Entrance examination training algorithm
Time limit: 1.0s Memory Limit: 256.0MB
Problem Description
chen was a gifted child, his dream is to become the world's greatest physician. To this end, he wanted to worship in the vicinity of the most prestigious physician as a teacher. Physician in order to determine his qualifications, gave him a problem. Physicians took him to a cave full of herbs says to him:. "Children, this cave has some different herbs, picking each plant requires some time, each plant has its own value and I will give you some time, during this time, you can pick some herbs maximum if you are a smart kid, you should be taken to make the total value of herbs. "
If you are chen, you can accomplish this task ?
Input format
of the first line has two integers T (1 <= T <= 1000) and M (1 <= M <= 100), separated by a space, and T represents a total time can be used herbs, M for the number of herbs cave. Next M lines each comprising two integers between 1 to 100 (including 1 and 100), respectively, represent the value of a strain picked herbs time this strain and herbs.
Output formats
include line, which contains a single integer representing within the stipulated time, you can adopt a maximum total value of herbs to.
Sample input
70. 3
71 is 100
69. 1
. 1 2
Sample output
3
Data size and conventions
for data of 30%, M <= 10;
for all the data, M <= 100.
Analysis: set indicates a total time of
processing the first to the
maximum value of the total strain herbs can be obtained, which is a recurrence relation
#include <stdio.h>
int max(int a, int b)
{
return a > b ? a : b;
}
int main()
{
int T, M;
int time[105] = { 0 }, value[105] = { 0 };
int f[105][1005] = { 0 };
scanf("%d %d", &T, &M);
for (int i = 1; i <= M; ++i)
scanf("%d %d", &time[i], &value[i]);
for (int i = 1; i <= M; ++i)
{
for (int t = 0; t < time[i]; ++t)
f[i][t] = f[i-1][t];
for (int t = time[i]; t <= T; ++t)
f[i][t] = max(f[i-1][t], f[i-1][t-time[i]] + value[i]);
}
printf("%d", f[M][T]);
return 0;
}
