Added 'AtCoder Educational DP' in Contest-Questions

Contest-Questions/AtCoder Educational DP/chessmetric.cpp

@@ -0,0 +1,26 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+#define endl "\n"
+
+int main() {
+
+	int t, a, b, n;
+	long long arr[105][105][50];
+	cin >> t >> a >> b;
+	arr[a + 2][b + 2][0] = 1;
+	cin >> a >> b >> n;
+
+	Fo(m, 1, n + 1) {
+		Fo(i, 2, t + 2) {
+			Fo(j, 2, t + 2) {
+				arr[i][j][m] += arr[i - 2][j - 1][m - 1] + arr[i - 2][j + 1][m - 1] + arr[i + 2][j - 1][m - 1] + arr[i + 2][j + 1][m - 1] + arr[i - 1][j - 2][m - 1] + arr[i - 1][j + 2][m - 1] + arr[i + 1][j - 2][m - 1] + arr[i + 1][j + 2][m - 1] + arr[i - 1][j - 1][m - 1] + arr[i - 1][j][m - 1] + arr[i - 1][j + 1][m - 1] + arr[i][j - 1][m - 1] + arr[i][j + 1][m - 1] + arr[i + 1][j - 1][m - 1] + arr[i + 1][j][m - 1] + arr[i + 1][j + 1][m - 1];
+			}
+		}
+	}
+
+	cout << arr[a + 2][b + 2][n];
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/coin.cpp

@@ -0,0 +1,27 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+
+int main() {
+
+	int n;
+	cin >> n;
+	long double dp[n + 2] = {0}, p;
+	dp[1] = 1;
+
+	fo(i, n) {
+		cin >> p;
+		for (int j = i + 2; j > 0; j--) {
+			dp[j] = dp[j] * (1 - p) + dp[j - 1] * p;
+		}
+	}
+
+	p = 0;
+	Fo(i, n / 2 + 2, n + 2) p += dp[i];
+
+	cout << setprecision(10) << p;
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/deque.cpp

@@ -0,0 +1,18 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define ll long long
+#define fo(i, n) for(i=0; i<n; i++)
+#define Fo(i, k, n) for(i=k; i<n; i++)
+
+int main() {
+
+	int n, i, j;
+	cin >> n;
+	ll dp[n], a[n];
+	fo(i, n) cin >> a[i], dp[i] = a[i];
+	Fo(i, 1, n) fo(j, (n - i)) dp[j] = max(a[i + j] - dp[j], a[j] - dp[j + 1]);
+	cout << dp[0];
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/frog.cpp

@@ -0,0 +1,23 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+#define endl "\n"
+
+int main() {
+
+	int n;
+	cin >> n;
+
+	long arr[n], temp[n];
+	fo(i, n) cin >> arr[i];
+
+	temp[0] = 0;
+	temp[1] = abs(arr[0] - arr[1]);
+
+	Fo(i, 2, n)
+	temp[i] = min(abs(arr[i] - arr[i - 1]) + temp[i - 1], abs(arr[i] - arr[i - 2]) + temp[i - 2]);
+
+	cout << temp[n - 1];
+}

Contest-Questions/AtCoder Educational DP/frog2.cpp

@@ -0,0 +1,27 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define endl "\n"
+
+int main() {
+
+	int n, k, var;
+	cin >> n >> k;
+
+	long arr[n], temp[n], mi;
+	fo(i, n) cin >> arr[i];
+
+	fo(i, n) {
+		var = i - 1;
+		mi = INT_MAX;
+		while (var >= 0 && var >= i - k) {
+			mi = min(abs(arr[i] - arr[var]) + temp[var], mi);
+			var--;
+		}
+		temp[i] = mi == INT_MAX ? 0 : mi;
+	}
+
+	cout << temp[n - 1];
+	return 1;
+}

Contest-Questions/AtCoder Educational DP/grid.cpp

@@ -0,0 +1,18 @@
+#include <iostream>
+using namespace std;
+const int MAXN = 1e3 + 7;
+const long long MOD = 1e9 + 7;
+int h, w, f[MAXN][MAXN];
+char a[MAXN][MAXN];
+int main() {
+	ios_base::sync_with_stdio(false), cin.tie(0);
+	cin >> h >> w;
+	for (int i = 1; i <= h; i++) cin >> (a[i] + 1);
+	f[0][1] = 1;
+	for (int i = 1; i <= h; i++)
+		for (int j = 1; j <= w; j++)
+			if (a[i][j] != '#')
+				f[i][j] = (f[i - 1][j] + f[i][j - 1]) % MOD;
+	cout << f[h][w] << endl;
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/kanpsack2.cpp

@@ -0,0 +1,47 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(long i=0; i<n; i++)
+#define Fo(i, k, n) for(long i=k; i<n; i++)
+#define endl "\n"
+
+int main() {
+
+	long long total = 0;
+	long n, w, temp1, temp2;
+	cin >> n >> w;
+
+	vector<pair<long, long>> item;
+	fo(i, n) {
+		cin >> temp1 >> temp2;
+		item.push_back(make_pair(temp1, temp2));
+		total += temp2;
+	}
+
+	long dp[n + 1][total + 1];
+	fo(i, n + 1) fo(j, total + 1) dp[i][j] = 0;
+
+	Fo(i, 1, n + 1) {
+		Fo(j, 1, total + 1) {
+			temp1 = item[i - 1].second;
+			if (j >= temp1) {
+				if (dp[i - 1][j] == 0) {
+					dp[i][j] = item[i - 1].first + dp[i - 1][j - temp1];
+				} else {
+					dp[i][j] = min(dp[i - 1][j], item[i - 1].second + dp[i - 1][j - temp1]);
+				}
+			} else {
+				dp[i][j] = dp[i - 1][j];
+			}
+			if (dp[i][j] != 0 && dp[i][j] <= w && temp2 <= j) {
+				temp1 = dp[i][j];
+				temp2 = j;
+			}
+		}
+	}
+
+	// cout << dp[n][total];
+	cout << temp2;
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/knapsack.cpp

@@ -0,0 +1,40 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+#define endl "\n"
+
+int main() {
+
+	int n, w, temp1, temp2;
+	cin >> n >> w;
+
+	long dp[n + 1][w + 1];
+	fo(i, n + 1) fo(j, w + 1) dp[i][j] = 0;
+
+	vector<pair<int, int>> item;
+	fo(i, n) {
+		cin >> temp1 >> temp2;
+		item.push_back(make_pair(temp1, temp2));
+	}
+
+	Fo(i, 1, n + 1) {
+		Fo(j, 1, w + 1) {
+			temp1 = item[i - 1].first;
+			if (j >= temp1) {
+				dp[i][j] = max(dp[i - 1][j], item[i - 1].second + dp[i - 1][j - temp1]);
+			} else {
+				dp[i][j] = dp[i - 1][j];
+			}
+		}
+	}
+
+	cout << dp[n][w];
+	// fo(i, n + 1) {
+	// 	fo(j, w + 1) cout << dp[i][j] << " ";
+	// 	cout << endl;
+	// }
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/lcs.cpp

@@ -0,0 +1,47 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+#define endl "\n"
+
+int dp[3002][3002];
+
+int main() {
+
+	string a, b;
+	cin >> a >> b;
+
+	int al = a.length(), bl = b.length(), find;
+	fo(i, al + 1) fo(j, bl + 1) dp[i][j] = 0;
+
+	Fo(i, 1, al + 1)
+	Fo(j, 1, bl + 1) {
+		dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
+		if (a[i - 1] == b[j - 1]) {
+			dp[i][j] = max(dp[i][j], dp[i - 1][j - 1] + 1);
+		}
+	}
+
+	find = dp[al][bl];
+	int i = al, j = bl;
+	char ans[find + 1];
+	ans[find] = '\0';
+
+	while (i > 0 && j > 0) {
+		if (a[i - 1] == b[j - 1]) {
+			ans[find - 1] = a[i - 1];
+			find--;
+			j--;
+			i--;
+		} else if (dp[i - 1][j] < dp[i][j - 1]) {
+			j--;
+		} else {
+			i--;
+		}
+	}
+
+	cout << ans;
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/longestPath.cpp

@@ -0,0 +1,41 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+#define endl "\n"
+
+const int N = 100005;
+bool visited[N];
+vector<int> adj[N];
+int memo[N];
+
+int traverse(int a) {
+	if (visited[a]) return memo[a];
+	int ans = 0;
+	for (int j : adj[a]) {
+		ans = max(ans, 1 + traverse(j));
+	}
+	visited[a] = true;
+	return memo[a] = ans;
+
+}
+
+int main() {
+
+	int e, v, temp1, temp2;
+	cin >> v >> e;
+
+	fo(i, e) {
+		cin >> temp1 >> temp2;
+		adj[temp1].emplace_back(temp2);
+	}
+	temp2 = 0;
+
+	fo(i, v)
+	temp2 = max(temp2, traverse(i + 1));
+
+	cout << temp2;
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/stones.cpp

@@ -0,0 +1,23 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+
+int arr[105];
+bool winner[100005];
+
+int main() {
+
+	int n, k;
+	scanf("%d %d", &n, &k);
+
+	fo(i, n) scanf("%d", &arr[i]);
+
+	fo(i, k) if (!winner[i])
+		fo(j, n) if (i + arr[j] <= k)
+			winner[i + arr[j]] = true;
+
+	cout << (winner[k] ? "First" : "Second");
+
+	return 0;
+}

Contest-Questions/AtCoder Educational DP/sushi.cpp

@@ -0,0 +1,33 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fo(i, n) for(int i=0; i<n; i++)
+#define Fo(i, k, n) for(int i=k; i<n; i++)
+#define endl "\n"
+
+int n, val[4];
+double dp[305][305][305];
+
+double dfs(int a, int b, int c) {
+	if (a == 0 && b == 0 && c == 0) return 0.0;
+	else if (dp[a][b][c]) return dp[a][b][c];
+	double ans = (double)n / (a + b + c);
+	if (a) ans += (double)a / (a + b + c) * dfs(a - 1, b, c);
+	if (b) ans += (double)b / (a + b + c) * dfs(a + 1, b - 1, c);
+	if (c) ans += (double)c / (a + b + c) * dfs(a, b + 1, c - 1);
+	return dp[a][b][c] = ans;
+}
+
+int main() {
+
+	int temp;
+	cin >> n;
+	fo(i, n) {
+		cin >> temp;
+		val[temp]++;
+	}
+
+	cout << setprecision(14) << dfs(val[1], val[2], val[3]);
+
+	return 0;
+}