# POJ 2229 sumsets Full Backpack or recursive _ backpack

Source: Internet
Author: User
Tags pow cmath

Sumsets

 Time Limit: 2000MS Memory Limit: 200000K Total submissions: 14968 accepted: 5978

Description farmer John commanded he cows to search for different sets of the numbers of that sum to a given number. The cows use is numbers that are, the integer power of 2. Here are the possible sets of numbers this sum to 7:

1) 1+1+1+1+1+1+1
2) 1+1+1+1+1+2
3) 1+1+1+2+2
4) 1+1+1+4
5) 1+2+2+2
6) 1+2+4

Help FJ count all possible representations for a given integer n (1 <= n <= 1,000,000).

Input a single and a single integer, N.

Output the number of ways to represent N as the indicated sum. Due to the potential huge size of this number, print only last 9 digits (in base representation).

Sample Input

`7`

Sample Output

`6`

Q: Given an n, only 2 power times are allowed, and how many different schemes are composed of N.

First of all this problem has a very good thinking: bare full backpack

Up to 20 items, the value is 2^0, 2^1, ..., 2^19.

It's a good way to run a full backpack and make a table. g++ can be passed, C + + has not been ...

```#include <cstdio> #include <cstring> #include <cmath> #include <cstdlib> #include <algorithm > #include <queue> #include <stack> #include <map> #include <set> #include <vector> #def  INE INF 0x3f3f3f #define EPS 1e-8 #define MAXN (1000000+1) #define MAXM (100000) #define RI (a) scanf ("%d", &a) #define Rl (a) scanf ("%lld", &a) #define RF (a) scanf ("%lf", &a) #define RS (a) scanf ("%s", a) #define PI (a) printf ("%d\n", (a) #define PF (a) printf ("%.2lf\n", (a)) #define PL (a) printf ("%lld\n", (a)) #define PS (a) printf ("%s\n", (a)) #define W ( A while (a--) #define CLR (A, B) memset (A, (b), sizeof (a)) #define MOD 1000000007 #define LL Long long #define Lson O&LT;&L
T;1, L, Mid #define Rson o<<1|1, mid+1, R #define LL o<<1 #define RR o<<1|1 using namespace std;
LL DP[MAXN];
int fac[21];
int Pow (int a, int n) {int ans = 1;
while (n) {ans *= A;
n--;
return ans;
} void Getdp () {   for (int i = 0; i < i++) Fac[i] = Pow (2, I);
Dp[0] = 1; for (int i = 0; i < i++) for (int j = Fac[i]; J < MAXN J + +) Dp[j] = (Dp[j] + dp[j-fac[i])%10
00000000;
int main () {GETDP (); int n; Ri (n);
Pl (Dp[n]);
return 0;
}```

Another kind of thinking:

Two kinds of DP state derivation dp[].

One, dp[i] = dp[i-1];

II, dp[i] = Dp[i-1] + dp[i>>1].

```#include <cstdio> #include <cstring> #include <cmath> #include <cstdlib> #include <algorithm > #include <queue> #include <stack> #include <map> #include <set> #include <vector> #def  INE INF 0x3f3f3f #define EPS 1e-8 #define MAXN (1000000+1) #define MAXM (100000) #define RI (a) scanf ("%d", &a) #define Rl (a) scanf ("%lld", &a) #define RF (a) scanf ("%lf", &a) #define RS (a) scanf ("%s", a) #define PI (a) printf ("%d\n", (a) #define PF (a) printf ("%.2lf\n", (a)) #define PL (a) printf ("%lld\n", (a)) #define PS (a) printf ("%s\n", (a)) #define W ( A while (a--) #define CLR (A, B) memset (A, (b), sizeof (a)) #define MOD 1000000007 #define LL Long long #define Lson O&LT;&L
T;1, L, Mid #define Rson o<<1|1, mid+1, R #define LL o<<1 #define RR o<<1|1 using namespace std;
LL DP[MAXN];
void Getdp () {dp[0] = 1;
for (int i = 1; i < MAXN i++) {if (I & 1) dp[i] = dp[i-1];
Else     Dp[i] = (Dp[i-1] + dp[i >> 1])% 1000000000;
int main () {GETDP ()}; int n; Ri (n);
Pl (Dp[n]);
return 0;
}```

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