Balance
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Time Limit: 1000MS |
Memory Limit: 30000K |
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Total Submissions: 6667 |
Accepted: 4013 |
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 Olympiad in Informatics. Now he would 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
解题报告：这道题题意就是给我们一个杠杆，给我们c个可以挂东西的位置,再给我们g个物品的质量，让我们求最多有多少种方法能使天平保持平衡（以中点为支点），因为杠杆所能加载的最大重量是15 * 20 * 25 = 7500；可以转化为01背包问题，力 = 力距 * 距离；
代码如下：
#include <iostream> #include <cstdio> #include <cstring> #include <cstdlib> using namespace std; const int MAX = 15010; int w[25], l[25], dp[25][MAX]; int main() { int c, g, i, j, v; while (scanf("%d%d", &c, &g) != EOF) { for (i = 1; i <= c; ++i) { scanf("%d", &l[i]); } for (i = 1; i <= g; ++i) { scanf("%d", &w[i]); } dp[0][7500] = 1; for (i = 1; i <= g; ++i) { for (j = 1; j <= c; ++j) { for (v = 0; v < MAX; ++v) { if (dp[i - 1][v] != 0) { dp[i][v + w[i] * l[j]] += dp[i - 1][v]; } } } } printf("%d\n", dp[g][7500]); } return 0; }