Blue Bridge Cup ALGO-21 training algorithm packing problem

Packing training algorithm problem  

Time limit: 1.0s Memory Limit: 256.0MB

 

Problem Description
　　has a box capacity V (a positive integer, 0 <= V <= 20000 ), while there are n items (0 <n <= 30) , each item has a volume (positive integer).
　　The remaining space requirements of n items, take any one of a number into the box so that the box is minimized.

 

The input format
　　of the first conduct an integer representing the capacity of the box;
　　second line an integer, indicates that there are n items;
　　next n rows, each row represents a respective integer volume of the n items.

 

Output formats
　　an integer representing the remaining space of the box.

 

Sample input
　　24
　　. 6
　　. 8
　　. 3
　　12 is
　　. 7
　　. 9
　　. 7

 

Sample output
0

Analysis: set as to the capacity of the box, first to the processing space after the items have been occupied. There recurrence relations:

 

#include <stdio.h>

int max(int a, int b)
{
    return a > b ? a : b;
}

int main()
{
    int V, n;
    int volume[35] = { 0 };
    int f[35][20005] = { 0 };

    scanf("%d", &V);
    scanf("%d", &n);
    for (int i = 1; i <= n; ++i)
        scanf("%d", &volume[i]);

    for (int i = 1; i <= n; ++i)
    {
        for (int v = 0; v < volume[i]; ++v)
            f[i][v] = f[i-1][v];
        for (int v = volume[i]; v <= V; ++v)
            f[i][v] = max(f[i-1][v], f[i-1][v-volume[i]] + volume[i]);
    }
    printf("%d", V - f[n][V]);

    return 0;
}