Alice and Bob Playing Flower Game - Math [JS]

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Description 

Solution: Math

Alice wins with an odd number of flowers.
Count all the combinations of creating an odd number.

  • x is odd, y is even.
  • x is even, y is odd.

To find how many even numbers <= n: floor(n / 2)

  • e.g. n = 5 -> [2,4] -> floor(n / 2) = 2
  • e.g. n = 6 -> [2,4,6] -> floor(n / 2) = 3

To find how many odd numbers <= n: ceil(n / 2)

  • e.g. n = 5 -> [1,3,5] -> ceil(n / 2) = 3
  • e.g. n = 6 -> [1,3,5] -> ceil(n / 2) = 3

Time Complexity: O(1)
Space Complexity: O(1)

var flowerGame = function(n, m) {
  let oddEven = countOdd(n) * countEven(m);
  let evenOdd = countEven(n) * countOdd(m);
  return oddEven + evenOdd;
};

function countOdd(x) {
  return Math.ceil(x / 2);
}

function countEven(x) {
  return Math.floor(x / 2);
}
Location: Auckland, New Zealand

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