HDU4336 Card Collector "the principle of tolerance and repulsion"

Topic Links:

http://acm.hdu.edu.cn/showproblem.php?pid=4336

Main topic:

Each pack of snacks has a card, a total of n different cards, the probability of obtaining the N cards is p[i] (1 <= i <= N).

What is the expectation of collecting all the cards.

Ideas:

PI indicates the probability of getting the first card and EI indicates the expectation of the card.

Suppose there are two cards now, by test instructions:

E1 = 1/p1,e2 = 1/p2,e12 (indicates the expectation of buying 1 or 2 of one packet) = 1/(P1+P2).

When we calculate E1 and E2, the E12 is repeated 2 times and should be subtracted once. According to the theorem of the tolerant repulsion:

E = E1 + e2-e12.

In the same vein, three cards:

E = E1 + E2 + e3-e12-e13-e23 + E123.

And so on, if the item is an odd number (the expectation of an odd card), the item is added when the expected items are calculated.

If the item is an even item 2 (the expectation of an even entry card), the item is subtracted.

AC Code:

#include <iostream> #include <algorithm> #include <cstdio> #include <cstring>using namespace Std;double p[50];int n;double Solve () {    double xh = 0;    for (int i = 1; i < (1 << N); ++i)   //traverse 2^n kind of situation  from 00 ... 01 to 11 ... One    {        double sum = 0;        int odd = 0;        for (int j = 0; j < N; ++j)      //For I (in each case), calculate the number of bits of the binary 1 for i        {            if ((1<<j) & i)      //i the right-to-left number corresponds to the first J-bit 1. c12/>{                odd++;          Number of bits in binary 1                sum + = p[j+1];  Will add up to the probability of 1 items.            }        }        if (odd & 1)//odd items plus, even items minus            xh + = 1/sum;        else            XH-= 1/sum;    }    return XH;} int main () {while    (~scanf ("%d", &n)    } {for        (int i = 1; I <= N; ++i)            scanf ("%lf", &p[i]);        printf ("%.6lf\n", Solve ());  Note LF and F    }    return 0;}

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HDU4336 Card Collector "the principle of tolerance and repulsion"