UVA1627-Team them up!（动态规划）

Time Limit: 3000 mSec

Problem Description

It’s frosh week, and this year your friends have decided that they would initiate the new computer science students by dropping water balloons on them. They’ve ?lled up a large crate of identical water balloons, ready for the event. But as fate would have it, the balloons turned out to be rather tough, and can be dropped from a height of several stories without bursting! So your friends have sought you out for help. They plan to drop the balloons from a tall building on campus, but would like to spend as little e?ort as possible hauling their balloons up the stairs, so they would like to know the lowest ?oor from which they can drop the balloons so that they do burst. You know the building has n ?oors, and your friends have given you k identical balloons which you may use (and break) during your trials to ?nd their answer. Since you are also lazy, you would like to determine the minimum number of trials you must conduct in order to determine with absolute certainty the lowest ?oor from which you can drop a balloon so that it bursts (or in the worst case, that the balloons will not burst even when dropped from the top ?oor). A trial consists of dropping a balloon from a certain ?oor. If a balloon fails to burst for a trial, you can fetch it and use it again for another trial.

 Output

 1 #include <bits/stdc++.h>
 2 
 3 using namespace std;
 4 
 5 typedef long long LL;
 6 
 7 const int maxn = 100 + 5;
 8 
 9 int k;
10 LL n, dp[maxn][65];
11 
12 LL DP(int k, int i) {
13     if (dp[k][i] > 0) return dp[k][i];
14     if (!k || !i) return dp[k][i] = 0;
15 
16     return dp[k][i] = DP(k - 1, i - 1) + DP(k, i - 1) + 1;
17 }
18 
19 int main()
20 {
21     //freopen("input.txt", "r", stdin);
22     memset(dp, -1, sizeof(dp));
23     while (~scanf("%d%lld", &k, &n) && k) {
24         int i;
25         for (i = 0; i <= 63; i++) {
26             if (DP(k, i) >= n) {
27                 printf("%d\n", i);
28                 break;
29             }
30         }
31         if (i == 64) printf("More than 63 trials needed.\n");
32     }
33     return 0;
34 }