Big Event in HDU
Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 52270 Accepted Submission(s): 17842
Problem Description
Nowadays, we all know that Computer College is the biggest department in HDU. But, maybe you don't know that Computer College had ever been split into Computer College and Software College in 2002.
The splitting is absolutely a big event in HDU! At the same time, it is a trouble thing too. All facilities must go halves. First, all facilities are assessed, and two facilities are thought to be same if they have the same value. It is assumed that there is N (0<N<1000) kinds of facilities (different value, different kinds).
The splitting is absolutely a big event in HDU! At the same time, it is a trouble thing too. All facilities must go halves. First, all facilities are assessed, and two facilities are thought to be same if they have the same value. It is assumed that there is N (0<N<1000) kinds of facilities (different value, different kinds).
Input
Input contains multiple test cases. Each test case starts with a number N (0 < N <= 50 -- the total number of different facilities). The next N lines contain an integer V (0<V<=50 --value of facility) and an integer M (0<M<=100 --corresponding number of the facilities) each. You can assume that all V are different.
A test case starting with a negative integer terminates input and this test case is not to be processed.
A test case starting with a negative integer terminates input and this test case is not to be processed.
Output
For each case, print one line containing two integers A and B which denote the value of Computer College and Software College will get respectively. A and B should be as equal as possible. At the same time, you should guarantee that A is not less than B.
Sample Input
2
10 1
20 1
3
10 1
20 2
30 1
-1
Sample Output
20 10
40 40
多重背包题，两边价值尽可能相近只需要一方的价值逼近总价值的一半即可，问题转化为容量为sum/2的多重背包，但多重背包算法会超时，优化为01背包即可。
AC代码如下：
1 #include <iostream> 2 #include <string.h> 3 #include <algorithm> 4 5 using namespace std; 6 7 int a[5005]; 8 int dp[125025]; 9 10 bool cmp(int a,int b) 11 { 12 return a > b; 13 } 14 int main(void) 15 { 16 int n; 17 while (scanf_s("%d", &n)) 18 { 19 if (n < 0) 20 break; 21 memset(dp, 0, sizeof(dp)); 22 memset(a, 0, sizeof(a)); 23 int sum = 0; 24 int cnt = 0; 25 while (n--) 26 { 27 int x, y; 28 scanf_s("%d%d", &x, &y); 29 sum += x * y; 30 while (y--) 31 { 32 a[cnt++] = x; 33 } 34 } 35 sort(a, a + cnt,cmp); 36 for (int i = 0; i < cnt; i++) 37 { 38 for (int j = sum / 2; j >= a[i]; j--) 39 dp[j] = max(dp[j], dp[j - a[i]] + a[i]); 40 } 41 int m = dp[sum / 2]; 42 int n = sum - m; 43 if (m > n) 44 cout << m << ' ' << n << endl; 45 else 46 cout << n << ' ' << m << endl; 47 } 48 return 0; 49 }