Poj 1837 balance (DP)

Balance

Time limit:1000 ms		Memory limit:30000 K
Total submissions:10655		Accepted:6609

Description

Gigel has a strange "balance" and he wants to poise it. Actually, the device is different from any other ordinary balance.
It orders two arms of negligible weight and each arm's length is 15. some hooks are attached to these arms and gigel wants to hang up some weights from his collection of G weights (1 <= G <= 20) knowing that these weights have distinct values in the range 1 .. 25. gigel may droop any weight of any hook but he is forced to use all the weights.
Finally, gigel managed to balance the device using the experience he gained at the National Olympus IAD in ICS. Now he wowould like to know in how many ways the device can be balanced.

Knowing the repartition of the hooks and the set of the weights write a program that calculates the number of possibilities to balance the device.
It is guaranteed that will exist at least one solution for each test case at the evaluation.

Input

The input has the following structure:
• The first line contains the number C (2 <= C <= 20) and the number G (2 <= G <= 20 );
• The next line contains C integer numbers (these numbers are also distinct and sorted in ascending order) in the range-15 .. 15 representing the repartition of the hooks; each number represents the position relative to the center of the balance on the X axis (when no weights are attached the device is balanced and lined up to the X axis; the absolute value of the distances represents the distance between the hook and the balance center and the sign of the numbers determines the arm of the balance to which the hook is attached: '-' for the left arm and '+' for the Right Arm );
• On the next line there are g natural, distinct and sorted in ascending order numbers in the range 1 .. 25 representing the weights 'values.

Output

The output contains the number M representing the number of possibilities to poise the balance.

Sample Input

2 4-2 3 3 4 5 8

Sample output

2

Source

The question of Romania oi 2002 is that the weight is attached to the lever to balance the lever. How many re-mounting methods do you have? DP [I] [J] indicates that J weight is generated when the I weight is placed, because the weight is 0 when the equilibrium is obtained. During calculation, the weight may be less than 0, therefore, we estimate that the maximum weight is 20*15*25 = 7500. Therefore, 7500 is regarded as 0, when j <0 is less than 0, the state equation DP [I] [J + W [k] * V [k] + = DP [I-1] can be obtained. [J]

1 # include <cstdio> 2 # include <iostream> 3 # include <cstring> 4 # include <stdlib. h> 5 # include <algorithm> 6 using namespace STD; 7 const int maxn = 20 + 5; 8 int W [maxn], V [maxn]; 9 int DP [maxn] [1, 15005]; 10 int main () 11 {12 INT n, m; 13 while (scanf ("% d", & N, & M )! = EOF) 14 {15 for (INT I = 1; I <= N; I ++) 16 scanf ("% d", & W [I]); 17 For (INT I = 1; I <= m; I ++) 18 scanf ("% d", & V [I]); 19 20 memset (DP, 0, sizeof (DP); 21 DP [0] [7500] = 1; 22 for (INT I = 1; I <= m; I ++) 23 {24 for (Int J = 0; j <= 15000; j ++) 25 {26 if (DP [I-1] [J]) // if it is 0, it indicates that this status is not obtained before. You do not need to calculate 27 {28 for (int K = 1; k <= N; k ++) 29 DP [I] [J + W [k] * V [I] + = DP [I-1] [J]; 30} 31} 32} 33 printf ("% d \ n", DP [m] [7500]); 34} 35 return 0; 36}

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Poj 1837 balance (DP)