算法 03-高精度

高精度加法

string HighPrecisionPlus(string a, string b) {
	string ans;
	reverse(a.begin(), a.end());		//逆置数字字符串，从最后一位开始处理
	reverse(b.begin(), b.end());

	int carry = 0, length = max((int)a.size(), (int)b.size());		//carry进位
	for (int i = 0; i < length; i++) {
		int ai = 0, bi = 0;
		if (i < (int)a.size()) {
			ai = (int)a[i] - 48;
		}
		if (i < (int)b.size()) {
			bi = (int)b[i] - 48;
		}

		int temp = ai + bi + carry;
                ans.push_back(temp % 10 + 48);
                carry = temp / 10;
	}
	if (carry) {		//循环结束后若进位为1则数字字符串位数+1
		ans.push_back(carry + 48);
	}

	reverse(ans.begin(), ans.end());	//逆置结果字符串
	return ans;
}

高精度乘法

string HighPrecisionTimes(string a, string b) {
	if (a == "0" || b == "0") return "0";
	string ans = "0";
	reverse(a.begin(), a.end());	//逆置数字字符串，从最后一位开始处理
	reverse(b.begin(), b.end());
	for (int i = 0; i < (int)a.size(); i++) {
		string ti;
		int carry = 0;		//carry表示进位
		for (int j = 0; j < (int)b.size(); j++) {
			int temp = ((int)a[i] - 48) * ((int)b[j] - 48) + carry;
			ti.push_back(temp % 10 + 48);
			carry = temp / 10;
		}
		if (carry) {
			ti.push_back(carry + 48);
		}
		reverse(ti.begin(), ti.end());
		for (int j = 0; j < i; j++) {	//向左偏移补0
			ti.push_back('0');
		}
		ans = HighPrecisionPlus(ans, ti);
	}
	return ans;
}

阶乘：高精度乘单精度

#include <iostream>
#include <cstring>

using namespace std;

int main() {
	int n, ans[100000];
	cin >> n;
	for (int i = 0; i < n; i++) {
		int a, b, length = 1, count = 0;
		cin >> a >> b;
		memset(ans, 0, sizeof(ans));
		ans[0] = 1;
		for (int j = 1; j <= a; j++) {
			int carry = 0;
			for (int k = 0; k < length; k++) {
				int temp = j * ans[k] + carry;
				carry = temp / 10;
				ans[k] = temp % 10;
			}
			while (carry) {
				ans[length] = carry % 10;
				length++;
				carry /= 10;
			}
		}
		for (int i = 0; i < length; i++) {
			if (ans[i] == b) count++;
		}
		cout << count << endl;
	}
}