POJ 1775 && Zoj 2358 Sum of factorials

Sum of Factorials

Time Limit: 1000MS

Memory Limit: 30000K

Descriptionjohn von Neumann, B. Dec, 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 is 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 T He University of Budapest. His Ph.D. dissertation on set theory is an important contribution to the subject. At the age of, von Neumann proposed a new definition of ordinal numbers, is universally adopted. While still in the He twenties, he made many contributions in both pure and applied mathematics that established him as a mat Hematician 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 on game theory, and with coauthor Oskar Morgenstern he wrote theory of games and economic B Ehavior (1944). There is 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 your to tell him whether or not the number can is expressed by the sum of some facto Rials. Well, it ' s just a piece of cake. For a given n, you ' ll check if there is some XI, and let n equal toσ1<=i<=tXI!. (t >=1 1, Xi >= 0, Xi = XJ iff. i = j). If The answer is yes, say "yes"; Otherwise, print out "NO". Inputyou'll get several non-negative integer n (n <= 1,000,000) from input file. Each of the are in a line by itself. The input is terminated by a line with a negative integer. Outputfor each n, you should the print exactly one word ("YES" or "NO") in a. No extra spaces is allowed. Sample Input

9-1

Sample Output

YES

Note 0! = 1;

Depth-First Search

Reference code:

#include <iostream> #include <string.h>using namespace Std;int a[20];bool used[20];void work () {A[0]=1;int mul=1;for (int i=1;a[i-1]<1000000+1;i++) {Mul*=i;a[i]=mul;}} BOOL DFS (int x,int i) {if (A[i]==x | | x==0) return true;if (a[i]>x) return false;for (; i<10;i++) {if (x-a[i]<0) Conti Nue;if (DFS (x-a[i],i+1)) return true; return false;} int main () {work (); int N;while (cin>>n&&n>=0) {if (n==0) {cout<< "NO" <<endl;continue;} if (DFS (n,0) ==true) cout<< "YES" <<endl;elsecout<< "NO" <<ENDL;} return 0;}

POJ 1775 && Zoj 2358 Sum of factorials