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Add number of function evaluations for Floyd
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Lines changed: 316 additions & 2 deletions

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‎source_code/cycles.ipynb‎

Lines changed: 316 additions & 2 deletions
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@@ -237,7 +237,7 @@
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{
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"cell_type": "code",
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"execution_count": 6,
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"execution_count": 10,
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"id": "92990251-8f03-46cb-9206-e71274ec87ba",
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"metadata": {},
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"outputs": [],
@@ -317,7 +317,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"execution_count": 4,
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"id": "aa224337-7847-41da-8859-d285c994c528",
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"metadata": {},
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"outputs": [],
@@ -768,6 +768,320 @@
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"Experiments with still larger values of the offset and cycle lengths will convince you that the memory consumption of the dictionary is so large that the Jupyter kernel crashes, while Floyd's algorithm still finds the correct result."
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]
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},
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{
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"cell_type": "markdown",
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"id": "71569a31-3a3e-4bfb-b9e9-a80007f0b679",
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"metadata": {},
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"source": [
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"# Function evaluations"
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]
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},
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{
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"cell_type": "markdown",
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"id": "be9d4358-615b-43de-9d7f-448e0a38bcb7",
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"metadata": {},
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"source": [
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"It is clear that Floyd's algorithm trades memory usage for function evaluations. Both the naive and the dictionary method will evaluate the function for offset and cycle length. To check how many times Floyd's algorithm evaluates the function, you can create a class with a `__call__` method. An instance of that class can be called as if it were a function, but it can do bookkeeping as well."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "b4e85177-119d-41aa-a26b-df0ba634183b",
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"metadata": {},
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"outputs": [],
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"source": [
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"class CountFunction:\n",
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"\n",
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" def __init__(self, offset, cycle_length):\n",
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" self._offset = offset\n",
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" self._cycle_length = cycle_length\n",
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" self._evaluations = 0\n",
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"\n",
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" def __call__(self, n):\n",
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" self._evaluations += 1\n",
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" if n < self._offset - 1:\n",
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" return n + 1\n",
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" return self._offset + ((n + 1 - self._offset) % self._cycle_length)\n",
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"\n",
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" @property\n",
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" def evaluations(self):\n",
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" return self._evaluations\n",
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"\n",
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" def reset(self):\n",
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" self._evaluations = 0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "14a13658-fb42-4e54-9ece-99945d6249b5",
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"metadata": {},
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"outputs": [],
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"source": [
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"f = CountFunction(100, 213)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "c5a2b685-3914-472c-8861-8e759143ea68",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(100, 213)"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"find_cycles_floyd(f, 0, 0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "e7e8fbfa-8c56-4d0d-9c89-03602b624c12",
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"1051"
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]
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},
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"execution_count": 9,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f.evaluations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "cce24ae6-8f22-4632-8ba5-04305c3a3dd8",
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"metadata": {},
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"outputs": [],
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"source": [
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"f.reset()"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"id": "235f5234-ee85-4680-85e9-fac1993a751c",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(100, 213)"
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]
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},
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"find_cycles_dict(f, 0, 500)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"id": "426ae31e-c22e-4ce2-8bf6-1dd035923f87",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"313"
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]
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},
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"execution_count": 13,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f.evaluations"
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]
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},
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{
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"cell_type": "markdown",
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"id": "47b936b2-db14-42bb-8f1c-a610ac1514ac",
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"metadata": {},
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"source": [
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"It is indeed obvious that the number of times the function is evaluated when using Floyd's algorithm is significantly higher."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"id": "c2d8c18f-6f57-4a89-881b-bda95d9d2cd3",
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"metadata": {},
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"outputs": [],
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"source": [
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"f = CountFunction(1023, 4095)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "b2d0db59-9887-4900-8603-3b516a88e9cf",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(1023, 4095)"
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]
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},
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"find_cycles_floyd(f, 0, 0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "b66e8003-70ca-446e-8bad-a6d49224689b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"18425"
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]
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},
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f.evaluations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"id": "27067bd1-7bad-46d9-9d17-adaf8a8f8c08",
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"metadata": {},
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"outputs": [],
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"source": [
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"f = CountFunction(1023, 3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "f66b25b9-141f-43d0-abdc-a295432b973d",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(1023, 3)"
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]
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},
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"find_cycles_floyd(f, 0, 0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"id": "c5bfce04-58bd-4ff6-bb77-b0ae49ef4ecb",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"5117"
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]
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},
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f.evaluations"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"id": "88a42d4b-02f9-47f8-a8f1-5c60ddc10c48",
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"metadata": {},
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"outputs": [],
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"source": [
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"f = CountFunction(10, 3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"id": "100f0e39-efed-4db4-b0c1-b2698305350b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"(10, 3)"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"find_cycles_floyd(f, 0, 0)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"id": "5a7525f4-a60e-4557-8971-9bc5c6e58b3d",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"58"
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},
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"execution_count": 22,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"f.evaluations"
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},
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{
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"cell_type": "markdown",
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"id": "e8131595-c098-44ea-aa68-e3f08440cb1f",

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