HDU 4968 Improving the GPA

HDU 4968 Improving the GPA

Problem Description Xueba: Using the 4-Point Scale, my GPA is 4.0.

In fact, the AVERAGE SCORE of Xueba is calculated by the following formula:
AVERAGE SCORE = ∑(Wi * SCOREi) / ∑(Wi) 1<=i<=N
where SCOREi represents the scores of the ith course and Wi represents the credit of the corresponding course.

To simplify the problem, we assume that the credit of each course is 1. In this way, the AVERAGE SCORE is ∑(SCOREi) / N. In addition, SCOREi are all integers between 60 and 100, and we guarantee that ∑(SCOREi) can be divided by N.

In SYSU, the university usually uses the AVERAGE SCORE as the standard to represent the students’ level. However, when the students want to study further in foreign countries, other universities will use the 4-Point Scale to represent the students’ level. There are 2 ways of transforming each score to 4-Point Scale. Here is one of them.


The student喎?http://www.Bkjia.com/kf/ware/vc/" target="_blank" class="keylink">vcyBhdmVyYWdlIEdQQSBpbiB0aGUgNC1Qb2ludCBTY2FsZSBpcyBjYWxjdWxhdGVkIGFzIGZvbGxvd3M6CjxjZW50ZXI+PHN0cm9uZz5HUEEgPSChxihHUEFpKSAvIE48L3N0cm9uZz48L2NlbnRlcj4KPGJyPgpTbyBnaXZlbiBvbmUgc3R1ZGVudKGvcyBBVkVSQUdFIFNDT1JFIGFuZCB0aGUgbnVtYmVyIG9mIHRoZSBjb3Vyc2VzLCB0aGVyZSBhcmUgbWFueSBkaWZmZXJlbnQgcG9zc2libGUgdmFsdWVzIGluIHRoZSA0LVBvaW50IFNjYWxlLiBQbGVhc2UgY2FsY3VsYXRlIHRoZSBtaW5pbXVtIGFuZCBtYXhpbXVtIHZhbHVlIG9mIHRoZSBHUEEgaW4gdGhlIDQtUG9pbnQgU2NhbGUuCjxicj4KCiAKPGJyPgpJbnB1dApUaGUgaW5wdXQgYmVnaW5zIHdpdGggYSBsaW5lIGNvbnRhaW5pbmcgYW4gaW50ZWdlciBUICgxIDwgVCA8IDUwMCksIHdoaWNoIGRlbm90ZXMgdGhlIG51bWJlciBvZiB0ZXN0IGNhc2VzLiBUaGUgbmV4dCBUIGxpbmVzIGVhY2ggY29udGFpbiB0d28gaW50ZWdlcnMgQVZHU0NPUkUsIE4gKDYwIDw9IEFWR1NDT1JFIDw9IDEwMCwgMSA8PSBOIDw9IDEwKS4KIAo8YnI+Ck91dHB1dApGb3IgZWFjaCB0ZXN0IGNhc2UsIHlvdSBzaG91bGQgZGlzcGxheSB0aGUgbWluaW11bSBhbmQgbWF4aW11bSB2YWx1ZSBvZiB0aGUgR1BBIGluIHRoZSA0LVBvaW50IFNjYWxlIGluIG9uZSBsaW5lLCBhY2N1cmF0ZSB1cCB0byA0IGRlY2ltYWwgcGxhY2VzLiBUaGVyZSBpcyBhIHNwYWNlIGJldHdlZW4gdHdvIHZhbHVlcy4KIAo8YnI+ClNhbXBsZSBJbnB1dAoKPHByZSBjbGFzcz0="brush:java;">4 75 1 75 2 75 3 75 10
Sample Output

3.0000 3.0000
2.7500 3.0000
2.6667 3.1667
2.4000 3.2000

HintIn the third case, there are many possible ways to calculate the minimum value of the GPA in the 4-Point Scale.
For example, 
Scores 78 74 73 GPA = (3.0 + 2.5 + 2.5) / 3 = 2.6667
Scores 79 78 68 GPA = (3.0 + 3.0 + 2.0) / 3 = 2.6667
Scores 84 74 67 GPA = (3.5 + 2.5 + 2.0) / 3 = 2.6667
Scores 100 64 61 GPA = (4.0 + 2.0 + 2.0) / 3 = 2.6667

題意：告訴你n個人的平均數，求最大的，最小的平均績點

思路：簡單的DP，dp[i][j]前i個人總分j的最大績點和

#include 
#include 
#include 
#include 
using namespace std;
const int maxn = 105;
const double inf = 90000000.0;

double dp[15][1010], tab[105];
double lp[15][1010];

int main() {
	for (int i = 60; i <= 69; i++)	
		tab[i] = 2.0;
	for (int i = 70; i <= 74; i++)
		tab[i] = 2.5;
	for (int i = 75; i <= 79; i++)	
		tab[i] = 3.0;
	for (int i = 80; i <= 84; i++)
		tab[i] = 3.5;
	for (int i = 85; i <= 100; i++)
		tab[i] = 4.0;

	memset(dp, 0, sizeof(dp));
	for (int i = 60; i <= 100; i++)
		dp[1][i] = tab[i];
	for (int i = 2; i <= 10; i++)
		for (int j = 60; j <= 100; j++)
			for (int k = j; k <= 1000; k++)
				if (dp[i-1][k-j] != 0)
					dp[i][k] = max(dp[i][k], dp[i-1][k-j]+tab[j]);

	for (int i = 0; i <= 10; i++)
		for (int j = 0; j <= 1000; j++)
			lp[i][j] = inf;

	for (int i = 60; i <= 100; i++)
		lp[1][i] = tab[i];

	for (int i = 2; i <= 10; i++)
		for (int j = 60; j <= 100; j++)
			for (int k = j; k <= 1000; k++)
				if (lp[i-1][k-j] != inf)
					lp[i][k] = min(lp[i][k], lp[i-1][k-j]+tab[j]);
	
	int v, n;
	int t;
	scanf("%d", &t);
	while (t--) {
		scanf("%d%d", &v, &n);
		printf("%.4lf %.4lf\n", lp[n][n*v]/n, dp[n][n*v]/n);
	}
	return 0;
}