range queries and one graph

CSES - CSES Problem Set/Counting_Rooms.cpp

@@ -0,0 +1,44 @@
+//  Counting Rooms
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+void dfs(vector<vector<vector<pair<int, int>>>> &m, pair<int, int> s,  vector<vector<bool>> &v) {
+    v[s.first][s.second] = true;
+    for (auto e: m[s.first][s.second]) {
+        if (!v[e.first][e.second]) dfs(m, e, v);
+    }
+}
+
+int main() {
+    int n, m; cin >> n >> m;
+//    map<pair<int, int>, vector<pair<int, int>>> map1;
+    vector<vector<vector<pair<int, int>>>> map1(n, vector<vector<pair<int, int>>>(m));
+    vector<string> in;
+    for (int i{}; i < n; i++) {
+        string s; cin >> s; in.push_back(s);
+    }
+    for (int i{}; i < n; i++) {
+        for (int j{}; j < m; j++) {
+            if (in[i][j] == '#') continue;
+            if (i > 0 && in[i-1][j] == '.') map1[i][j].push_back({i-1, j});
+            if (i < n - 1 && in[i+1][j] == '.') map1[i][j].push_back({i+1, j});
+            if (j > 0 && in[i][j-1] == '.') map1[i][j].push_back({i, j-1});
+            if (j < m - 1 && in[i][j+1] == '.') map1[i][j].push_back({i, j+1});
+        }
+    }
+//    set<pair<int, int>> v;
+    vector<vector<bool>> v(n, vector<bool>(m, false));
+    int count = 0;
+    for (int i{}; i < n; i++) {
+        for (int j{}; j < m; j++) {
+            if (in[i][j] == '#') continue;
+            if (v[i][j]) continue;
+            count++;
+            dfs(map1, {i, j}, v);
+        }
+    }
+    cout << count << endl;
+    return 0;
+}

CSES - CSES Problem Set/Dynamic_Programming/Array_Description.cpp

@@ -0,0 +1,49 @@
+#include <iostream>
+#include <vector>
+using namespace std;
+
+// solution from usaco - need to understand this further. my approach was very similar
+
+typedef long long ll;
+#define pb push_back
+#define pi pair<int, int>
+#define f first
+#define mp make_pair
+#define s second
+
+ll dp[100001][101];
+const ll MOD = (10e8) + 7;
+int main() {
+    ios_base::sync_with_stdio(0);
+    cin.tie(0);
+    int n, m;
+    cin >> n >> m;
+    int arr[n];
+    for (int i = 0; i < n; i++) { cin >> arr[i]; }
+    if (arr[0] == 0) {
+        fill(dp[0], dp[0] + 101, 1);
+    } else {
+        dp[0][arr[0]] = 1;
+    }
+    for (int i = 1; i < n; i++) {
+        if (arr[i] == 0) {
+            for (int j = 1; j <= m; j++) {
+                dp[i][j] += dp[i - 1][j];
+                if (j - 1 > 0) dp[i][j] += dp[i - 1][j - 1];
+                if (j + 1 <= m) dp[i][j] += dp[i - 1][j + 1];
+                dp[i][j] %= MOD;
+            }
+        } else {
+            dp[i][arr[i]] += dp[i - 1][arr[i]];
+            if (arr[i] - 1 > 0) dp[i][arr[i]] += dp[i - 1][arr[i] - 1];
+            if (arr[i] + 1 <= m) dp[i][arr[i]] += dp[i - 1][arr[i] + 1];
+            dp[i][arr[i]] %= MOD;
+        }
+    }
+    ll ans = 0;
+    for (int i = 1; i <= m; i++) {
+        ans += dp[n - 1][i];
+        ans %= MOD;
+    }
+    cout << ans;
+}

CSES - CSES Problem Set/Dynamic_Programming/Book_Shop.cpp

@@ -0,0 +1,24 @@
+//  Book Shop
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int main() {
+    int n, x; cin >> n >> x;
+    vector<int> price(n);
+    vector<int> pages(n);
+    for (auto &e: price) cin >> e;
+    for (auto &e: pages) cin >> e;
+
+    int dp[1000001];
+    for (int i{}; i < n; i++) {
+        for (int j = x; j >= price[i]; j--) {
+            dp[j] = max(dp[j], dp[j - price[i]] + pages[i]);
+        }
+    }
+
+    cout <<  dp[x] << endl;
+
+    return 0;
+}

CSES - CSES Problem Set/Dynamic_Programming/Grid_Paths.cpp

@@ -0,0 +1,31 @@
+//  Grid Paths
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+const int MOD = 1e9 + 7;
+
+using ll = long long;
+
+ll dp[1001][1001];
+
+int main() {
+    int n; cin >> n;
+    vector<string> in(n);
+    for (int i{}; i < n; i++) cin >> in[i];
+    dp[0][0] = in[0][0] != '*';
+    for (int i = 1; i < n; i++) {
+        if (in[0][i] == '*') continue;
+        else dp[0][i] = dp[0][i - 1];
+    }
+    for (int i = 1; i < n; i++) {
+        for (int j{}; j < n; j++) {
+            if (in[i][j] == '*') continue;
+            dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
+            dp[i][j] %= MOD;
+        }
+    }
+    cout << dp[n-1][n-1] << endl;
+    return 0;
+}

CSES - CSES Problem Set/Range_Queries/Dynamic_Range_Sum_Queries.cpp

@@ -0,0 +1,64 @@
+//  Dynamic Range Sum Queries
+
+#include<bits/stdc++.h>
+using ll = long long;
+using namespace std;
+
+vector<ll> construct(vector<ll> &input) {
+    vector<ll> output(2 * input.size());
+    for (int i = 0; i < input.size(); i++) {
+        output[input.size() + i] = input[i];
+    }
+    for (int i = input.size() - 1; i > 0; i--) {
+        output[i] = output[2*i] + output[2*i + 1];
+    }
+    return output;
+}
+
+void update(int k, ll x, int n, vector<ll> &tree) {
+    k += n;
+    tree[k] = x;
+    k /= 2;
+    for (; k >= 1; k /= 2) {
+        tree[k] = tree[2*k + 1] + tree[2*k];
+    }
+}
+
+ll query(int a, int b, int n, vector<ll> &tree) {
+    a--; b--;
+    a += n; b += n;
+    ll s = 0;
+    while (a <= b) {
+        if (a % 2 == 1) {
+            s += tree[a];
+            a++;
+        }
+        if (b % 2 == 0) {
+            s += tree[b];
+            b--;
+        }
+        a /= 2; b /= 2;
+    }
+    return s;
+}
+
+int main() {
+    int n, q; cin >> n >> q;
+    vector<ll> in(n);
+    for (int i{}; i < n; i++) {
+        cin >> in[i];
+    }
+    auto seg = construct(in);
+    for (int i{}; i < q; i++) {
+        int t; cin >> t;
+        if (t == 2) {
+            int a, b; cin >> a >> b;
+            cout << query(a, b, n, seg) << endl;
+        } else if (t == 1) {
+            int k; ll u; cin >> k >> u;
+            k--;
+            update(k, u, n, seg);
+        }
+    }
+    return 0;
+}

CSES - CSES Problem Set/Range_Queries/Static_Range_Minimum_Queries.cpp

@@ -0,0 +1,51 @@
+//  Static Range Minimum Queries
+
+#include<bits/stdc++.h>
+
+using namespace std;
+using ll = long long;
+
+vector<ll> construct(vector<ll> &input) {
+    int n = input.size();
+    vector<ll> output(2*n);
+    for (int i{}; i < n; i++) {
+        output[n + i] = input[i];
+    }
+    for (int i = n - 1; i > 0; i--) {
+        output[i] = min(output[2*i], output[2*i + 1]);
+    }
+    return output;
+}
+
+ll query(int a, int b, int n, vector<ll> &tree) {
+    a += n; b += n;
+    ll s = INT_MAX;
+    while (a <= b) {
+        if (a % 2 == 1) {
+            s = min(s, tree[a]);
+            a++;
+        }
+        if (b % 2 == 0) {
+            s = min(s, tree[b]);
+            b--;
+        }
+        a /= 2; b /= 2;
+    }
+    return s;
+}
+
+int main() {
+    int n, q; cin >> n >> q;
+    vector<ll> in(n);
+    for (int i = 0; i < n; i++) {
+        cin >> in[i];
+    }
+    vector<ll> seg = construct(in);
+    cout << endl;
+    for (int i{}; i < q; i++) {
+        int a, b; cin >> a >> b;
+        a--; b--;
+        cout << query(a, b, n, seg) << endl;
+    }
+    return 0;
+}

CSES - CSES Problem Set/Range_Queries/Static_Range_Sum_Queries.cpp

@@ -0,0 +1,24 @@
+//  Static Range Sum Queries
+
+#include<bits/stdc++.h>
+
+using namespace std;
+using ll = long long;
+
+int main() {
+    int n, q; cin >> n >> q;
+    vector<ll> pref(n, 0);
+    ll x; cin >> x;
+    pref[0] = x;
+    for (int i = 1; i < n; i ++) {
+        ll y; cin >> y;
+        pref[i] = y + pref[i-1];
+    }
+    for (int i{}; i < q; i++) {
+        int a, b; cin >> a >> b;
+        if (a >= 2 ) cout << pref[b - 1] - pref[a - 2] << endl;
+        else cout << pref[b - 1] << endl;
+    }
+
+    return 0;
+}