uva 10288 - Coupons(概率)

题目链接：uva 10288 - Coupons

题目大意：给定n，为有n中兑换卷，现在每开一次箱子，就能等概率的获得其中的一种兑换卷。问说平均情况下需要开多少个箱子才能集齐n种兑换卷。

解题思路：dp[i]表示还有i种没获得，dp[i]=n−in∗dp[i]+in∗dp[i−1]+1
===》dp[i]=dp[i−1]+ni

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;typedef long long type;struct Fraction {    type member; // 分子；    type denominator; // 分母；    Fraction (type member = 0, type denominator = 1);    void operator = (type x) { this->set(x, 1); }    Fraction operator * (const Fraction& u);    Fraction operator / (const Fraction& u);    Fraction operator + (const Fraction& u);    Fraction operator - (const Fraction& u);    void set(type member, type denominator);};inline type gcd (type a, type b) {    return b == 0 ? a : gcd(b, a % b);}/*Code*//////////////////////////////////////////////////////const int maxn = 33;typedef long long ll;Fraction dp[maxn+5][maxn+5];void init () {    for (int i = 1; i <= maxn; i++) {        dp[i][0] = 0;        for (int j = 1; j <= i; j++)            //dp[i][j] = (dp[i][j-1] * Fraction(j, i) + Fraction(1, 1)) / Fraction(j, i);            dp[i][j] = dp[i][j-1] + Fraction(i, j);    }}inline int countbit (ll u) {    int ret = 0;    while (u) {        ret++;        u /= 10;    }    return ret;}void put_ans (Fraction u) {    type d = u.member / u.denominator;    type member = u.member % u.denominator;    int cn = countbit(d);    int cd = countbit(u.denominator);    int n = cn + (cn == 0 ? 0 : 1);    if (member) {        for (int i = 0; i < n; i++) printf(" ");        printf("%lld\n", member);    }    printf("%lld", d);    if (member) {        if (d)            printf(" ");        for (int i = 0; i < cd; i++) printf("-");        printf("\n");        for (int i = 0; i < n; i++) printf(" ");        printf("%lld", u.denominator);    }    printf("\n");}int main () {    int n;    init();    while (scanf("%d", &n) == 1) {        put_ans(dp[n][n]);    }    return 0;}/////////////////////////////////////////////////////Fraction::Fraction (type member, type denominator) {    this->set(member, denominator);}Fraction Fraction::operator * (const Fraction& u) {    return Fraction(member * u.member, denominator * u.denominator);}Fraction Fraction::operator / (const Fraction& u) {    return Fraction(member * u.denominator, denominator * u.member);}Fraction Fraction::operator + (const Fraction& u) {    return Fraction(member * u.denominator + denominator * u.member, denominator * u.denominator);}Fraction Fraction::operator - (const Fraction& u) {    return Fraction(member * u.denominator - denominator * u.member, denominator * u.denominator);}void Fraction::set (type member, type denominator) {    type tmp_d = gcd(member, denominator);    this->member = member / tmp_d;    this->denominator = denominator / tmp_d;}