 3, 6, 12, 24, 30, 42].另一种可能的解决方案是 [1, 2, 4, 5, 8, 16, 21, 42]。
我已经写了以下内容,但它在输入 456 时失败,通过返回 [1,2,4,8,16,32,64,128,200,256,456] ,序列中没有数字可以加在一起得到 200。
如何修复以下代码? 我做错了什么?
public static int[] hit(int n)
{
List<int> nums = new List<int>();
int x = 1;
while (x < n)
{
nums.Add(x);
x = x * 2;
if (x > n)
{
nums.Add(n - (x / 2));
nums.Add(n);
}
}
nums.Sort();
int[] arr = nums.ToArray();
return arr;
}
我知道
这背后会有一个数学证明,但我的猜测是将数字除以 2,如果它平均除以,则重复该过程。如果有余数,则为 1。 所以你会有整数商和商加一。 由于保证一个在集合中,因此已经处理了 2 个数字中较大的一个。 因此,只需对较小的重复该过程即可。 这个问题当然意味着一个相对微不足道的递归解决方案,所以我将把它留给海报来实现。
我想我明白了:
public Set<Integer> shortList(int n){
Set<Integer> result = new HashSet<Integer>();
Stack<Integer> stack = new Stack<Integer>();
result.add(n);
int num=n, den=0;
while(num>1){
while(num > den){
num--; den++;
if(num%den==0)
stack.push(num);
}//num>den
if(!stack.isEmpty()){
num = stack.pop();
result.add(num);
stack.clear();
}else{
result.add(num);
result.add(den);
}
den=0;
}
return result;
}//
结果(未排序)
for 42: [1, 2, 3, 21, 6, 7, 42, 14]
for 15: [1, 2, 4, 5, 10, 15]
for 310: [1, 2, 155, 4, 5, 310, 10, 124, 62, 31, 15, 30]
这是我
在C++中的解决方案(可以简单地更改为 C#):
void printSequenceTo(unsigned n)
{
if (n == 1) { printf("1"); return; }
if (n & 1) {
int factor = 3;
do {
if (n % factor == 0) {
printSequenceTo(n / factor * (factor-1));
factor = 0;
break;
}
factor += 2;
} while (factor * factor <= n);
if (factor) printSequenceTo(n-1);
}
else
printSequenceTo(n/2);
printf(",%u", n);
}
演示:http://ideone.com/8lXxc
当然,可以使用筛子进行分解来加速。
请注意,这是对已接受答案的显着改进,但仍然不是最佳的。
这是我
的尝试。它可能会被优化,但它显示了我的想法:
private static IEnumerable<int> OptimalSequence(int lastElement)
{
var result = new List<int>();
int currentElement = 1;
do
{
result.Add(currentElement);
currentElement = currentElement * 2;
} while (currentElement <= lastElement);
var realLastElement = result.Last();
if (lastElement != realLastElement)
{
result.Add(lastElement);
FixCollection(result, lastElement - realLastElement);
}
return result;
}
private static void FixCollection(List<int> result, int difference)
{
for (int i = 0; i < result.Count; i++)
{
if (result[i] == difference) break;
if (result[i] > difference)
{
result.Insert(i, difference);
FixCollection(result, difference - result[i-1]);
break;
}
}
}
编辑我无法正式证明这一点,但我的答案和克里斯·盖斯勒的答案给出了相同大小的序列(至少我检查了 1 到 10000 之间的数字),因为两种算法都补偿奇数。一些例子:
Number 1535
1,2,3,4,7,8,15,16,31,32,63,64,127,128,255,256,511,512,1024,1535
Number 2047
1,2,3,4,7,8,15,16,31,32,63,64,127,128,255,256,511,512,1023,1024,2047
Number 3071
1,2,3,4,7,8,15,16,31,32,63,64,127,128,255,256,511,512,1023,1024,2048,3071
Number 4095
1,2,3,4,7,8,15,16,31,32,63,64,127,128,255,256,511,512,1023,1024,2047,2048,4095
Number 6143
1,2,3,4,7,8,15,16,31,32,63,64,127,128,255,256,511,512,1023,1024,2047,2048,4096,6143
Number 8191
1,2,3,4,7,8,15,16,31,32,63,64,127,128,255,256,511,512,1023,1024,2047,2048,4095,4096,8191
==============
Number 1535
1,2,4,5,10,11,22,23,46,47,94,95,190,191,382,383,766,767,1534,1535
Number 2047
1,2,3,6,7,14,15,30,31,62,63,126,127,254,255,510,511,1022,1023,2046,2047
Number 3071
1,2,4,5,10,11,22,23,46,47,94,95,190,191,382,383,766,767,1534,1535,3070,3071
Number 4095
1,2,3,6,7,14,15,30,31,62,63,126,127,254,255,510,511,1022,1023,2046,2047,4094,4095
Number 6143
1,2,4,5,10,11,22,23,46,47,94,95,190,191,382,383,766,767,1534,1535,3070,3071,6142,6143
Number 8191
1,2,3,6,7,14,15,30,31,62,63,126,127,254,255,510,511,1022,1023,2046,2047,4094,4095,8190,8191
public static int[] hit(int n)
{
List<int> nums = new List<int>();
nums.Add(n);
int x = 0;
int Right = 0;
int Left = 0;
do
{
//even num
if (n % 2 == 0)
{
x = n / 2;
//result of division is also even 20/2 = 10
if (x % 2 == 0 || n>10 )
{
nums.Add(x);
n = x;
}
else
{
nums.Add(x + 1);
nums.Add(x - 1);
n = x - 1;
}
}
//numbers that can only be divided by 3
else if (n % 3 == 0)
{
x = n / 3;//46/3 =155
Right = x * 2;//155*2 = 310
Left = x;//155
nums.Add(Right);
nums.Add(Left);
n = x;
}
//numbers that can only be divided by 5
else
{
x = n / 2;
Right = x + 1;
Left = x;
nums.Add(Right);
nums.Add(Left);
n = Left;
}
} while (n > 2);
nums.Add(1);
nums.Reverse();
int[] arr = nums.ToArray();
return arr;
}