add: Notes & UVA src

Author: khanhvu207

Notes/[Tutorial] A Way to Practice Competitive Programming.pdf

@@ -0,0 +1,55 @@
+#include <iostream>
+#include <cstring>
+using namespace std;
+
+int n, x, a[55], b[55], p[55], dp[55][55], h[55][55];
+
+int optimize (int l, int r)
+{
+	int tmp=1e9, sum=p[r]-p[l-1];
+	//Knuth's optimization
+	for (int k=h[l][r-1]; k<=h[l+1][r]; ++k)
+		if (dp[l][k-1]+dp[k][r]+sum<=tmp)
+		{
+			tmp=dp[l][k-1]+dp[k][r]+sum;
+			h[l][r]=k;
+		}
+	dp[l][r]=tmp;
+	return dp[l][r];
+}
+
+int main()
+{
+	ios_base::sync_with_stdio(false); cin.tie(NULL);
+	while (cin >> x)
+	{
+		if (x<1) return 0;
+		memset(dp, 0, sizeof dp);
+		memset(h, 0, sizeof h);
+		cin >> n;
+		for (int i=1; i<=n; ++i)
+			cin >> b[i];
+		
+		a[1]=b[1];
+		for (int i=2; i<=n+1; ++i)
+			if (i>n)
+				a[i]=x-b[i-1];
+			else
+				a[i]=b[i]-b[i-1];
+		++n;
+
+		for (int i=1; i<=n; ++i)
+			p[i]=p[i-1]+a[i];
+		
+		for (int i=1; i<=n; ++i)
+			dp[i][i]=0,
+			h[i][i]=i;
+		
+		for (int d=1; d<=n-1; ++d)
+			for (int i=1; i<=n-d; ++i)
+				dp[i][i+d]=optimize(i, i+d);
+		
+		cout << "The minimum cutting is " << dp[1][n] << ".\n";
+	}
+	return 0;
+}

Notes/combinatorics/VIETMATHS.NET-cac-bai-toan-ve-day-catalan.pdf

@@ -0,0 +1,68 @@
+#include <iostream>
+#include <cstdio>
+#include <vector>
+#include <list>
+using namespace std;
+const int N = 65;
+
+int n, deg[N];
+list<pair<int, int> > euler;
+vector<pair<int, bool> > g[N];
+
+void euler_cycle(list<pair<int, int> >::iterator it, int u) {
+	for (auto &i : g[u]) 
+		if (i.second) {
+			int v = i.first;
+			i.second = false;
+			for (auto &edge : g[v])
+				if (edge.first == u && edge.second) {
+					edge.second = false;
+					break;
+				}
+			euler_cycle(euler.insert(it, {v, u}), v);
+		}
+}
+
+int main() {
+	ios::sync_with_stdio(0);
+	cin.tie(NULL);
+	//freopen("input.in", "r", stdin);
+	//freopen("output.out", "w", stdout);
+
+	int tc;
+	cin >> tc;
+	for (int c = 1; c <= tc; ++c) {
+		if (c != 1) cout << '\n';
+		cout << "Case #" << c << '\n';
+		for (int i = 0; i < N; ++i) 
+			g[i].clear(), deg[i] = 0;
+
+		cin >> n;
+		for (int i = 0, u, v; i < n; ++i) {
+			cin >> u >> v;
+			g[u].emplace_back(v, true);
+			g[v].emplace_back(u, true);
+			++deg[u];
+			++deg[v];
+		}
+
+		bool good = true;
+		int start = -1;
+		for (int i = 1; i <= 50; ++i)
+			if (deg[i] % 2) {
+				good = false;
+				break;
+			} else if (deg[i] && start == -1) {
+				start = i;
+			}
+
+		if (!good) {
+			cout << "some beads may be lost\n";
+		} else {
+			euler.clear();
+			euler_cycle(euler.begin(), start);
+			for (const auto &i : euler)
+				cout << i.first  << ' ' << i.second << '\n';
+		}
+	}
+}

Notes/combinatorics/catalan.pdf

@@ -0,0 +1,79 @@
+#include <iostream>
+#include <cstdio>
+#include <vector>
+#include <stack>
+using namespace std;
+const int N = 100;
+
+int n, deg[N];
+vector<pair<int, bool> > g[N];
+
+void eulerCycle(int s) {
+	vector<int> res;
+	stack<int> st;
+	st.push(s);
+	while (!st.empty()) {
+		int u = st.top();
+		bool flag = false;
+		for (auto &i : g[u]) 
+			if (i.second) {
+				flag = true;
+				i.second = false;
+				int v = i.first;
+				for (auto &edge : g[v])
+					if (edge.first == u && edge.second) {
+						edge.second = false;
+						break;
+					}
+				st.push(v);
+				break;
+			}
+		if (!flag) {
+			res.emplace_back(u);
+			st.pop();
+		}
+	}
+	for (int i = 0; i + 1 < (int)res.size(); ++i)
+		cout << res[i] << ' ' << res[i + 1] << '\n';
+}
+
+int main() {
+	ios::sync_with_stdio(0);
+	cin.tie(NULL);
+	//freopen("input.in", "r", stdin);
+	//freopen("output.out", "w", stdout);
+
+	int tc;
+	cin >> tc;
+	for (int c = 1; c <= tc; ++c) {
+		if (c != 1) cout << '\n';
+		cout << "Case #" << c << '\n';
+		for (int i = 1; i <= 50; ++i) 
+			deg[i] = 0, g[i].clear();
+
+		cin >> n;
+		for (int i = 0, u, v; i < n; ++i) {
+			cin >> u >> v;
+			g[u].emplace_back(v, true);
+			g[v].emplace_back(u, true);
+			++deg[u];
+			++deg[v];
+		}
+		
+		bool good = true;
+		int start = -1;
+		for (int u = 1; u <= 50; ++u)
+			if (deg[u] & 1) {
+				good = false;
+				break;
+			} else if (deg[u] && start == -1) {
+				start = u;
+			}
+		
+		if (!good) {
+			cout << "some beads may be lost\n";
+			continue;
+		}
+		eulerCycle(start);
+	}
+}

Notes/combinatorics/stirling_numbers.pdf

@@ -0,0 +1,97 @@
+#include <iostream>
+#include <cmath>
+#include <vector>
+#include <algorithm>
+#include <iomanip>
+using namespace std;
+const double eps = 1e-9;
+
+struct point 
+{
+    double x, y;
+    point() { x = 0, y = 0; }
+    point(double xx, double yy) : x(xx), y(yy) {}
+};
+struct vec
+{
+    double x, y;
+    vec() { x = 0, y = 0; }
+    vec(double xx, double yy) : x(xx), y(yy) {}
+};
+vec tovec (const point &a, const point &b) { return vec(b.x - a.x, b.y - a.y); }
+double cross (const vec &a, const vec &b) { return (a.x * b.y - b.x * a.y); }
+double dist (const point &a, const point &b) { return hypot(a.x - b.x, a.y - b.y); }
+bool collinear (const point &O, const point &a, const point &b) { return fabs(cross(tovec(O, a), tovec(O, b))) < eps; }
+bool ccw (const point &O, const point &a, const point &b) { return cross(tovec(O, a), tovec(O, b)) > 0; }
+
+int n, C = 0;
+point pivot;
+vector<point> p, CVH;
+
+bool grahamScan (const point &L, const point &R)
+{
+    if (collinear(pivot, L, R))
+        return dist(pivot, L) - dist(pivot, R) < eps;
+    return cross(tovec(pivot, L), tovec(pivot, R)) > 0;
+}
+
+vector<point> findCVH (vector<point> P)
+{
+    if (n <= 3)
+    {
+        if (!(P[0].x == P[n - 1].x && P[0].y == P[n - 1].y)) P.push_back(P[0]);
+        return P;
+    }
+    int P0 = 0;
+    for (int i = 1; i < n; ++i)
+        if (P[i].y < P[P0].y || (P[i].y == P[P0].y && P[i].x > P[P0].x)) P0 = i;
+    
+    point tmp = P[0]; P[0] = P[P0]; P[P0] = tmp;
+
+    pivot = P[0];
+    sort(P.begin() + 1, P.end(), grahamScan); 
+
+    vector<point> S;
+    S.push_back(P[n - 1]);
+    S.push_back(P[0]);
+    S.push_back(P[1]);
+    int i = 2;
+    while (i < n)
+    {
+        int top = (int)S.size() - 1;
+        if (ccw(S[top - 1], S[top], P[i])) S.push_back(P[i++]);
+            else S.pop_back();
+    }
+    return S;
+}
+
+double areaPoly (const vector<point> &Poly)
+{
+    double S = 0.0;
+    point Origin = point(0, 0);
+    for (int i = 0; i < (int)Poly.size() - 1; ++i)
+        S += cross(tovec(Origin, Poly[i]), tovec(Origin, Poly[i + 1]));
+    S = fabs(S / 2.0);
+    return S;
+}
+
+int main()
+{
+    ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
+
+    while (cin >> n)
+    {
+        if (n < 1) return 0;
+        p.clear();
+        for (int i = 0; i < n; ++i)
+        {
+            double x, y; cin >> x >> y;
+            p.push_back(point(x, y));
+        }      
+        CVH = findCVH(p);
+        p.push_back(p[0]);
+        double res = (1.0 - areaPoly(p) / areaPoly(CVH)) * 100.0;
+        cout << "Tile #" << ++C << '\n' << "Wasted Space = ";
+        cout << fixed << setprecision(2) << res << " %\n"; cout << '\n';
+    }
+}