杭电OJ 1023

题目：http://acm.hdu.edu.cn/showproblem.php?pid=1023

开始时看不明白题意，后来才知道要参照1022。其实就是求进出栈的先后次序的排列组合，是一个典型的卡特兰数列。涉及到大数运算，为了避免大数的除法，就不用卡特兰数的通项公式解了，直接用递归式解，这样只要写大数的加法和乘法，以下为AC代码。

#include <cstdio> #include <cstring> typedef struct { int num_[1000]; int length_; } BigNum; void InitBigNum(BigNum *p_bn, int value) { p_bn->num_[0] = value; p_bn->length_ = 1; } void CopyBigNum(const BigNum &src, BigNum *p_dest) { p_dest->length_ = src.length_; for (int i=0; i<p_dest->length_; ++i) { p_dest->num_[i] = src.num_[i]; } } void PrintBigNum(const BigNum &bn) { printf("%d", bn.num_[bn.length_-1]); int table[4]; int temp = 1000; for (int i=0; i<4; i++) { table[i] = temp; temp /= 10; } for (int i=bn.length_-2; i>-1; --i) { for (int j=0; j<4; ++j) { printf("%d", bn.num_[i] / table[j] % 10); } } printf("\n"); } void Add(const BigNum &bn_a, const BigNum &bn_b, BigNum *p_sum) { const BigNum *p_long, *p_short; if (bn_a.length_ >= bn_b.length_) { p_long = &bn_a; p_short = &bn_b; } else { p_long = &bn_b; p_short = &bn_a; } int co = 0; for (int i=0; i<p_short->length_; ++i) { int temp = p_long->num_[i] + p_short->num_[i] + co; p_sum->num_[i] = temp % 10000; co = temp / 10000; } for (int i=p_short->length_; i<p_long->length_; ++i) { int temp = p_long->num_[i] + co; p_sum->num_[i] = temp % 10000; co = temp / 10000; } p_sum->length_ = p_long->length_; for (int i=p_long->length_; ; ++i) { if (co == 0) break; p_sum->num_[i] = co % 10000; co /= 10000; ++p_sum->length_; } } void Mul(const BigNum &bn_a, const BigNum &bn_b, BigNum *p_mul) { const BigNum *p_long, *p_short; if (bn_a.length_ >= bn_b.length_) { p_long = &bn_a; p_short = &bn_b; } else { p_long = &bn_b; p_short = &bn_a; } p_mul->length_ = p_long->length_ + p_short->length_; memset(p_mul->num_, 0, p_mul->length_ * sizeof(int)); for (int short_index=0; short_index<p_short->length_; ++short_index) { int co = 0; for (int long_index=0; long_index<p_long->length_; ++long_index) { int temp = p_short->num_[short_index] * p_long->num_[long_index] + co; p_mul->num_[short_index+long_index] += temp % 10000; co = temp / 10000; } for (int i=short_index+p_long->length_; ; ++i) { if (co == 0) break; p_mul->num_[i] += co % 10000; co /= 10000; } } if (p_mul->num_[p_mul->length_-1] == 0) --p_mul->length_; } BigNum catalan_array[101]; void InitCatalan() { InitBigNum(&catalan_array[0], 1); InitBigNum(&catalan_array[1], 1); for (int i=2; i<101; ++i) { BigNum sum; InitBigNum(&sum, 0); for (int j=0; j<i; ++j) { BigNum mul; Mul(catalan_array[j], catalan_array[i-1-j], &mul); BigNum temp; Add(sum, mul, &temp); CopyBigNum(temp, &sum); } CopyBigNum(sum, &catalan_array[i]); } } int main() { InitCatalan(); int a; while (scanf("%d", &a) != EOF) { PrintBigNum(catalan_array[a]); } return 0; }