[Usaco 3.1.6] stamps

[Description]

It is known that a set of face values (for example, {1 point, 3 points}) of N stamps and an upper limit k indicate that K stamps can be attached to an envelope. Calculate the maximum continuous postage from 1 to M.

For example, suppose there are stamps of one or three points; you can paste up to five stamps. It is easy to post a postage of 1 to 5 points (just paste it with a one-point stamp), and the next postage is not hard:

• 6 = 3 + 3
• 7 = 3 + 3 + 1
• 8 = 3 + 3 + 1 + 1
• 9 = 3 + 3 + 3
• 10 = 3 + 3 + 3 + 1
• 11 = 3 + 3 + 3 + 1 + 1
• 12 = 3 + 3 + 3 + 3
• 13 = 3 + 3 + 3 + 3 + 1.

However, using five stamps with one or three points is impossible to post a postage of 14 points. Therefore, for the set of the two stamps and the maximum K = 5, the answer is M = 13.

[Format] program name: stampsinput format :( file stamps. In)

Row 3:	Two integers, K and N. K (1 <= k <= 200) is the total number of available stamps. N (1 <= n <= 50) is the number of stamps.
Row 2nd. The end of the file:	N integers, 15 in each line, list the face values of all N stamps. The face values cannot exceed 10000.

Output Format :( file stamps. out)

A separate row and an integer. The number of free stamps attached to a single row is no more than that of K stamps in a continuous set starting from 1.

[Analysis]

For general DP, pay attention to the questions.

1 # include <iostream> 2 # include <cstdio> 3 # include <cmath> 4 # include <cstring> 5 # include <algorithm> 6 const int maxn = 50 + 10; 7 const int INF = 200 + 10; 8 using namespace STD; 9 int s [maxn], F [2000000 + 10]; 10 int main () 11 {12 int K, n, I, j; 13 // file operation 14 freopen ("stamps. in "," r ", stdin); 15 freopen (" stamps. out "," W ", stdout); 16 scanf (" % d ", & K, & N); 17 for (I = 1; I <= N; I ++) scanf ("% d", & S [I]); 18 F [0] = 0; 19 for (I = 1; I <= 2000000; I ++) 20 {21 f [I] = inf; 22 for (j = 1; j <= N; j ++) if (I-s [J]> = 0) f [I] = min (F [I], F [I-s [J] + 1 ); 23 if (F [I]> K) break; 24} 25 printf ("% d", I-1); 26 return 0; 27}