I have a set of N chemical compounds enumerated 1, 2,…, N. For each compound, I have the fraction of each of its constituents, “A”, “B”, and so on. Compounds can also contain other compounds, in which case the corresponding fraction is given. For instance, for N = 5, a sample set is

mixes = {
    1: {
        "A": 0.32,
        "B": 0.12,
        "C": 0.15,
        2: 0.41
    },
    2: {
        "C": 0.23,
        "D": 0.12,
        "E": 0.51,
        4: 0.14
    },
    3: {
        "A": 0.24,
        "E": 0.76
    },
    4: {
        "B": 0.13,
        "F": 0.01,
        "H": 0.86
    },
    5: {
        "G": 0.1,
        2: 0.4,
        3: 0.5
    }
}

I would like an algorithm that gives the net fraction of each constituent in every compoound, i.e.

mixes = {
    1: {
        "A": 0.32,
        "B": 0.12 + 0.41 * 0.14 * 0.13,
        "C": 0.15 + 0.41 * 0.23,
        "D": 0.41 * 0.12,
        "E": 0.41 * 0.51,
        "F": 0.41 * 0.14 * 0.01,
        "H": 0.41 * 0.14 * 0.86
    },
    2: {
        "B": 0.14 * 0.13,
        "C": 0.23,
        "D": 0.12,
        "E": 0.51,
        "F": 0.14 * 0.01,
        "H": 0.14 * 0.86
    },
    3: {
        "A": 0.24,
        "E": 0.76
    },
    4: {
        "B": 0.13,
        "F": 0.01,
        "H": 0.86
    },
    5: {
        "A": 0.5 * 0.24,
        "G": 0.1,
        "B": 0.4 * 0.14 * 0.13,
        "C": 0.4 * 0.23,
        "D": 0.4 * 0.12,
        "E": 0.4 * 0.51 + 0.5 * 0.76,
        "F": 0.4 * 0.14 * 0.01,
        "H": 0.4 * 0.14 * 0.86
    }
}

My current approach involves recursion, but I´d like to know if there´s a clever way to do this. Perhaps using a tree-like data structure may help?