Codeforces 354 B Pyramid of Glasses （dp）

傷城~ 2022-08-23 04:57 120阅读 0赞

# Pyramid of Glasses #

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Mary has just graduated from one well-known University and is now attending celebration party. Students like to dream of a beautiful life, so they used champagne glasses to construct a small pyramid. The height of the pyramid is *n*. The top level consists of only 1 glass, that stands on 2 glasses on the second level (counting from the top), then 3 glasses on the third level and so on.The bottom level consists of *n* glasses.

Vlad has seen in the movies many times how the champagne beautifully flows from top levels to bottom ones, filling all the glasses simultaneously. So he took a bottle and started to pour it in the glass located at the top of the pyramid.

Each second, Vlad pours to the top glass the amount of champagne equal to the size of exactly one glass. If the glass is already full, but there is some champagne flowing in it, then it pours over the edge of the glass and is equally distributed over two glasses standing under. If the overflowed glass is at the bottom level, then the champagne pours on the table. For the purpose of this problem we consider that champagne is distributed among pyramid glasses immediately. Vlad is interested in the number of completely full glasses if he stops pouring champagne in *t* seconds.

Pictures below illustrate the pyramid consisting of three levels.

![babd65bb134f49f3bd405a04391a1f3d79b85d99.png][] ![d22903e8a2e3805de7dcdcae275527437bd09255.png][]

Input

The only line of the input contains two integers *n* and *t* (1 ≤ *n* ≤ 10, 0 ≤ *t* ≤ 10 000) — the height of the pyramid and the number of seconds Vlad will be pouring champagne from the bottle.

Output

Print the single integer — the number of completely full glasses after *t* seconds.

Examples

input

3 5

output

input

4 8

output

Note

In the first sample, the glasses full after 5 seconds are: the top glass, both glasses on the second level and the middle glass at the bottom level. Left and right glasses of the bottom level will be half-empty.

题目链接：[点击打开链接][Link 1]

###### **题意：** ######

向金字塔形的酒杯堆（每层的酒杯数等于该层层数）上倒酒，每秒到的酒的量为一杯

n为酒杯层数，t为时间，求倒满了几杯酒

###### 思路： ######

a\[i\]\[j\]代表从第i行j列个酒杯上流过的酒的量，所以a\[i\]\[j\]>=0时表示该酒杯已满，

j=1，j=i，a\[i\]\[j\]分别为a\[i-1\]\[j\]/2-1和a\[i-1\]\[j-1\]/2-1；其他则为其上面两项/2相加-1；

注意a\[i\]\[j\]为负时会影响下一层的结果，所以要赋值为0，并从结果中减去该情况；

###### 代码： ######

###### `#include<stdio.h> #include<math.h> #include<string.h> using namespace std; double a[15][15]; int main() { int n,t; while(~scanf("%d %d",&n,&t)) { a[1][1]=(t-1); int ans=0; for(int i=2; i<=n; i++) { for(int j=1; j<=i; j++) { if(j==1) { a[i][j]=a[i-1][j]/2-1; if(a[i][j]<0) { a[i][j]=0; ans--; } } else if(j==i) { a[i][j]=a[i-1][j-1]/2-1; if(a[i][j]<0) { a[i][j]=0; ans--; } } else { a[i][j]=a[i-1][j]/2+a[i-1][j-1]/2-1; if(a[i][j]<0) { a[i][j]=0; ans--; } } } } for(int i=1; i<=n; i++) { for(int j=1; j<=i; j++) { if(a[i][j]>=0) ans++; } } printf("%d\n",ans); } return 0; }`         ######

[babd65bb134f49f3bd405a04391a1f3d79b85d99.png]: http://codeforces.com/predownloaded/ba/bd/babd65bb134f49f3bd405a04391a1f3d79b85d99.png
[d22903e8a2e3805de7dcdcae275527437bd09255.png]: /images/20220721/c2d77626a4464d82b723179e82a6fb27.png
[Link 1]: http://www.codeforces.com/problemset/problem/676/B