uva 11728 Alternate Task

　　vjudge 上题目链接：uva 11728

　　其实是个数论水题，直接打表就行：

 #include<cstdio>
 #include<algorithm>
 using namespace std;

 int ans[];
 inline void init(int n = ) {
     for(int i = ; i <= n; ++i) {
         int sum = ;
         for(int j = ; j <= i; ++j)
             if(i % j == )   sum += j;
         if(sum <= )   ans[sum] = i;
     }
 }

 int main() {
     int s,Case = ;
     init();
     while(~scanf("%d",&s),s)
         printf("Case %d: %d\n",++Case, !ans[s]? -: ans[s]);
     return ;
 }

　　可我一开始却杀鸡用了牛刀，想得超复杂，就因为大白书上提示"唯一分解定理，回溯"什么的，于是我就按着这样的思路去做了，结果写得超复杂，感觉过了也没有任何意义了。。。

 #include<cstdio>
 #include<cstring>
 #include<vector>
 #include<algorithm>
 using namespace std;

 bool vis[];
 int pri[];
 inline int init_pri(int n = ) {
     int c = ;
     for(int i = ; i <= n; ++i)
         if(!vis[i]) {
             pri[++c] = i;
             for(int j = i << ; j <= n; j += i)    vis[j] = ;
         }
     return c;
 }

 struct node {
     int sum, p, r, pow;
     node() {}
     node(int sum, int p, int r, int pow): sum(sum), p(p), r(r), pow(pow) {}
     bool operator < (const node & n2) const {
         if(sum == n2.sum)   return p < n2.p;
         return sum < n2.sum;
     }
     void print() const {
         printf("sum = %d  p = %d  r = %d  pow = %d\n",sum,p,r,pow);
     }
 };

 vector<node> fac;

 inline void init() {
     init_pri();
     for(int i = ; pri[i] <= ; ++i) {
         int sum = , mul = , len = ;
         while(sum <= ) {
             mul *= pri[i];
             sum += mul;
             if(sum > )  break;
             fac.push_back(node(sum, pri[i], ++len, mul));
         }
     }
     sort(fac.begin(), fac.end());
 }

 int find(const vector<node> &c, int low, int up, int x) {
     int mid;
     while(low <= up) {
         mid = low + up >> ;
         if(c[mid].sum == x)   return mid;
         else if(x < c[mid].sum)    up = mid - ;
         else    low = mid + ;
     }
     return low;
 }

 int ans;
 bool sign[];

 void dfs(int s, int id, int n) {
     if(s == ) {
         if(n > ans)  ans = n;
         return ;
     }
     if(s <=  || id < )   return ;
     if(!sign[fac[id].p] && s % fac[id].sum == ) {
         sign[fac[id].p] = ;
         dfs(s / fac[id].sum, id - , n * fac[id].pow);
         sign[fac[id].p] = ;
     }
     dfs(s, id - , n);
 }

 int main() {
     int s, Case = ;
     init();
     while(~scanf("%d",&s), s) {
         printf("Case %d: ",++Case);
         if(s == ) {
             puts("");
             continue;
         }
         if(s == ) {
             puts("-1");
             continue;
         }
         ans = -;
         int id = find(fac, , fac.size() - , s);
         if(fac[id].sum > s)   --id;
         memset(sign, , sizeof(sign));
         dfs(s, id, );
         printf("%d\n",ans);
     }
     return ;
 }