Sum of Factorials

http://acm.pku.edu.cn/JudgeOnline/problem?id=1775

Description

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 contribution 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 Foundations 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 him whether or not the number can be expressed by the sum of some factorials.
Well, it's just a piece of cake. For a given n, you'll check if there are some xi, and let n equal to Σ_1<=i<=tx_i!. (t >=1 1, xi >= 0, xi = xj iff. i = j). If the answer is yes, say "YES"; otherwise, print out "NO".

Input

You will get several non-negative integer n (n <= 1,000,000) from input file. Each one is in a line by itself.
The input is terminated by a line with a negative integer.

Output

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


Solving

쓸데없이 문제만 긴 것 같다. 자연수 n이 주어졌을 때 n이 몇몇 팩토리얼의 합으로 이루어지는지 검사해야 한다.

일단 11!이 되면 n의 최대 범위인 1000000을 넘으므로 10! 까지만 고려하면 된다. 1! ~ 10! 까지 계산해 놓은 다음 10! 에서 1! 까지 n에서 작으면 빼고 n을 갱신한다. 이 과정을 1!까지 반복 한 후 남은 수가 0이면 n은 문제의 조건을 만족하는 자연수 이다.

#include <cstdio> #include <cstdlib> #include <vector> using namespace std; int main() { int n; int i = 0; int fac[11] = {1}; for (i = 1; i <= 10; i++) { fac[i] = fac[i-1]*i; } while (scanf("%d", &n) > 0) { if (n == 0) {printf("NO\n");continue;} if (n < 0) break; for (i = 10; i >= 0; i--) { if (n >= fac[i]) n-=fac[i]; } if (n == 0) printf("YES\n"); else printf("NO\n"); } return 0; }