Merge pull request #116 from Arham07/Arham07-patch-2

Add solution for Counting Towers #112

Author: ks-iitjmu

3_dp/Counting Towers.cpp

@@ -0,0 +1,25 @@
+#include <bits/stdc++.h>
+using namespace std;
+const long long MOD = 1e9 + 7;
+
+int main() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int t;
+    cin >> t;
+    const int MAXN = 1e6;
+    vector<long long> dpA(MAXN + 1), dpB(MAXN + 1);
+    dpA[1] = dpB[1] = 1;
+
+    for (int i = 2; i <= MAXN; i++) {
+        dpA[i] = (2 * dpA[i - 1] + dpB[i - 1]) % MOD;
+        dpB[i] = (dpA[i - 1] + 4 * dpB[i - 1]) % MOD;
+    }
+
+    while (t--) {
+        int n;
+        cin >> n;
+        cout << (dpA[n] + dpB[n]) % MOD << "\n";
+    }
+}

Counting bits.cpp

@@ -0,0 +1,31 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+long long countOnes(long long n) {
+long long count = 0;
+for (long long i = 0; (1LL << i) <= n; i++) {
+long long cycle_len = 1LL << (i + 1);
+long long full_cycles = (n + 1) / cycle_len;
+count += full_cycles * (1LL << i);
+
+```
+    long long remainder = (n + 1) % cycle_len;
+    count += max(0LL, remainder - (1LL << i));
+}
+return count;
+```
+
+}
+
+int main() {
+ios::sync_with_stdio(false);
+cin.tie(nullptr);
+
+```
+long long n;
+cin >> n;
+cout << countOnes(n) << "\n";
+return 0;
+```
+
+}