Zoj 1883-tight words

Question: If each letter of a word does not differ by 1, it is called closeness. We will give you a letter set {0 ~ K },

A word with a length of N is a close probability.

Analysis: probability DP. The probability of the characters at the end position is the State DP.

Status: set f (I, j) as the word with the length of I, and take the close probability from the set {0,..., k;

Transfer: f (I, j) = (f (I-1, J-1) + f (I, j) + f (I, j + 1)/(k + 1 );

Note ).

#include <iostream>#include <cstdlib>#include <stdio.h>usingnamespace std;double F[ 101 ][ 10 ];int main(){    int k,n;     while ( cin >> k >> n ) {        double r = 1.0/(1+k);        for ( int i = 0 ; i <= k ; ++ i )            F[ 1 ][ i ] = r;        for ( int i = 2 ; i <= n ; ++ i )        for ( int j = 0 ; j <= k ; ++ j ) {            F[ i ][ j ] = F[ i-1 ][ j ]*r;            if ( j > 0 ) F[ i ][ j ] += F[ i-1 ][ j-1 ]*r;            if ( j < k ) F[ i ][ j ] += F[ i-1 ][ j+1 ]*r;        }        double sum = 0.0;        for ( int i = 0 ; i <= k ; ++ i )            sum += F[ n ][ i ];        printf("%.5lf\n",sum*100);    }    return 0;}

Zoj 1883-tight words