10081 - Tight words/10081.cpp

   1 /*
   2   Problem: 10081 - Tight words
   3   Author: Andrés Mejía-Posada
   4   (http://blogaritmo.factorcomun.org)
   5
   6  */
   7
   8 using namespace std;
   9 #include <algorithm>
  10 #include <iostream>
  11 #include <iterator>
  12 #include <sstream>
  13 #include <fstream>
  14 #include <cassert>
  15 #include <climits>
  16 #include <cstdlib>
  17 #include <cstring>
  18 #include <string>
  19 #include <cstdio>
  20 #include <vector>
  21 #include <cmath>
  22 #include <queue>
  23 #include <deque>
  24 #include <stack>
  25 #include <map>
  26 #include <set>
  27
  28 #define D(x) cout << #x " is " << x << endl
  29
  30  double dp[101][10];
  31
  32 int main(){
  33
  34   for (int k, n; scanf("%d %d", &k, &n)==2; ){
  35
  36     for (int last=0; last<=9; ++last) dp[1][last] = 1.0/(k+1);
  37
  38     for (int len=2; len<=n; ++len){
  39       for (int last=0; last<=k; ++last){
  40         dp[len][last] = dp[len-1][last];
  41         if (last > 0) dp[len][last] += dp[len-1][last-1];
  42         if (last < k) dp[len][last] += dp[len-1][last+1];
  43         dp[len][last] /= k+1;
  44       }
  45     }
  46
  47     double ans = 0;
  48     for (int last=0; last<=k; ++last) ans += dp[n][last];
  49     printf("%.5lf\n", 100.0 * ans);
  50   }
  51
  52
  53   return 0;
  54 }