From c02795b43eb076a8be65782dc178a00a51f99396 Mon Sep 17 00:00:00 2001
From: Arham Javed <101502781+Arham07@users.noreply.github.com>
Date: Mon, 20 Oct 2025 03:16:36 -0700
Subject: [PATCH 1/3] Add solution for Counting Bits #107

---
 Counting bits.cpp | 31 +++++++++++++++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 Counting bits.cpp

diff --git a/Counting bits.cpp b/Counting bits.cpp
new file mode 100644
index 0000000..3140a06
--- /dev/null
+++ b/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;
+```
+
+}

From b25ee9689f6e7544a84a326df761d6ae8ba8bff0 Mon Sep 17 00:00:00 2001
From: Arham Javed <101502781+Arham07@users.noreply.github.com>
Date: Mon, 20 Oct 2025 03:29:59 -0700
Subject: [PATCH 2/3] Add solution for Counting Towers #112

---
 3_dp/Counting Towers.cpp | 26 ++++++++++++++++++++++++++
 1 file changed, 26 insertions(+)
 create mode 100644 3_dp/Counting Towers.cpp

diff --git a/3_dp/Counting Towers.cpp b/3_dp/Counting Towers.cpp
new file mode 100644
index 0000000..5abe338
--- /dev/null
+++ b/3_dp/Counting Towers.cpp	
@@ -0,0 +1,26 @@
+#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";
+    }
+}

From 3ebcabe03c13e532101a77b20b7946d7faab3aa3 Mon Sep 17 00:00:00 2001
From: Arham Javed <101502781+Arham07@users.noreply.github.com>
Date: Mon, 20 Oct 2025 03:30:31 -0700
Subject: [PATCH 3/3] Fix formatting issues in Counting Towers.cpp

---
 3_dp/Counting Towers.cpp | 1 -
 1 file changed, 1 deletion(-)

diff --git a/3_dp/Counting Towers.cpp b/3_dp/Counting Towers.cpp
index 5abe338..e1a1b04 100644
--- a/3_dp/Counting Towers.cpp	
+++ b/3_dp/Counting Towers.cpp	
@@ -8,7 +8,6 @@ int main() {
 
     int t;
     cin >> t;
-
     const int MAXN = 1e6;
     vector<long long> dpA(MAXN + 1), dpB(MAXN + 1);
     dpA[1] = dpB[1] = 1;