pku1189 钉子和小球

http://poj.org/problem?id=1189

DP，“数塔”

#include <stdio.h>
#include <string.h>

int a[56][56];
long long dp[56][56];

long long gcd(long long x, long long y)
{
    return y? gcd(y, x%y): x;
}


int main()
{
    int i, j, k, n, m;
    long long r;
    char s[1234] = "\0";
    memset(dp, 0, sizeof(dp));
    scanf("%d%d%*c", &n, &m);
    for(i=1; i<=n; i++)
    {
        gets(s);
        k = 1;
        for(j=0; s[j]; j++)
        {
            if(s[j]=='*')
            {
                a[i][k] = 1;
                k ++;
                continue;
            }
            if(s[j]=='.')
            {
                a[i][k] = 0;
                k ++;
                continue;
            }
        }
    }
    dp[1][1] = (long long)1<<56;
    //printf("%lld\n", dp[1][1]);
    for(i=1; i<=n; i++)
    {
        for(j=1; j<=i; j++)
        {
            if(a[i][j])
            {
                dp[i+1][j] += (dp[i][j]>>1);
                dp[i+1][j+1] += (dp[i][j]>>1);
            }
            else
            {
                dp[i+2][j+1] += dp[i][j];
            }
            //printf("%lld ", dp[i][j]);
        }
        //printf("\n");
    }
    r = dp[i][m+1];
    if(r == 0)
    {
        printf("0/1\n");
        return 0;
    }
    if(gcd(dp[1][1], r)==1)
    {
        printf("%lld\n", r);
        return 0;
    }
    printf("%lld/%lld\n", (long long)r/gcd(dp[1][1], r), (long long)dp[1][1]/gcd(dp[1][1], r));
    return 0;
}