ural 1244. Gentlemen

1244. Gentlemen

Time limit: 0.5 second
Memory limit: 64 MB

Let's remember one old joke:

Once a gentleman said to another gentleman:
— What if we play cards?
— You know, I haven't played cards for ten years…
— And I haven't played for fifteen years…
So, little by little, they decided to resurrect their youth. The first gentleman asked a servant to bring a pack of cards, and before starting playing out weighed in his hand the pack.
— It seems to me, one card is missing from the pack… — he said and gave the pack to the other gentleman.
— Yes, the nine of spades, — the man agreed.

An incomplete pack of cards is given. The program should determine which cards are missing.

Input

The first line contains a positive integer, which is the weight in milligrams of the given incomplete pack. The second line contains an integer N, 2 ≤ N ≤ 100 — the number of cards in the complete pack. In the next N lines there are integers from 1 to 1000, which are the weights of the cards in milligrams. It's guaranteed that the total weight of all cards in the complete pack is strictly greater than the weight of the incomplete pack.

Output

If there is no solution, then output the single number 0. If there are more than one solutions, then you should write −1. Finally, if it is possible to determine unambiguously which cards are missing in the incomplete pack as compared to the complete one, then output the numbers of the missing cards separated with a space in ascending order.

Samples

input	output
270 4 100 110 170 200	2 4
270 4 100 110 160 170	-1
270 4 100 120 160 180	0

Problem Author: Alexander Petrov
Problem Source: Ural State University Personal Programming Contest, March 1, 2003

Tags: dynamic programming (hide tags for unsolved problems)

Difficulty: 284

题意：给出x 。然后n个ai，问哪几个ai能够组成x。若无解，输出0，不止一个解，输出-1，否则输出那几个数的编号

分析：背包。路径。

 #include <cstdio>

 #include <cstring>

 #include <cstdlib>

 #include <cmath>

 #include <deque>

 #include <vector>

 #include <queue>

 #include <iostream>

 #include <algorithm>

 #include <map>

 #include <set>

 #include <ctime>

 #include <iomanip>

 using namespace std;

 typedef long long LL;

 typedef double DB;

 #define For(i, s, t) for(int i = (s); i <= (t); i++)

 #define Ford(i, s, t) for(int i = (s); i >= (t); i--)

 #define Rep(i, t) for(int i = (0); i < (t); i++)

 #define Repn(i, t) for(int i = ((t)-1); i >= (0); i--)

 #define rep(i, x, t) for(int i = (x); i < (t); i++)

 #define MIT (2147483647)

 #define INF (1000000001)

 #define MLL (1000000000000000001LL)

 #define sz(x) ((int) (x).size())

 #define clr(x, y) memset(x, y, sizeof(x))

 #define puf push_front

 #define pub push_back

 #define pof pop_front

 #define pob pop_back

 #define ft first

 #define sd second

 #define mk make_pair

 inline void SetIO(string Name)

 {

     string Input = Name+".in",

     Output = Name+".out";

     freopen(Input.c_str(), "r", stdin),

     freopen(Output.c_str(), "w", stdout);

 }

 inline int Getint()

 {

     int Ret = ;

     char Ch = ' ';

     bool Flag = ;

     while(!(Ch >= '' && Ch <= ''))

     {

         if(Ch == '-') Flag ^= ;

         Ch = getchar();

     }

     while(Ch >= '' && Ch <= '')

     {

         Ret = Ret *  + Ch - '';

         Ch = getchar();

     }

     return Flag ? -Ret : Ret;

 }

 const int N = , M = ;

 int n, m, Arr[N];

 int Dp[M], G[M];

 bool Visit[N];

 vector<int> Ans;

 inline void Input()

 {

     scanf("%d", &m);

     scanf("%d", &n);

     For(i, , n) scanf("%d", Arr + i);

 }

 inline void Search(int x)

 {

     if(!x) return;

     Visit[G[x]] = ;

     Search(x - Arr[G[x]]);

 }

 inline void Solve()

 {

     Dp[] = ;

     int Max = ;

     For(i, , n)

     {

         Max += Arr[i];

         if(Max > m) Max = m;

         Ford(j, Max, Arr[i])

             if(Dp[j - Arr[i]])

             {

                 Dp[j] += Dp[j - Arr[i]];

                 if(!G[j]) G[j] = i;

             }

     }

     if(Dp[m] > ) puts("-1");

     else if(!Dp[m]) puts("");

     else

     {

         Search(m);

         For(i, , n)

             if(!Visit[i]) Ans.pub(i);

         int Length = sz(Ans);

         Rep(i, Length - ) printf("%d ", Ans[i]);

         printf("%d\n", Ans.back());

     }

 }

 int main()

 {

     #ifndef ONLINE_JUDGE

     SetIO("C");

     #endif

     Input();

     Solve();

     return ;

 }