cf problem solution--E. Optimal Slots

https://codeforces.com/group/5yyKg9gx7m/contest/275848/problem/E

E. Optimal Slots

The main hall of your residency is open for use by the local community and public. Since it was built on public donations, there is no charge of using it. Every weekend particularly on public holidays there are up to 50 reservations to use it for multiple events with different durations.

You have been assigned by the residents to develop a program in choosing events to get most out of allocation time per weekend and have as short unused time as possible. Program should find the event(s) which fill(s) the allocation time best and print it in the same sequence as appears in the reservation list.

Input
Each test case consist of a single line.

The line starts with two integer T and N which is the time allocated for the hall to be used in the particular weekend and the number of events. The next T integer are the durations of the events (as appear in the reservation list). For example from the first line in sample data: T=5 hours, N, number of events =5, first event lasts for 1 hour, second is 2 hours, third is 3 hours, fourth is 4 hours, and the last one is 5 hours.

The input process will be terminated by a line containing 0.

Output
For each line of input value, in a single line, first, output a list of integers which are the selected events duration and another integer which is the sum of the selected events duration.

If there are multiple possible list of events, events that appear earlier in the list takes priority.

Example
inputCopy
5 5 1 2 3 4 5
10 9 11 9 3 5 8 4 9 3 2
16 8 12 6 11 11 13 1 10 7
13 5 10 12 2 13 10
28 14 18 19 26 15 18 24 7 21 14 25 2 12 9 6
0
outputCopy
1 4 5
3 5 2 10
6 10 16
13 13
19 7 2 28

 Title description;

Choose among n numbers so that their sum is as close to T as possible. Print out the selected number. If there are multiple plans, output the plan that appears first, and then print the sum.

analysis:

It is a simple 01 backpack maximum problem. T is the total cost and a [i] is the value. The key is to print the path. Pay attention to output the first plan. There is also a template.

Code:

#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<sstream>
#include<vector>
#include<stack>
#include<deque>
#include<cmath>
#include<map>
using namespace std;
typedef long long ll;
const int maxn=1e4+6;
int a[maxn];
int dp[maxn];
int T,n;
bool path[maxn][maxn];
void init()
{
    memset (dp, 0 , sizeof dp); 
    memset (path, 0 , sizeof path); 
} 
void solve () 
{ 
    // Contrary to the method of printing from the back 
    for ( int i = n- 1 ; i> = 0 ; i-- ) 
    { 
        for ( int j = T; j> = a [i]; j-- ) 
        { 
            // Need to add the equal sign, the scheme that does not appear may not be the first 
            if (dp [j] < = dp [ja [i]] + a [i]) 
            { 
                dp [j] = dp [ja [i]] + a [i]; 
                path [i] [j] = 1;
            }
        }
    }
    int j=T;
    //从最先出现的开始，i:1~n-1; 
    for(int i=0;i<n;i++)
    {
        if(path[i][j])
        {
            printf("%d ",a[i]);
            j-=a[i];
        }
    }
    printf("%d\n",T-j);
}
int main()
{
    while(1)
    {
        init();
        cin>>T;
        if(T==0) break;
        cin>>n;
        for(int i=0;i<n;i++)
        {
            scanf("%d",&a[i]);
        }
        solve();
    }
    return 0;
}