算法分析与设计-第二次实验

算法设计与分析课的实验，一共四道题目，都是用文件读写，并且给出了每道题的随机数据生成方法。博客仅放上代码，以供参考。

---

01背包问题

#include 
#include 
#include 
using namespace std;

const int maxn = 100005;

void solve(string filename)
{
	int n, c, w[maxn], v[maxn], res[maxn] = {};
	fstream infile(filename.c_str());
	infile >> n >> c;
	cout << "n = " << n << "  c = " << c << endl;
	for (int i = 0; i < n; ++i) {
		infile >> w[i];
	}
	for (int i = 0; i < n; ++i) {
		infile >> v[i];
	}
	clock_t start, end;
	start = clock();
	for (int j = 0; j < n; ++j) {
		for (int i = c; i >= 0; --i) {
			if (i >= w[j])
				res[i] = max(res[i - w[j]] + v[j], res[i]);
		}
	}
	cout << "The ans = " << res[c] << endl;
	end = clock();
	cout << "The time = " << end - start << " ms" << endl << endl << endl;
}

int main() {
	solve("forBags5_10.txt");
	solve("forBags100_10000.txt");
	solve("forBags1000_100000.txt");
}
/*
5 10
2 2 6 5 4
6 3 5 4 6
*/

随机数据生成：

#include 
#include 
#include 
#define random(a, b) rand()%(b-a+1) + a
using namespace std;

void creatData100_10000()
{
	fstream outfile("forBags100_10000.txt", ios::out);
	outfile << 100 << ' ' << 10000 << ' ';
	for (int i = 0; i < 100; ++i) {
		outfile << random(10, 300) << ' ';
	}
	for (int i = 0; i < 100; ++i) {
		outfile << random(50, 100) << ' ';
	}
}

void creatData1000_100000()
{
	fstream outfile("forBags1000_100000.txt", ios::out);
	outfile << 1000 << ' ' << 100000 << ' ';
	for (int i = 0; i < 1000; ++i) {
		outfile << random(10, 300) << ' ';
	}
	for (int i = 0; i < 1000; ++i) {
		outfile << random(50, 100) << ' ';
	}
}

int main()
{
	creatData100_10000();
	creatData1000_100000();
}

---

部分背包问题

#include 
#include 
#include 
#include 
using namespace std;

const int maxn = 100005;

bool cmp(pair<int, int> x, pair<int, int> y) {
	return ((double)x.second / (double)x.first) > ((double)y.second / (double)y.first);
}

void solve(string filename)
{
	int n, c;
	pair<int, int> bags[maxn];
	double ans = 0.0;
	fstream infile(filename.c_str());
	infile >> n >> c;
	cout << "n = " << n << "  c = " << c << endl;
	for (int i = 0; i < n; ++i) {
		infile >> bags[i].first;
	}
	for (int i = 0; i < n; ++i) {
		infile >> bags[i].second;
	}
	clock_t start, end;
	start = clock();
	sort(bags, bags + n, cmp);
	for (int i = 0; i < n; ++i) {
		if (bags[i].first > c) {
			break;
		}
		c -= bags[i].first;
		ans += bags[i].second;
	}
	ans += bags[n - 1].second * c / bags[n - 1].first;
	cout << "The ans = " << ans << endl;
	end = clock();
	cout << "The time = " << end - start << " ms" << endl << endl << endl;
}

int main() {
	solve("forBags5_10.txt");
	solve("forBags100_10000.txt");
	solve("forBags1000_100000.txt");
	solve("forBags100000_100000.txt");
}

随机数据生成

#include 
#include 
#include 
#define random(a, b) rand()%(b-a+1) + a
using namespace std;

void creatData100_10000()
{
	fstream outfile("forBags100_10000.txt", ios::out);
	outfile << 100 << ' ' << 10000 << ' ';
	for (int i = 0; i < 100; ++i) {
		outfile << random(10, 300) << ' ';
	}
	for (int i = 0; i < 100; ++i) {
		outfile << random(50, 100) << ' ';
	}
}

void creatData1000_100000()
{
	fstream outfile("forBags1000_100000.txt", ios::out);
	outfile << 1000 << ' ' << 100000 << ' ';
	for (int i = 0; i < 1000; ++i) {
		outfile << random(10, 300) << ' ';
	}
	for (int i = 0; i < 1000; ++i) {
		outfile << random(50, 100) << ' ';
	}
}

void creatData100000_100000()
{
	fstream outfile("forBags100000_100000.txt", ios::out);
	outfile << 100000 << ' ' << 100000 << ' ';
	for (int i = 0; i < 100000; ++i) {
		outfile << random(10, 300) << ' ';
	}
	for (int i = 0; i < 100000; ++i) {
		outfile << random(50, 100) << ' ';
	}
}

int main()
{
	creatData100_10000();
	creatData1000_100000();
	creatData100000_100000();
}

---

会场安排问题

#include 
#include 
#include 
#include 
using namespace std;

const int maxn = 1000005;
pair<int, int> line[maxn];
int n;

bool cmp(pair<int, int> x, pair<int, int> y) {
	if (x.second != y.second) return x.second < y.second;
	return x.first < y.first;
}

void solve(string filename)
{
	fstream infile(filename.c_str());
	infile >> n;
	for (int i = 0; i < n; ++i) {
		infile >> line[i].first >> line[i].second;
	}
	clock_t start, end;
	start = clock();
	sort(line, line + n, cmp);
	int m = 0, ans = 0;
	while (m != n) {
		int tmp = 0;
		for (int i = 0; i < n; ++i) {
			if (line[i].first >= tmp) {
				tmp = line[i].second;
				line[i].first = line[i].second = -1;
				m++;
			}
		}
		ans++; 
	}
	cout << "n = " << n << endl;
	cout << "ans = " << ans << endl;
	end = clock();
	cout << "time = " << end - start << " ms" << endl << endl;
}

int main() {
	solve("data100.txt");
	solve("data10000.txt");
	solve("data30000.txt");
}
/*
5
1 23
12 28
25 35
27 80
36 50
*/

随机数据生成

#include 
#include 
#include 
#define random(a, b) rand()%(b-a+1) + a
using namespace std;

void creatData(string filename, int n) {
	fstream outfile(filename.c_str(), ios::out);
	outfile << n << ' ';
	for (int i = 0, x, y; i < n; ++i) {
		x = random(1, n*10);
		y = random(x + 1, n*10);
		outfile << x << ' ' << y << ' ';
	}
}

int main()
{
	creatData("data100.txt", 100);
	creatData("data10000.txt", 10000);
	creatData("data30000.txt", 30000);
}

---

树的最大连通分支

#include 
#include 
#include 
#include 
#include 
using namespace std;

const int maxn = 100005;
vector<int> con[maxn];
int val[maxn] = {}, maxAns;
bool vis[maxn] = {};
fstream outfile("output.txt", ios::out);

int treeIt(int root) {
	vis[root] = true;
	int ans = 0;
	int len = con[root].size();
	for (int i = 0, tmp; i < len; ++i) {
		if (vis[con[root][i]]) continue;
		tmp = treeIt(con[root][i]);
//		cout << "root = " << root << " sub = "<< con[root][i] << " tmp = " << tmp << endl;
		ans += tmp;
	}
	ans += val[root];
	maxAns = max(maxAns, ans);
//	cout << "tmp ans = " << ans << endl;
//	cout << "tmp maxAns = " << maxAns << endl;
	return (ans > 0 ? ans : 0);
}

void solve(string filename)
{
	for (int i = 0; i < maxn; ++i) {
		con[i].clear();
	}
	memset(vis, false, sizeof(vis));
	int n;
	fstream infile(filename.c_str());
	infile >> n;
	for (int i = 1; i <= n; ++i) {
		infile >> val[i];
	}
	for (int i = 0, x, y; i < n - 1; ++i) {
		infile >> x >> y;
		con[x].push_back(y);
		con[y].push_back(x);
	}
	clock_t start, end;
	start = clock();
	int ans = treeIt(1);
//	cout << "ans = " << ans << endl;
	cout << "n = " << n << endl;
	outfile << "n = " << n << endl;
	cout << "maxAns = " << maxAns << endl;
	outfile << "maxAns = " << maxAns << endl;
	end = clock();
	cout << "time = " << end - start << " ms" << endl << endl;
	outfile << "time = " << end - start << " ms" << endl << endl;
}

int main() {
	solve("creatTree5.txt");
	solve("creatTree10.txt");
	solve("creatTree1000.txt");
	solve("creatTree10000.txt");
	solve("creatTree100000.txt");
}
/*
5
-1 1 3 1 -1
4 1
1 3
1 2
4 5
*/

随机树数据生成
详见博主发布的博客：随机树生成算法（就是树！）

#include 
#include 
#include 
#include 
#define random(a, b) rand()%(b-a+1) + a
using namespace std;

void creatData(int n, string filename) {
	fstream file(filename.c_str(), ios::out);
	int *tree = new int [n];
	for (int i = 0; i < n; ++i) {
		tree[i] = i + 1;
	}
	int root = random(0, n - 1);
	swap(tree[root], tree[n - 1]);
	int nxt_idx = n - 2;
	queue<int> Que;
	file << n << endl;
	for (int i = 0; i < n; ++i) {
		file << random(-1024, 1024) << ' ';
	}
	file << endl;
	Que.push(tree[n - 1]);
	while (!Que.empty()) {
		int now = Que.front();
		Que.pop();
		int cnt = random(1, 3);
		for (int i = 0; i < cnt; ++i) {
			int tmp_idx = random(0, nxt_idx); 
			swap(tree[tmp_idx], tree[nxt_idx]);
			file << now << ' ' << tree[nxt_idx] << endl;
			Que.push(tree[nxt_idx]);
			nxt_idx--;
			if (nxt_idx == -1) break;
		}
		if (nxt_idx == -1) break;
	}
}

int main()
{
	creatData(10, "creatTree10.txt");
	creatData(1000, "creatTree1000.txt");
	creatData(10000, "creatTree10000.txt");
	creatData(100000, "creatTree100000.txt");
	creatData(1000000, "creatTree1000000.txt");
}
/*
一个生成随机树（此树非彼数）的算法，树的结点编号从1开始，这个算法生成了树的结点个数、树的结点的权值、树的每条边的结点。 
如下面是一棵10结点的二叉树的生成结果： 
10
-23 -44 -51 -9 13 51 62 11 -63 19 
6 9
6 4
9 2
9 3
4 7
4 1
2 5
2 8
3 10 
*/