list manipulation - Huffman encoding on Mathematica

Taking reference of Huffman code algorithm,

 list={{{{{{}, {{x7, 4}, {1, {{f, 3}}}, {0, {{q, 1}}}}},
    {{x8,9}, {1, {{b, 5}}}, {0, {{x7, 4}}}}}, 
    {{x9,12}, {1, {{e, 6}}}, {0, {{a, 6}}}}}, 
    {{x10,19}, {1, {{h, 10}}}, {0, {{x8, 9}}}}}, 
    {{x11,31}, {1, {{x10, 19}}}, {0, {{x9, 12}}}}}

This is in midway of creating the Huffman code for any string.

x* represents the new node made from two smallest nodes and 4 next to it represents the sum of the frequencies of the two child nodes under it.

Information on structure of list:

{{parent_node,fre1},{code,{{child_node1,freq2}}},{code,{{child_node2,freq3}}}}

freq1 = freq2 + freq3

{{x7, 4}, {1, {{f, 3}}}, {0, {{q, 1}}}}

x7 is parent of f and q

4 = 3 + 1

This unique node(x7) is added in list, sorted and operation repeated again. I am facing problem with creating a final output as Huffman codes for each character, for example, h = 11, a = 00 walking from top to bottom. Final result could be {{h,11},{a,00}} and with other characters.

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