Solution to 'Mushroom Picker' Codility task with O(n+m) complexity thanks to use of prefix sums. Source: https://codility.com/media/train/3-PrefixSums.pdf

codility-mushroom-picker.js

const a = [2,3,7,5,1,3,9]
const startI = 4
const moves = 6

const mushroomPicker = (A, k, m) => {
	let maxSum = 0
  let sumFromMovesL = 0 // stores prefix sum for each step moving left
  
  for (
    let movesL = 0;
    k - movesL >= 0 // iterate left until reaching the beginning of an array A
    && movesL <= m; // and do it also as long as we don't use all moves
    movesL++
  ) {
    let sumFromMovesR = 0
    const currPos = k - movesL // get current position relative to beginning k
   	sumFromMovesL+= A[currPos] // add current value to already calculated prefix sums of moves to the left
    
    for (
      let movesR = 0;
      movesR <= m - movesL * 2 // iterate right only if can actually move back to position k (still have enough moves despite reducing them by number of moves left)
      && k + 1 + movesR < A.length;  // and if next position is still in the array A
      movesR++
    ) {
      const newPos = k + 1 + movesR // get next new position (+1 because we don't want to sum already used position k where we got back)
      sumFromMovesR+= A[newPos] // add to existing prefix sum for moves right
    }
    
    maxSum = Math.max(maxSum, sumFromMovesL + sumFromMovesR) // simply get the max number from calculated for each scenario sums
  }
  
  return maxSum
}