find-max-profit.js

// you can write to stdout for debugging purposes, e.g.
// console.log('this is a debug message');

function solution(A) {
  // write your code in JavaScript (Node.js 8.9.4)
  let maxSoFar = 0;
  let maxEndingHere = 0;
  let minPrice = A[0];

  for (let i = 0; i < A.length; i++) {
    // console.log(A[i])

    // console.log('min price', minPrice);
    maxEndingHere = Math.max(0, A[i] - minPrice);
    // console.log('max ending here', maxEndingHere)
    minPrice = Math.min(minPrice, A[i]);
    maxSoFar = Math.max(maxEndingHere, maxSoFar);
  }
  
  if (maxSoFar <= 0) return 0;
  return maxSoFar;
}

/*
An array A consisting of N integers is given. It contains daily prices of a stock share for a period of N consecutive days. If a single share was bought on day P and sold on day Q, where 0 ≤ P ≤ Q < N, then the profit of such transaction is equal to A[Q] − A[P], provided that A[Q] ≥ A[P]. Otherwise, the transaction brings loss of A[P] − A[Q].

For example, consider the following array A consisting of six elements such that:

  A[0] = 23171
  A[1] = 21011
  A[2] = 21123
  A[3] = 21366
  A[4] = 21013
  A[5] = 21367
If a share was bought on day 0 and sold on day 2, a loss of 2048 would occur because A[2] − A[0] = 21123 − 23171 = −2048. If a share was bought on day 4 and sold on day 5, a profit of 354 would occur because A[5] − A[4] = 21367 − 21013 = 354. Maximum possible profit was 356. It would occur if a share was bought on day 1 and sold on day 5.

Write a function,

function solution(A);

that, given an array A consisting of N integers containing daily prices of a stock share for a period of N consecutive days, returns the maximum possible profit from one transaction during this period. The function should return 0 if it was impossible to gain any profit.

For example, given array A consisting of six elements such that:

  A[0] = 23171
  A[1] = 21011
  A[2] = 21123
  A[3] = 21366
  A[4] = 21013
  A[5] = 21367
the function should return 356, as explained above.

Write an efficient algorithm for the following assumptions:

N is an integer within the range [0..400,000];
each element of array A is an integer within the range [0..200,000].
*/