I forgot to make commits for each problem so here's a bunch in one go.

.gitignore

@@ -31,4 +31,3 @@
 *.exe
 *.out
 *.app
-

bit-strings.cpp

@@ -0,0 +1,22 @@
+#include <iostream>
+
+int
+main(void)
+{
+	int n;
+	std::cin >> n;
+
+	long x = 1;
+	long b = 2;
+	while (n != 0)
+	{
+		if (n % 2 == 1)
+		{
+			x = x * b % 1000000007;
+		}
+		b = b * b  % 1000000007;
+		n >>= 1;
+	}
+
+	std::cout << x << std::endl;
+}

increasing-array.cpp

@@ -0,0 +1,39 @@
+#include <iostream>
+#include <cstdlib>
+#include <string>
+#include <sstream>
+
+int
+main(void)
+{
+	// oops, I left my debug printing in my first submission :<
+	size_t n;
+	std::cin >> n;
+	int *a = (int *)calloc(n, sizeof(int));
+
+	std::string input;
+	getline(std::cin, input); // discard extra newline
+	getline(std::cin, input);
+	std::istringstream iss(input);
+
+	std::string s;
+	for (size_t i = 0; getline(iss, s, ' '); i++)
+	{
+		a[i] = stoi(s);
+	}
+
+	long moves = 0;
+	int diff = 0;
+	for (size_t i = 1; i < n; i++)
+	{
+		if (a[i] > a[i-1])
+		{
+			continue;
+		}
+
+		diff = a[i-1] - a[i];
+		a[i] += diff;
+		moves += diff;
+	}
+	std::cout << moves;
+}

longest-repeating-sequence.cpp

@@ -0,0 +1,33 @@
+#include <iostream>
+#include <string>
+
+int
+main(void)
+{
+
+	std::string input;
+	getline(std::cin, input);
+
+	long longest_length = 1;
+	long current_length = 1;
+	char new_letter, current_letter = '0';
+	for (size_t i = 0; i < input.length(); i++)
+	{
+		new_letter = input[i];
+		if (new_letter != current_letter)
+		{
+			if (current_length > longest_length)
+			{
+				longest_length = current_length;
+			}
+			current_length = 0;
+			current_letter = new_letter;
+		}
+		current_length++;
+	}
+	if (current_length > longest_length)
+	{
+		longest_length = current_length;
+	}
+	std::cout << longest_length;
+}

missing-number.cpp

@@ -0,0 +1,33 @@
+#include <iostream>
+#include <cstdlib>
+#include <string>
+#include <sstream>
+
+int
+main(void)
+{
+
+	size_t n;
+	std::cin >> n;
+	bool *a = (bool *)calloc(n, sizeof(bool));
+
+	std::string input;
+	getline(std::cin, input); // discard extra newline
+	getline(std::cin, input);
+	std::istringstream iss(input);
+
+	std::string s;
+	while (getline(iss, s, ' '))
+	{
+		a[stoi(s)-1] = 1;
+	}
+
+	for (size_t i = 0; i < n; i++)
+	{
+		if (!a[i])
+		{
+			std::cout << i+1;
+			break;
+		}
+	}
+}

number-spiral.cpp

@@ -0,0 +1,37 @@
+#include <iostream>
+
+int
+main(void)
+{
+	long t;
+	std::cin >> t;
+
+	long x, y, c;
+	for (long i = 0; i < t; i++)
+	{
+		std::cin >> y >> x;
+		if (x > y)
+		{
+			if (x % 2 == 0)
+			{
+				c = (x * x) - (x + x) + y + 1;
+			}
+			else
+			{
+				c = (x * x) - y + 1;
+			}
+		}
+		else
+		{
+			if (y % 2 == 0)
+			{
+				c = (y * y) - x + 1;
+			}
+			else
+			{
+				c = (y * y) - (y + y) + x + 1;
+			}
+		}
+		std::cout << c << std::endl;
+	}
+}

permutations.cpp

@@ -0,0 +1,30 @@
+#include <iostream>
+#include <string>
+
+int
+main(void)
+{
+	long n;
+	long x;
+	std::cin >> n;
+
+	std::string solution = "";
+
+	if (n == 2 || n == 3)
+	{
+		std::cout << "NO SOLUTION";
+		return 0;
+	}
+
+	for (x = 2; x <= n; x += 2)
+	{
+		solution += std::to_string(x) + " ";
+	}
+
+	for (x = 1; x <= n; x += 2)
+	{
+		solution += std::to_string(x) + " ";
+	}
+
+	std::cout << solution;
+}

trailing-zeroes.cpp

@@ -0,0 +1,29 @@
+#include <iostream>
+
+int
+main(void)
+{
+	int n;
+	std::cin >> n;
+
+	if (n < 0)
+	{
+		std::cout << -1 << std::endl;
+		return 1;
+	}
+
+	int x = 0;
+
+	// Observed pattern where the number of trailing zeroes increases by
+	// one for every additional factor of 5.
+	// e.g. 0! to 4! has 0, 5! to 9! has 1, 10! to 14! has 2, and so on.
+	// Turns out you need to consider additional powers of 5 (25, 125, etc).
+	// This was not obvious at first since 25! overflowed.
+	for (int i = 5; n / i >= 1; i *= 5)
+	{
+		x += n / i;
+	}
+
+	std::cout << x << std::endl;
+	return 0;
+}

two-knights.cpp

@@ -0,0 +1,13 @@
+#include <iostream>
+
+int
+main(void)
+{
+	long n;
+	std::cin >> n;
+
+	for (long k = 1; k <= n; k++)
+	{
+		std::cout << ((k * k) * ((k * k) - 1)) / 2 - 4 * (k - 1) * (k - 2) << std::endl;
+	}
+}

two-sets.cpp

@@ -0,0 +1,43 @@
+#include <iostream>
+#include <vector>
+
+int
+main(void)
+{
+	long n;
+	std::cin >> n;
+
+	std::vector<long> A, B;
+
+	// If sum of {1, 2, ..., n} is odd, no way to make 2 sets with equal sum
+	long sum = (n * (n + 1)) / 2;
+	if (sum % 2 == 1)
+	{
+		std::cout << "NO";
+		return 0;
+	}
+	std::cout << "YES" << std::endl;
+
+	// Break sum in half; this is what each set will add up to
+	sum /= 2;
+
+	for (long i = n; i > 0; i--)
+	{
+		if (i <= sum)
+		{
+			A.push_back(i);
+			sum -= i;
+		}
+		else
+		{
+			B.push_back(i);
+		}
+	}
+
+	std::cout << A.size() << std::endl;
+	for (long x : A)
+		std::cout << x << " ";
+	std::cout << std::endl << B.size() << std::endl;
+	for (long x : B)
+		std::cout << x << " ";
+}

weird-algorithm.cpp

@@ -0,0 +1,23 @@
+#include <iostream>
+
+using namespace std;
+
+int
+main(void)
+{
+	long x;
+	cin >> x;
+	while (x != 1)
+	{
+		cout << x << " ";
+		if (x % 2 == 0)
+		{
+			x /= 2;
+		}
+		else
+		{
+			x = (x * 3) + 1;
+		}
+	}
+	cout << x;
+}