Which Diseases Get Mixed Up?

A plant-health app looks at photos of leaves and names the condition. A gardener checked a batch by hand: actual[i] is the true condition of photo i and predicted[i] is the app's answer.

Write confusion_matrix(actual, predicted) that returns a tuple (labels, matrix):

• labels is the sorted list of every label that appears in actual or in predicted;
• matrix[r][c] is the number of photos whose actual label is labels[r] and whose predicted label is labels[c]. Rows are actual labels, columns predicted labels.

The setup provides leaf_photos(n, seed, skill=0.7), which returns (actual, predicted) for n random photos, with conditions "healthy", "blight", "rust" and "mildew".

Examples

Input:  actual    = ["rust", "healthy", "rust", "blight", "healthy"]
        predicted = ["blight", "healthy", "rust", "blight", "rust"]
Output: (["blight", "healthy", "rust"], [[1, 0, 0], [0, 1, 1], [1, 0, 1]])
Explanation: row "rust" has one photo called "blight" and one called "rust";
row "healthy" has one right and one called "rust". The diagonal holds the 3 correct answers.

Input:  actual = ["a", "a"], predicted = ["b", "b"]
Output: (["a", "b"], [[0, 2], [0, 0]])
Explanation: "b" never occurs as a true label, but it still gets a row (of zeros) and a column.

Constraints

• 0 <= len(actual) == len(predicted) <= 10**5
• labels are non-empty strings; there are at most 20 different labels

Goals

• Count every combination of actual and predicted label in a confusion matrix
• Lay out the matrix with actual labels as rows and predicted labels as columns
• Include labels that occur only among the predictions