deepnn builds the graph for a deep net for classifying digits.

    Args:
        x: an input tensor with the dimensions (N_examples, 784), where 784 is
            the number of pixels in a standard MNIST image.

    Returns:
        A tuple (y, keep_prob). y is a tensor of shape (N_examples, 10), with
            values equal to the logits of classifying the digit into one of 10
            classes (the digits 0-9). keep_prob is a scalar placeholder for the
            probability of dropout.

def deepnn(x):
    """deepnn builds the graph for a deep net for classifying digits.

    Args:
        x: an input tensor with the dimensions (N_examples, 784), where 784 is
            the number of pixels in a standard MNIST image.

    Returns:
        A tuple (y, keep_prob). y is a tensor of shape (N_examples, 10), with
            values equal to the logits of classifying the digit into one of 10
            classes (the digits 0-9). keep_prob is a scalar placeholder for the
            probability of dropout.
    """
    # Reshape to use within a convolutional neural net.
    # Last dimension is for "features" - there is only one here, since images
    # are grayscale -- it would be 3 for an RGB image, 4 for RGBA, etc.
    with tf.name_scope("reshape"):
        x_image = tf.reshape(x, [-1, 28, 28, 1])

    # First convolutional layer - maps one grayscale image to 32 feature maps.
    with tf.name_scope("conv1"):
        W_conv1 = weight_variable([5, 5, 1, 32])
        b_conv1 = bias_variable([32])
        h_conv1 = tf.nn.relu(conv2d(x_image, W_conv1) + b_conv1)

    # Pooling layer - downsamples by 2X.
    with tf.name_scope("pool1"):
        h_pool1 = max_pool_2x2(h_conv1)

    # Second convolutional layer -- maps 32 feature maps to 64.
    with tf.name_scope("conv2"):
        W_conv2 = weight_variable([5, 5, 32, 64])
        b_conv2 = bias_variable([64])
        h_conv2 = tf.nn.relu(conv2d(h_pool1, W_conv2) + b_conv2)

    # Second pooling layer.
    with tf.name_scope("pool2"):
        h_pool2 = max_pool_2x2(h_conv2)

    # Fully connected layer 1 -- after 2 round of downsampling, our 28x28 image
    # is down to 7x7x64 feature maps -- maps this to 1024 features.
    with tf.name_scope("fc1"):
        W_fc1 = weight_variable([7 * 7 * 64, 1024])
        b_fc1 = bias_variable([1024])

        h_pool2_flat = tf.reshape(h_pool2, [-1, 7 * 7 * 64])
        h_fc1 = tf.nn.relu(tf.matmul(h_pool2_flat, W_fc1) + b_fc1)

    # Dropout - controls the complexity of the model, prevents co-adaptation of
    # features.
    with tf.name_scope("dropout"):
        keep_prob = tf.placeholder(tf.float32)
        h_fc1_drop = tf.nn.dropout(h_fc1, keep_prob)

    # Map the 1024 features to 10 classes, one for each digit
    with tf.name_scope("fc2"):
        W_fc2 = weight_variable([1024, 10])
        b_fc2 = bias_variable([10])

        y_conv = tf.matmul(h_fc1_drop, W_fc2) + b_fc2
    return y_conv, keep_prob