How to set 100% height of a nested table while using DOCTYPE tag?

I have a child table inside the cell of parent table. I want to stretch the child ta开发者_StackOverflow社区ble so that i covers full space in the cell of parent table. Also i need to keep the DOCTYPE tag. Please suggest how to achieve this.

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See - How to set 100% table height in html

This solution will work independent of DOCTYPE