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mrb00l34n 2015-07-22 11:31:38 -04:00
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2
README.md
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@ -216,7 +216,7 @@ Challenges, solutions, and unit tests are presented in the form of **IPython/Jup
| Print all valid combinations of n-pairs of parentheses | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
| Implement a paint fill function | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
| Find all permutations to represent n cents, given 1, 5, 10, 25 cent coins | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
| Find the number of ways to represent n cents given k arbitrary cent coins | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_ways/coinchange_ways_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_ways/coinchange_ways_solution.ipynb) |
| Find the number of ways to represent n cents given an array of coins | [Challenge](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_ways/coinchange_ways_challenge.ipynb)│[Solution](http://nbviewer.ipython.org/github/donnemartin/interactive-coding-challenges/blob/master/recursion_dynamic/coin_change_ways/coinchange_ways_solution.ipynb) |
| Add a challenge | [Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md)│[Contribute](https://github.com/donnemartin/interactive-coding-challenges/blob/master/CONTRIBUTING.md) |
<br/>

18
recursion_dynamic/coinchange_ways/coinchange_ways_challenge.ipynb
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@ -34,9 +34,9 @@
"source": [
"## Explanation\n",
"\n",
"How many ways are there of making change for n, given k distinct coins? For example:\n",
"How many ways are there of making change for n, given an array of distinct coins? For example:\n",
"\n",
"Input: n = 4, k = 2, coins = [1,2]\n",
"Input: n = 4, coins = [1, 2]\n",
"\n",
"Output: 3. 1+1+1+1, 1+2+1, 2+2, would be the ways of making change.\n",
"\n",
@ -49,9 +49,9 @@
"source": [
"## Test Cases\n",
"\n",
"* Input: n = 0, k = 2, coins = [1,2] -> Output: 0\n",
"* Input: n = 100, k = 3, coins = [1,2,3] -> Output: 884\n",
"* Input: n = 1000, k = 100, coins = [1,2,3...99,100] -> Output: 15658181104580771094597751280645\n"
"* Input: n = 0, coins = [1, 2] -> Output: 0\n",
"* Input: n = 100, coins = [1, 2, 3] -> Output: 884\n",
"* Input: n = 1000, coins = [1, 2, 3...99, 100] -> Output: 15658181104580771094597751280645\n"
]
},
{
@ -78,7 +78,7 @@
},
"outputs": [],
"source": [
"def change_ways(n,k,coins):\n",
"def change_ways(n, coins):\n",
" # TODO: Implement me\n",
" return n"
]
@ -115,9 +115,9 @@
"class Challenge(object):\n",
"\n",
" def test_coinchange_ways(self,solution):\n",
" assert_equal(solution(0,2,[1,2]), 0)\n",
" assert_equal(solution(100,3,[1,2,3]), 884)\n",
" assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)\n",
" assert_equal(solution(0, [1, 2]), 0)\n",
" assert_equal(solution(100, [1, 2, 3]), 884)\n",
" assert_equal(solution(1000, range(1, 101)), 15658181104580771094597751280645)\n",
" print('Success: test_coinchange_ways')\n",
"\n",
"\n",

18
recursion_dynamic/coinchange_ways/coinchange_ways_solution.ipynb
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@ -33,7 +33,7 @@
"## Hints\n",
"\n",
"* Can you think of a way to build up to a solution?\n",
"* If there are 2 ways of making 3, and you are now given a coin of value v, how many ways can you make 3+v?\n",
"* If there are 2 ways of making 3, and you are now given a coin of value v, how many ways can you make 3 + v?\n",
"* Can you think of a way to divide the problem into smaller subproblems?"
]
},
@ -46,15 +46,15 @@
"One possible solution using dynamic programming:\n",
"* Create an array, s.t arr[i] = # of ways to make change for i\n",
"* Initialize arr[0] = 1, arr[i>0] = 0\n",
"* For each coin, and for each index from coin to n, increment arr[i] by arr[i-coin]\n",
"* For each coin, and for each index from coin to n, increment arr[i] by arr[i - coin]\n",
"\n",
"How does this work?\n",
"* As we iterate through each coin, we are adding the ways of making arr[i-coin] to arr[i]\n",
"* As we iterate through each coin, we are adding the ways of making arr[i - coin] to arr[i]\n",
"* If we have 2 ways of making 4, and are now iterating on a coin of value 3, there should be 2 ways of making 7.\n",
"* We are essentially adding the coin we are iterating on to the # of ways of making arr[i].\n",
"\n",
"Complexity:\n",
"* Time: O(mn)\n",
"* Time: O(mn); let the number of coins be m. We iterate from arr[coin] -> arr[n], or ~ n operations on each coin, hence n*m. \n",
"* Space: O(n)"
]
},
@ -73,10 +73,10 @@
},
"outputs": [],
"source": [
"def change_ways(n,k,coins):\n",
"def change_ways(n, coins):\n",
" arr = [1] + [0] * n\n",
" for coin in coins:\n",
" for i in xrange(coin,n + 1):\n",
" for i in range(coin, n + 1):\n",
" arr[i] += arr[i - coin]\n",
" return 0 if n == 0 else arr[n]"
]
@ -112,9 +112,9 @@
"class Challenge(object):\n",
"\n",
" def test_coinchange_ways(self,solution):\n",
" assert_equal(solution(0,2,[1,2]), 0)\n",
" assert_equal(solution(100,3,[1,2,3]), 884)\n",
" assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)\n",
" assert_equal(solution(0, [1, 2]), 0)\n",
" assert_equal(solution(100, [1, 2, 3]), 884)\n",
" assert_equal(solution(1000, range(1, 101)), 15658181104580771094597751280645)\n",
" print('Success: test_coinchange_ways')\n",
"\n",
"\n",

6
recursion_dynamic/coinchange_ways/test_coinchange_ways.py
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@ -4,9 +4,9 @@ from nose.tools import assert_equal
class Challenge(object):
def test_coinchange_ways(self,solution):
assert_equal(solution(0,2,[1,2]), 0)
assert_equal(solution(100,3,[1,2,3]), 884)
assert_equal(solution(1000,100,range(1,101)), 15658181104580771094597751280645)
assert_equal(solution(0, [1, 2]), 0)
assert_equal(solution(100, [1, 2, 3]), 884)
assert_equal(solution(1000, range(1, 101)), 15658181104580771094597751280645)
print('Success: test_coinchange_ways')