Problem C. Sum of Factorials

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Input file: standard input
Output file: standard output

John von Neumann, b. Dec. 28, 1903, d. Feb. 8, 1957, was a
Hungarian-American mathematician who made important contributions to the
foundations of mathematics, logic, quantum physics, meteorology, science,
computers, and game theory. He was noted for a phenomenal memory and the
speed with which he absorbed ideas and solved problems. In 1925 he received
a B.S. diploma in chemical engineering from Zurich Institute and in 1926 a
Ph.D. in mathematics from the University of Budapest, His Ph.D.
dissertation on set theory was an important contributions to the subject.
At the age of 20, von Neumann proposed a new definition of ordinal numbers
that was universally adopted. While still in his twenties, he made many
contributions in both pure and applied mathematics that established him as
a mathematician of unusual depth. His Mathematical Foundation of Quantum
Mechanics (1932) built a solid framework for the new scientific discipline.
During this time he also proved the mini-max theorem of GAME THEORY. He
gradually expanded his work in game theory, and with coauthor Oskar
Morgenstern he wrote Theory of Games and Economic Behavior (1944).
There are some numbers which can be expressed by the sum of factorials. For
example 9, 9 = 1! + 2! + 3! . Dr. von Neumann was very interested in such
numbers. So, he gives you a number n, and wants you to tell whether or not
the number can be expressed by the sum of some factorials.
Well, it is just a piece of case. For a given n, you will check if there
are some xi, and let n equal to
∑t (上标) i=1(下标) xi! (t≥1, xi≥0, xi = xj <==> i = j)
      t
即  ∑    xi! (t≥1, xi≥0, xi = xj <==> i = j)
      i=1
If the answer is yes, say "YES"; otherwise, print out
"NO".

Input
You will get a non-negative integer n (n≤1,000,000) from input file.

Output
For the n in the input file, you should print exactly one word ("YES" or
"NO") in a single line. No extra spaces are allowed.

Sample input and output
Standard input                      standard output
9                                   YES
2                                   YES

// Since the max input value is 1000000
#define MAX_NUM 10
int _tmain(int argc, _TCHAR* argv[])
{
 unsigned long values[MAX_NUM];
 int i = 1;
 values[i – 1] = 1;
 for (i = 2; i <= MAX_NUM; ++i)
 {
  values[i – 1] = values[i – 2] * i;
 }
 
 unsigned long input = 0;
 cin >> input;
 while (input > 0)
 {
  unsigned long b = 0;
  int start = MAX_NUM – 1;
  int i;
  for (i = start; i >= 0; –i)
  {
   b += values[i];
   if (input < b)
   {
    b -= values[start];
    –start;
    continue;
   }
   else if (input == b)
   {
    cout << "YES" << endl;
    break;
   }
  }
  if (i < 0)
  {
   cout << "NO" << endl;
  }
  cin >> input;
 }
 return 0;
}

整理 — 深入剖析数组与指针

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数组与指针声明有如此多的共同点,以至于我们通常觉得它们之间没有区别。其实不然。
首先,我们有必要重申一下一些常见形式的代码:
int a[3] = {0, 0, 0};
int *pa = a;
pa[1] = 1; //语句1
a[1] = 2; //语句2
从功效上看,语句1跟语句2一样设置数组中第2个元素的值。
但是其所产生的汇编代码却不一样,如下所示。
mov eax, dword ptr[pa]
mov dword ptr [eax + 4], 1 // 语句1
mov dword ptr [ebp-18h], 2 // 语句2
 
由此,我们可以看出变量名a实际上是一个常量,并且只能作为右值(rvalue)。
显然,
pa++; // 编译通过
a++; // 编译错误
 
另外,在使用sizeof时,它们的区别也是一目了然的。
sizeof(pa)只与编译器相关,受逻辑地址空间大小的影响;而sizeof(a)与数组长度成正比。
比如,在32位编译器中,
sizeof(pa)=4
sizeof(a)=3*sizeof(int)
 
有一个情况需要特别注意,就是当数组名作形参时。例如一下代码
void func(int a[])
{
int i = sizeof(a);
}
在这里,形参a仅仅是一个指针。