Uva10934 Dropping Water balloons 【Dp】
有一个n层楼高的楼房,可以从任意一层往下丢水球,这个水球有一个抗击打系数,表示它从最高多少层仍下去不会碎,问最多摔碎K次的情况下,你最少扔多少次能测出这个系数。
【题解】
转化模型,猜$[1, n]$内的数$Y$,每次猜一个$X$,你会得到回答$X>Y$或$X=Y$或$X>Y$。在最多猜k次$X>Y$的情况下,最少猜多少次才能猜对。
设f[i, j]表示用了i次询问,得到了j次$X>Y$的回答后游戏就会结束的情况下,最多测出多长。
$f[i,j] = f[i-1, j-1] + f[i-1, j] + 1$
那么就转移啦。
后面的答案就是找到最小的$ans$使得$f[ans][k] >= N$
// Uva Online Judge 10934 # include <stdio.h> # include <algorithm> using namespace std; long long f[101][101]; int k; long long n; int main() { for (int i=1; i<=63; ++i) for (int j=1; j<=63; ++j) f[i][j] = f[i-1][j] + f[i-1][j-1] + 1; while(~scanf("%d%lld", &k, &n) && k) { int ans; k = min(63, k); bool ok=1; for (int i=0; i<=63; ++i) if(f[i][k] >= n) { ans = i; ok = 0; break; } if(ok) { puts("More than 63 trials needed."); } else { printf("%d\n", ans); } } return 0; }
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