range queries and one graph

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/Coin_Combinations_I.cpp

@@ -0,0 +1,26 @@
+//  Coin Combinations I
+
+#include<bits/stdc++.h>
+
+using namespace std;
+using ll = long long;
+
+const int MOD = 1e9 + 7;
+ll dp[(int)1e6 + 1];
+
+int main() {
+    int n; int x; cin >> n >> x;
+    dp[0] = 1;
+    vector<int> in(n);
+    for (int i = 0; i < n; i++) cin >> in[i];
+    for (int i = 0; i <= x; ++i) {
+        for (int j = 0; j < n; j++) {
+            if (in[j] <= i) {
+                dp[i] += dp[i - in[j]];
+                dp[i] %= MOD;
+            }
+        }
+    }
+    cout << dp[x] << endl;
+    return 0;
+}

CSES - CSES Problem Set/Dynamic_Programming/Coin_Combinations_II.cpp

@@ -0,0 +1,24 @@
+//  Coin Combinations II
+
+#include<bits/stdc++.h>
+
+using namespace std;
+using ll = long long;
+
+const int MOD = 1e9 + 7;
+ll dp[(int)1e6 + 1];
+
+int main() {
+    dp[0] = 1;
+    int n, x;
+    cin >> n >> x;
+    for (int i{}; i < n; i++) {
+        int c; cin >> c;
+        for (int j = c; j <= x; j++) {
+            dp[j] += dp[j-c];
+            dp[j] %= MOD;
+        }
+    }
+    cout << dp[x] << endl;
+    return 0;
+}

CSES - CSES Problem Set/Dynamic_Programming/Dice_Combinations.cpp

@@ -0,0 +1,22 @@
+//  Dice Combinations
+
+#include<bits/stdc++.h>
+
+using namespace std;
+using ll = long long;
+
+const ll N = 1e6;
+const ll MOD = 1e9 + 7;
+
+ll ways[N + 1];
+
+int main() {
+    ll n; cin >> n;
+    ways[0] = 1;
+    for (ll i = 1; i <= n; i++) {
+        for (ll j = 1; j <= 6 && j <= i; j++) {
+            ways[i] = (ways[i] + (ways[i - j])) % MOD;
+        }
+    }
+    cout << ways[n];
+}

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/Dynamic_Programming/Minimizing_Coins.cpp

@@ -0,0 +1,23 @@
+//  Minimizing Coins
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int main() {
+    int n, x;
+    cin >> n >> x;
+    vector<int> dp(x + 1, INT_MAX - 5);
+    dp[0] = 0;
+    for (int i{}; i < n; i++) {
+        int c; cin >> c;
+        for (int j = c; j <= x; j++) {
+            if (j >= c) {
+                dp[j] = min(dp[j - c] + 1, dp[j]);
+            }
+        }
+    }
+    if (dp[x] != INT_MAX - 5) cout << dp[x] << endl;
+    else cout << -1 << endl;
+    return 0;
+}

CSES - CSES Problem Set/Dynamic_Programming/Removing_Digits.cpp

@@ -0,0 +1,28 @@
+//  Removing Digits
+
+#include<bits/stdc++.h>
+
+using namespace std;
+
+int dp[(int)1e6 + 1];
+
+
+int solve(int n) {
+    if (dp[n]) return dp[n];
+    int count = INT_MAX;
+    if (n == 0) return 0;
+    for (int i = 1; i <= 10 * n; i*= 10) {
+        int remove = (n / i) - (n / (10 * i)) * 10;
+        if (!remove) continue;
+        count = min(count, 1 + solve(n - remove));
+    }
+    dp[n] = count;
+    return count;
+}
+
+
+int main() {
+    int n; cin >> n;
+    cout << solve(n) << endl;
+    return 0;
+}