mirror of
https://github.com/donnemartin/interactive-coding-challenges.git
synced 2024-03-22 13:11:13 +08:00
Add insert m into n challenge
This commit is contained in:
Donne Martin
parent
470b38cdc4
commit
b1ea49f0c8
0
bit_manipulation/insert_m_into_n/__init__.py
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0
bit_manipulation/insert_m_into_n/__init__.py
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173
bit_manipulation/insert_m_into_n/insert_m_into_n_challenge.ipynb
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173
bit_manipulation/insert_m_into_n/insert_m_into_n_challenge.ipynb
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@ -0,0 +1,173 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Challenge Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Given two 16 bit numbers, n and m, and two indices i, j, insert m into n such that m starts at bit j and ends at bit i.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)\n",
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"* [Solution Notebook](#Solution-Notebook)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Can we assume j > i?\n",
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" * Yes\n",
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"* Can we assume i through j have enough space for m?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* None as an input -> Exception\n",
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"* Negative index for i or j -> Exception\n",
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"* General case\n",
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"<pre>\n",
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"i = 2\n",
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"j = 6\n",
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"n = 0000 0100 0000 0000\n",
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"m = 0000 0000 0001 0011\n",
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"result = 0000 0100 0100 1100\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"Refer to the [Solution Notebook](). If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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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": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class Bits(object):\n",
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"\n",
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" def insert_m_into_n(self, m, n, i, j):\n",
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" # TODO: Implement me\n",
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" pass"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"**The following unit test is expected to fail until you solve the challenge.**"
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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": null,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"# %load test_insert_m_into_n.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestBit(object):\n",
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"\n",
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" def test_insert_m_into_n(self):\n",
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" n = int('0000010000111101', base=2)\n",
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" m = int('0000000000010011', base=2)\n",
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" expected = int('0000010001001101', base=2)\n",
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" bits = Bits()\n",
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" assert_equal(bits.insert_m_into_n(m, n, i=2, j=6), expected)\n",
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" print('Success: test_insert_m_into_n')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestBit()\n",
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" test.test_insert_m_into_n()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Solution Notebook\n",
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"\n",
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"Review the [Solution Notebook]() for a discussion on algorithms and code solutions."
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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221
bit_manipulation/insert_m_into_n/insert_m_into_n_solution.ipynb
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bit_manipulation/insert_m_into_n/insert_m_into_n_solution.ipynb
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@ -0,0 +1,221 @@
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{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Solution Notebook"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Problem: Given two 16 bit numbers, n and m, and two indices i, j, insert m into n such that m starts at bit j and ends at bit i.\n",
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"\n",
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"* [Constraints](#Constraints)\n",
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"* [Test Cases](#Test-Cases)\n",
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"* [Algorithm](#Algorithm)\n",
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"* [Code](#Code)\n",
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"* [Unit Test](#Unit-Test)"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Constraints\n",
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"\n",
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"* Can we assume j > i?\n",
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" * Yes\n",
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"* Can we assume i through j have enough space for m?\n",
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" * Yes\n",
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"* Can we assume the inputs are valid?\n",
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" * No\n",
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"* Can we assume this fits memory?\n",
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" * Yes"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Test Cases\n",
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"\n",
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"* None as an input -> Exception\n",
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"* Negative index for i or j -> Exception\n",
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"* General case\n",
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"\n",
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"<pre>\n",
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"i = 2, j = 6\n",
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" j i\n",
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"n = 0000 0100 0011 1101\n",
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"m = 0000 0000 0001 0011\n",
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"result = 0000 0100 0100 1101\n",
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"</pre>"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Algorithm\n",
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"\n",
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"<pre>\n",
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" j i\n",
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"n = 0000 0100 0011 1101\n",
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"m = 0000 0000 0001 0011\n",
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"\n",
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"lmask = 1111 1111 1111 1111 -1\n",
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"lmask = 1111 1111 1000 0000 -1 << (j + 1)\n",
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"\n",
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"rmask = 0000 0000 0000 0001 1\n",
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"rmask = 0000 0000 0000 0100 1 << i\n",
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"rmask = 0000 0000 0000 0011 (1 << i) -1\n",
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"\n",
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"mask = 1111 1111 1000 0011 lmask | rmask\n",
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"\n",
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"n = 0000 0100 0011 1101\n",
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"mask = 1111 1111 1000 0011 n & mask \n",
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"--------------------------------------------------\n",
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"n2 = 0000 0100 0000 0001\n",
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"\n",
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"n2 = 0000 0100 0000 0001\n",
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"mask2 = 0000 0000 0100 1100 m << i\n",
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"--------------------------------------------------\n",
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"result = 0000 0100 0100 1101 n2 | mask2\n",
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"</pre>\n",
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"\n",
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"Complexity:\n",
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"* Time: O(b), where b is the number of bits\n",
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"* Space: O(b), where b is the number of bits"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Code"
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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": 1,
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"source": [
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"class Bits(object):\n",
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"\n",
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" def insert_m_into_n(self, m, n, i, j):\n",
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" if None in (m, n, i, j):\n",
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" raise TypeError('Argument cannot be None')\n",
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" if i < 0 or j < 0:\n",
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" raise ValueError('Index cannot be negative')\n",
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" left_mask = -1 << (j + 1)\n",
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" right_mask = (1 << i) - 1\n",
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" n_mask = left_mask | right_mask\n",
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" # Clear bits from j to i, inclusive\n",
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" n_cleared = n & n_mask\n",
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" # Shift m into place before inserting it into n\n",
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" m_mask = m << i\n",
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" return n_cleared | m_mask"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Unit Test"
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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": 2,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Overwriting test_insert_m_into_n.py\n"
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]
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}
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],
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"source": [
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"%%writefile test_insert_m_into_n.py\n",
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"from nose.tools import assert_equal\n",
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"\n",
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"\n",
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"class TestBit(object):\n",
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"\n",
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" def test_insert_m_into_n(self):\n",
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" n = int('0000010000111101', base=2)\n",
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" m = int('0000000000010011', base=2)\n",
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" expected = int('0000010001001101', base=2)\n",
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" bits = Bits()\n",
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" assert_equal(bits.insert_m_into_n(m, n, i=2, j=6), expected)\n",
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" print('Success: test_insert_m_into_n')\n",
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"\n",
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"\n",
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"def main():\n",
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" test = TestBit()\n",
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" test.test_insert_m_into_n()\n",
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"\n",
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"\n",
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"if __name__ == '__main__':\n",
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" main()"
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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": 3,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Success: test_insert_m_into_n\n"
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]
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}
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],
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"source": [
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"%run -i test_insert_m_into_n.py"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.5.0"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 0
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}
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21
bit_manipulation/insert_m_into_n/test_insert_m_into_n.py
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21
bit_manipulation/insert_m_into_n/test_insert_m_into_n.py
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from nose.tools import assert_equal
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class TestBit(object):
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def test_insert_m_into_n(self):
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n = int('0000010000111101', base=2)
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m = int('0000000000010011', base=2)
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expected = int('0000010001001101', base=2)
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bits = Bits()
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assert_equal(bits.insert_m_into_n(m, n, i=2, j=6), expected)
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print('Success: test_insert_m_into_n')
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def main():
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test = TestBit()
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test.test_insert_m_into_n()
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if __name__ == '__main__':
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main()
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