?? 1972.cpp
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/* This Code is Submitted by wywcgs for Problem 1972 on 2006-07-01 at 11:21:00 */
#include <cstdio>
#include <algorithm>
using namespace std;
const int N = 1024;
const double INF = 1e20;
int main()
{
int n, i, j;
double l, r, pn[N];
while(scanf("%d", &n) != EOF && n != 0) {
scanf("%lf %lf", &l, &r);
if(l < r) swap(l, r);
pn[0] = 0;
for(i = 1; i <= n; i++) {
pn[i] = INF;
for(j = i/2; j >= 0; j--) {
int k = i-1-j;
pn[i] = min(pn[i], (1+pn[j]*l+pn[k]*r)/(1-l-r)+pn[j]+pn[k]);
}
}
printf("%.2lf\n", pn[n]);
}
return 0;
}
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