feat: Graph methods for circuit analysis (part 1)

[DanielKotov]

Create graph description for Ultra Circuit Builder.

The original idea was to create to directed graph for arithmetic circuit, that bases on Ultra Arithmetization.

The constructor creates graph based on blocks for ultra: arithmetic, elliptic, delta range and lookup. In the time of this process gate counter for every variable depends on gate. Also was created algorithm for finding connected components using depth first search algorithm.

Tests from ultra_curcuit_builder were being used for testing the prototype.

summary: there's a constructor for creating graph for Ultra Circuit Builder with additional algorithm for analyzing Circuit.

[github-actions[bot]]

Changes to circuit sizes

Generated at commit: 163db00603fa968ad17c926e17dfbbeba68c0f9d, compared to commit: 86b249022167762fb9558aedf579f5648097592a

🧾 Summary (100% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
rollup_block_merge	0 ➖	0.00%	-12 ✅	-0.00%
rollup_root	0 ➖	0.00%	-12 ✅	-0.00%
rollup_block_root	0 ➖	0.00%	-24 ✅	-0.00%
parity_root	0 ➖	0.00%	-36 ✅	-0.00%
rollup_merge	0 ➖	0.00%	-24 ✅	-0.00%
rollup_base_private	0 ➖	0.00%	-1,476 ✅	-0.05%
rollup_base_public	0 ➖	0.00%	-1,476 ✅	-0.06%
parity_base	0 ➖	0.00%	-36 ✅	-0.12%

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Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
rollup_block_merge	5,057 (0)	0.00%	1,911,809 (-12)	-0.00%
rollup_root	5,041 (0)	0.00%	1,911,795 (-12)	-0.00%
rollup_block_root	4,021 (0)	0.00%	2,857,288 (-24)	-0.00%
parity_root	5,031 (0)	0.00%	3,801,549 (-36)	-0.00%
rollup_merge	3,415 (0)	0.00%	1,909,442 (-24)	-0.00%
rollup_base_private	345,125 (0)	0.00%	3,272,730 (-1,476)	-0.05%
rollup_base_public	345,984 (0)	0.00%	2,314,712 (-1,476)	-0.06%
parity_base	4,298 (0)	0.00%	30,695 (-36)	-0.12%