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Add staged_predict functions to C API #2584

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Mb-NextTime
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I hereby agree to the terms of the CLA available at: https://yandex.ru/legal/cla/?lang=en.

I am adding functions to apply model a trained model and calculate the results for each i-th tree of the model taking into consideration only the trees in the range [0; i).
The Python, R and Command-line versions already have it, but the C API is missing it.

@andrey-khropov
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Looks good to me

robot-piglet pushed a commit that referenced this pull request Feb 8, 2024
@andrey-khropov
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This change has been merged in 0adc70a

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