习题7-7(uva-12558)

最新推荐文章于 2023-11-13 10:10:07 发布

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该博客主要介绍了一个C++程序，通过深度优先搜索（DFS）解决寻找最简分数组合的问题。程序首先定义了计算最大公约数（GCD）的函数，然后利用DFS遍历所有可能的分数组合，避免使用给定的禁止项，并找到最小的分数表示。最终，程序会输出一个最简分数序列来表示给定的两个整数比。

#include <iostream>
#include <istream>
#include <sstream>
#include <vector>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <numeric>
#include <chrono>
#include <ctime>
#include <cmath>
#include <cctype>
#include <string>
#include <cstdio>
#include <iomanip>


#include <thread>
#include <mutex>
#include <condition_variable>
#include <functional>
#include <iterator>
using namespace std;
long long int result[256],temp[256];
unordered_set<long long int > noUse;
int maxn;
long long int  gcd(long long int  a, long long int  b) {
	return b == 0 ? a : gcd(b, a % b);
}

long long int  GetFirst(long long int  a, long long int  b) {
	return ceil(b * 1.0/ a);
}

bool dfs(long long int  a, long long int  b, int cur, long long int  first) {

	if (cur == 0) {
		if (a == 0) {
			//最小的分数越大越好
			bool isBig = false;
			for (int i = maxn - 1; i >= 0; i--) {
				if(temp[i] == result[i]) continue;
				if (result[i] == -1 || temp[i] < result[i]) {
					isBig = true;
				}
				break;
			}
			if (isBig) memmove(result, temp, sizeof(result));
			return true;
		}
		return false;
	}

	long long int  start = max(first, GetFirst(a, b));
	bool ret = false;
	for (long long int  i = start; ; i++) {
		if (a * i > b * cur)break;
		if (noUse.find(i) != noUse.end())continue;
		long long int  nb = b * i;
		long long int  na = a * i - b;
		long long int  nc = gcd(na, nb);
		na /= nc;
		nb /= nc;
		temp[maxn - cur] = i;
		if (dfs(na, nb, cur - 1, i + 1)) ret = true;
	}
	return ret;
}

int main()
{
	int n,a,b,id = 0,cnt,t;
	cin >> n;
	while (n--) {
		noUse.clear();
		memset(result, -1, sizeof(result));

		cin >> a >> b >> cnt;

		for (int i = 0; i < cnt; i++) {
			cin >> t;
			noUse.insert(t);
		}
		
		for ( maxn = 1;; maxn++) {
			if(dfs(a,b, maxn,GetFirst(a,b))) break;
		}
		cout << "Case " << ++id << ": " << a << "/" << b << "=";
		for (int i = 0; i < maxn; i++) {
			if (i)cout << "+";
			cout << "1/" << result[i];
		}
		cout << endl;
	}
	return 0;
}