var e = [[5, 7, 8, 6, 3],
		 [0, 0, 7, 0, 4],
		 [4, 6, 3, 4, 9],
		 [3, 1, 0, 5, 8]];

function maxCarrots(matrix) {
    if (matrix.length == 1 && matrix[0].length == 1) {
        return matrix[0][0];
    } else {
        var center = findCenter(matrix);
        var visited = traverseGarden(matrix, center);
        return visited.reduce(function (a, b) { return a + b; }, 0);
    }
}

function findCenter(matrix) {
    var height = matrix.length;
    var width = matrix[0].length;
    var midHeight = Math.floor(height / 2);
    var midWidth = Math.floor(width / 2);
    if (height % 2 == 1 && width % 2 == 1) {
        return [midHeight,midWidth];
    } else if (height % 2 == 1 && width % 2 == 0) {
        if (matrix[midHeight][midWidth] > matrix[midHeight][midWidth - 1]) {
            return [midHeight, midWidth];
        } else {
            return [midHeight, midWidth - 1];
        }
    } else if (height % 2 == 0 && width % 2 == 1) {
        if (matrix[midHeight][midWidth] > matrix[midHeight - 1][midWidth]) {
            return [midHeight, midWidth];
        } else {
            return [midHeight - 1, midWidth];
        }
    } else {
        var maxValues = [matrix[midHeight - 1][midWidth - 1], matrix[midHeight - 1][midWidth], matrix[midHeight][midWidth - 1], matrix[midHeight][midWidth]];
        var maxIndex = maxValues.reduce((maxIndex, curValue, curIndex, maxValues) => curValue > maxValues[maxIndex] ? curIndex : maxIndex, 0);
        switch (maxIndex) {
            case 0:
                return [midHeight - 1, midWidth - 1];
            case 1:
                return [midHeight - 1, midWidth];
            case 2:
                return [midHeight, midWidth - 1];
            case 3:
                return [midHeight, midWidth];
        }
    }
}

function traverseGarden(matrix, center) {
    var pos = center;
    var centerValue = matrix[center[0]][center[1]];
    var visited = [centerValue]
    while (findMaxMove(matrix, pos)[0] > 0) {
        var move = findMaxMove(matrix, pos);
        var nextVal = move[0];
        var nextPos = move[1];
        visited.push(nextVal);
        pos = nextPos;
    }
    return visited;
}

function findMaxMove(matrix, pos) {
    var x = pos[0];
    var y = pos[1];

    var up = x-1 in matrix && matrix[x - 1][y] ? matrix[x - 1][y] : Number.NEGATIVE_INFINITY;
    var down = x+1 in matrix && matrix[x + 1][y] ? matrix[x + 1][y] : Number.NEGATIVE_INFINITY;
    var left = y-1 in matrix[0] && matrix[x][y - 1] ? matrix[x][y - 1] : Number.NEGATIVE_INFINITY;
    var right = y+1 in matrix[0] && matrix[x][y + 1] ? matrix[x][y + 1] : Number.NEGATIVE_INFINITY;

    var moves = [up, down, left, right];
    var maxMove = moves.reduce((maxIndex, curValue, curIndex, moves) => curValue > moves[maxIndex] ? curIndex : maxIndex, 0);

    var value = moves[maxMove];

    matrix[x][y] = 0

    switch (maxMove) {
            case 0:
                return [value, [x - 1, y]];
            case 1:
                return [value, [x + 1, y]];
            case 2:
                return [value, [x, y - 1]];
            case 3:
                return [value, [x, y + 1]];
        }
}

maxCarrots(e)