6 i am retarded

The Last Algorithms Course You'll Need/5. Two Crystal Balls.c

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+#include <math.h>
+#include <stdio.h>
+
+// complexity is O(sqrt(N))
+// well we need ot find an exact moment,
+// let's say "height" at which our crystal
+// balls break, for that we only have 2 balls,
+// so we can't do binary search, since the range
+// is tooooo huge, therefore we run a linear
+// growth bigger than N, but small enough to find where
+// the first ball breaks, then we take the interval
+// between: [the previous non-break] and [where it broken]
+// and run a normal linear search
+// therefore we run sqrt(n) + sqrt(n) times
+// so it's O(sqrt(N)
+
+#define SIZE 999
+
+int two_crystal_balls_search(int array[], int size, int value)
+{
+	int i = 0;
+	int step = sqrt((double)(size));
+	for (; i < size; i = i + step)
+		if (array[i] >= value)
+			break;
+
+	printf("Step is: %d\n", step);
+	printf("The first one broke at: %d\n", i);
+
+	i = i - step;
+	for (; i < i + step; ++i)
+		if (array[i] >= value)
+			return i;
+
+	return -1;
+}
+
+int main()
+{
+	int array[SIZE];
+	for (int i = 0; i < SIZE; ++i)
+		array[i] = i;
+
+	printf("The balls break at: %d\n", two_crystal_balls_search(array, SIZE, 567));
+}

The Last Algorithms Course You'll Need/6. Bubble Sort.c

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+#include <stdio.h>
+
+#define SIZE 10 
+
+// complexity is O(n^2)
+// how is that calculated?
+// well we run two loops, even if the first one is N
+// the second one is first N, then N - 1, then N - 2, ...
+// all the way down to N - N + 1
+// what's the sum of them? 
+// imagine sum of all form 1 to 100
+// okay, 1 + 100 = 101
+// okay, 2 + 99 = 101
+// etc all the way down to 50 and 51,
+// so we have 50 times 101 to calculate sum of 1 to 100
+// which means:
+// 101 * 50    or
+// (N+1) * N/2   or
+// N^2 + N    which makes
+// O(N^2 + N)   then we drop the non-significant + N
+// O(N^2)
+
+void bubble_sort(int array[], int size)
+{
+	for (int i = 0; i < size; ++i)
+	{
+		for (int j = 1; j < size - i; ++j)
+		{
+			if (array[j] < array[j-1])
+			{
+				int temp = array[j];
+				array[j] = array[j-1];
+				array[j-1] = temp;
+			}
+		}
+	}
+}
+
+int main()
+{
+	int array[SIZE] = { 5, 7, 3, 2, 11, 16, 1, 4, 3, 2 };
+	bubble_sort(array, SIZE);
+	for (int i = 0; i < SIZE; ++i)
+		printf("%d ", array[i]);
+	printf("\n");
+}