51nod1354 Selected Numbers

01 Backpack tle.

Problem solving report (by System Message)
A DP, similar to a backpack, that is in the product state. First of all, the number of the election is not the K-minus. Then find out the approximate K, discretization. Then Dp[i][j] indicates the state of the first I-digit product is J. DP[I+1][J*A[I+1]]]+=DP[I][J].
DP[I+1][J]+=DP[I][J];
Total complexity is O (n*d (k) *log (d (k)))
D (k) indicates the number of factors in K. One more log is because of discretization, corresponding to the subscript when the two points to find.

In fact, I think that is to remove the useless state only with his approximate to update. Online some of the solving the map is also to avoid the useless state.

#include <cstdio> #include <cstring> #include <cctype> #include <algorithm> #include <cmath > #include <map>using namespace std; #define REP (I,s,t) for (int. i=s;i<=t;i++) #define DWN (i,s,t) for (int i=s;i >=t;i--) #define CLR (x,c) memset (x,c,sizeof (x)) int read () {int X=0;char c=getchar (); while (!isdigit (c)) C=getchar (); while (IsDigit (c)) x=x*10+c-' 0 ', C=getchar (); return x;} const int Nmax=1e4+5;const int Mod=1e9+7;int a[nmax],ans[nmax];void mm (int &a) {if (a>=mod) a-=mod;} int main () {int t=read (), while (t--) {int n=read (), K=read (), cnt=0,u,v,d;for (v=1;v*v<k;v++) if (k%v==0) a[++cnt]=v,a[ ++cnt]=k/v;if (v*v==k) a[++cnt]=v;sort (a+1,a+cnt+1); Rep (i,1,cnt) Ans[i]=0;ans[1]=1;rep (i,1,n) {u=read (); if (k%u) Continue;dwn (j,cnt,1) {v=lower_bound (a+1,a+cnt+1,a[j]*u)-a;if (a[v]==a[j]*u) mm (Ans[v]+=ans[j]);}} printf ("%d\n", ans[cnt]);} return 0;}

　　

1354 Select a digital base time limit: 1 seconds space limit: 131072 KB score: 80 Difficulty: 5-level algorithm topic collection attention when given a sequence a[0],a[1],a[2],..., a[n-1] and an integer k, we want to find out, How many sub-sequences satisfy such a condition: multiply all elements in the current sub-sequence to exactly equal K. Sample explanation:

For the first data, we can choose [3] or [1 (first 1), 3] or [1 (second 1), 3] or [1,1,3]. So the answer is 4.

Input

Multiple sets of test data. The first line of the input file has an integer t (0< t <= 20), which indicates that there is a T group of data. The next 2*t line will give each set of data a two-line data, the first line contains two integers n, K (1<=n<=1000,2<=k<=100000000) Their meaning has been mentioned above. The second line contains a[0],a[1],a[2],..., a[n-1] (1<= a[i]<=k) separated by a single space. All inputs are integers.

Output

For each data, the answer to 1000000007 after the output can be.

Input example

23 31 1 33 62 3 6

Output example

42

51nod1354 Selected Numbers