MaxProfit.md

A zero-indexed 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 a zero-indexed 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.

Assume that:

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

Complexity:

• expected worst-case time complexity is O(N);
• expected worst-case space complexity is O(1), beyond input storage (not counting the storage required for input arguments).

Elements of input arrays can be modified.

function solution(A) {
    if (A.length < 2) {
        return 0;
    }
    var msf = 0;
    var meh = 0;
    for (var i = 1; i < A.length; i++) {
        meh = Math.max(0, meh + A[i] - A[i - 1]);
        msf = Math.max(msf, meh);
    }
    return msf > 0 ? msf : 0;
}