UVA - 10344

Problem I

23 Out of 5

Input: standard input

Output: standard output

Time Limit: 1 second

Memory Limit: 32 MB

Your task is to write a program that can decide whether you can find an arithmetic expression consisting of five given numbers (1<=i<=5) that will yield the value 23.
For this problem we will only consider arithmetic expressions of the following from:

where : {1,2,3,4,5} -> {1,2,3,4,5} is a bijective function

and  {+,-,*} (1<=i<=4)

Input

The Input consists of 5-Tupels of positive Integers, each between 1 and 50.
Input is terminated by a line containing five zero‘s. This line should not be processed.

Output

For each 5-Tupel print "Possible" (without quotes) if their exists an arithmetic expression (as described above) that yields 23. Otherwise print "Impossible".

Sample Input

1 1 1 1 1

1 2 3 4 5

2 3 5 7 11

0 0 0 0 0

Sample Output

Impossible

Possible

Possible

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <cstring>
 4 #include <algorithm>
 5 using namespace std;
 6
 7 int cal(int a,char c,int b) {
 8     if (c == ‘+‘) return a + b;
 9     if (c == ‘-‘) return a - b;
10     if (c == ‘*‘) return a * b;
11 }
12
13 int a[5];
14 char s[4] = {"+-*"};
15 int dfs(int sum ,int cur) {
16     if (cur == 5) {
17         if (sum == 23) return 1;
18         else return 0;
19     }
20     for (int i = 0;i < 3;i++) {
21         if (dfs(cal(sum,s[i],a[cur]),cur + 1)) return 1;
22     }
23     return 0;
24 }
25
26 int main () {
27     // freopen("1.in","r",stdin);
28     while (cin >> a[0]) {
29         for (int i = 1;i < 5;i++) {
30             cin >> a[i];
31         }
32         if (a[0] == 0) break;
33         int ok = 0;
34         sort(a,a + 5);
35         do {
36             if(dfs(a[0],1)) {
37                 cout << "Possible" << endl;
38                 ok = 1;
39                 break;
40             }
41         }while (next_permutation(a,a + 5));
42         if (ok == 0) cout << "Impossible" << endl;
43     }
44 }