Day 25

2 files changed, 1388 insertions, 9 deletions

diff --git a/2023/inputs/day_25.txt b/2023/inputs/day_25.txt
new file mode 100644
index 0000000..fcc1f16
--- /dev/null
+++ b/2023/inputs/day_25.txt
@@ -0,0 +1,1244 @@
+ncx: ncb zdz zlz pcj
+mrt: rjs
+mrq: bvd
+mrk: zsg ksb cml hqh
+zhx: rdv
+jxx: vcv
+zrx: zss ngj mph fcm zlk
+mhk: bnf pcb hjk vxf
+lmc: nhr slp ltz mzl ddm
+lfb: npj xxj zzs zrz
+zxf: fnz
+kpq: rtq kjs kdr
+rgr: cpx xlc slp
+frp: cpx xfc
+ntr: xtb
+vtl: sht cfl lxr knj
+cjj: vkh rmz
+xtz: jpp cjj zpf
+bcs: snl kkm rfk xgt
+rcx: bvd ntx pgg fbm
+bgk: mtg
+fqx: jbh hzz gvp pgv
+tks: cln vcl
+klh: pfh
+jmk: mgn nvg
+dsz: pjj mlx
+jxr: lsf mph
+gbg: mdn
+zmg: vbt cjv mqj cpf
+lmq: mtg hlx qtn
+vcd: qcj ksb mkg
+xhl: xpt xtv tmc
+dzn: qkp
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+rvm: fhm fnq hlx vrb zbx
+xgx: svg
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+sdx: vxx vqq
+tbl: ntr
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+fvd: ngp gxp xfs ljj bbg
+grc: pmz mvk slp bxb txr
+ppf: gdx gxp bkp qfp vdv
+mqd: src
+dnk: ldx jpg pxs kts
+brk: xpp
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+dhs: thl rtq kls
+tzp: jmk
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+zpx: gnk
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+zql: kfm tqj qfx
+rsb: gqv
+hfq: mlx vrb pjm qdr
+xhp: gzg vbk jnj
+cbc: hbz hhp mgn bxd
+nmf: tft qmx bsq hqv
+gsb: zss vsx
+ljg: qbj xmf
+xqs: rfg tvz zfr
+xgc: qtn pfh brc vrv
+frn: lmh qxg vxx
+vlv: dbc jbt
+tck: pgx tgn xjc
+nxz: mjl vdz njc rkv
+zgv: ldh mxn tns
+bhk: kgj frp rdv vxx
+qhj: pdh
+dbv: ltp bxj tgx
+mkp: hqz htf bvq qzj
+gjj: pcj xms xtb
+ltp: krt
+bcn: xbz qmj pjm
+lvs: tzx gnx nmq zsj
+djb: pxc
+rhh: xrp qnn tqj rmn xmc
+vtp: jvf chz
+pct: pzn
+dls: fqb xxj vhf
+hpp: qpr chz xtb prx
+rtq: jbt
+fbr: hbd zhp tnh jrm
+zlk: rmn vhp
+fqv: lfx
+qqd: fnz pzn rlm fqb
+npc: vjb
+zrt: vjp
+jkn: bll xhh
+thd: szj ckr flh lfx hmf
+mhx: hgf
+jfs: zfv mmb bqf
+ltz: tjk tdb dbj
+hgj: psp ttg
+dbc: tjq xbb
+lpx: qvf mnz qzz jpg
+vmh: tnr fnq lhx
+kbx: dvd xtd hrf xfs
+pxd: rrr fsk nxq xpf
+hjg: hxp jrp
+mms: cgs slt dfl
+kbh: gnk qtm njp jhz
+vmz: zxf hbs grs
+cqq: xvp pxc
+xhz: ngg sgn dgm
+qmj: lll
+jjk: vgc nfs
+ptz: txz
+xpc: gpt ccn bnx
+gpx: sht smj
+bxz: mrt
+kcm: msn fzg
+gdd: qtm
+rkp: kcx rdv fpj mrq bts
+fhm: vst qpx nvv
+qpf: jtl kqd mvt fvb
+lxd: rsd jtg
+kbc: zlp vgc
+rrl: fql mdz bdh
+xnn: xtv pkp
+lfk: tnr krx mrp
+vqm: cbj
+mpx: qbn ljm
+xln: lqc zqv bfb
+zkn: dff
+vdz: bkx
+srv: gpm cps vdv
+bkk: rvd shh mvk zbr prd gfb
+pql: ptl
+bvl: nmq svn mlx
+rjc: vgb htf
+tnh: ccn
+kgh: ldb
+zlc: jfz
+qlx: mkq lcr ckr
+hxt: zsb zzs zqq
+xhc: xfc
+rkk: pzx fkp gnt svj
+vbx: vgb gxj pgg ckr sbd
+gmg: drh ngg sht skk fcm
+nrj: bnx dzj
+fxn: zxt fhg qmx jmz lkg
+tdv: mss zck
+hrq: qnt xms vfx
+gnx: ttq
+nnx: zqp dqb xpz sxc
+tpc: krh hbs tnl qzx msh
+mnt: dfz bdh pxf
+ksp: jgr
+dqb: vdv zns
+gnn: snc gkh
+tdl: njp vgc
+pkb: qmj
+qgb: qht xsm pzx gld
+gsf: npj ldx tvz
+bvt: pct gzj vdc rbg jxq snm
+phr: nmb
+prd: hpt sff hbm pqd zkn
+npb: xrv
+psr: sbj dxp
+jxc: pkb lcj qhj czg
+hgf: mbf
+srt: pxt dgm jbc zlc
+vjb: hbq lfx
+xdm: mxp rlm
+gzb: fcz
+hmj: pbd ckv ldx xfr
+xxl: mhx
+mfx: zpd ppv zbr
+mcb: lgt vmr mpx cbc chf
+bxj: krk bpz
+jls: fbm vff vgb nzf jfc hxp
+tnl: gvz dnx dfg pdh
+lxt: msn
+gsl: qfp
+xfr: frl
+tfx: jgp
+jhx: vvc mxp
+qgl: pch
+mtv: cqq
+vts: bvd gpf
+lkq: czg kts bgl
+ndb: gfb
+lkv: qhl gqp dqp fmj
+zsd: smv mhg hqf fgn
+xzn: qth vfx
+chn: hsr
+hzs: qvs qnm vml
+csc: qxg xsz
+cgf: tlh dgz
+tvz: njs
+xdc: brk hgf vhr frh
+htr: sxr
+btv: bql qhh dqm
+hzt: qsg
+tpx: gfb
+ppz: htr rlm gch lqc
+fbd: ddd vtl vfx pch
+zps: vnc mhg
+qtr: zrz rmz
+hlg: pfb flp fjp mqx
+ksb: mbf
+zds: mvk hjg jrg
+jfg: qfb xdb
+ldj: ldb ldk qcn hbq
+dbn: mqv jhz rgx dlt
+kcc: tnh
+zrn: vsx ptf lrf hrr
+plz: rvr qbn tcr lks xdb
+ljj: djb hnz qgk
+vxf: hbt
+znr: qgk
+kqx: hzz lmq mzn
+vqq: ztg plt
+jkg: mzl fxm ppv
+kmh: pqn rfc nmb npb
+rnh: tsh bll szt
+rlp: bgk qxx mzn qtn gcb
+xpz: krc slp nnc
+dxx: jfs cqj pdp
+gdr: cds cpf mss
+svb: bkc zsg
+qfx: zss fnq hdv
+vrr: rkn xhl jlx xdm pct
+ckv: tbl
+ddp: zlj qgj snl
+pkv: xlc
+jtd: qkp
+mpl: qxg frn bkx
+msp: dpg tpx gnt lkv
+bgr: kqx mpt dsz zpf
+flp: fqm ggm lgt
+hqf: pmc gnz jch
+dmp: krk zlq dqd rzq
+gft: lcm thl
+lrf: lkh qsg znd gvx pnv
+vhq: zkt qgq sxv
+gzg: zfv qhl
+jbh: cck xgf vcv qhp qzz
+lkr: xtv dlt ksp
+ndf: fql zqp tqk
+ldt: mjr vmb
+vrv: rtk
+nbp: rzp sht kjv
+rlk: sdx rpb pkv tdb
+vrj: zjr jjc ktq fsc
+pft: lmj xfs
+xfs: pmh
+zns: dgs ztg gcc
+rkv: fgl zrt bkc vxk
+pvk: gcs kzf dbr
+mjl: tzn ghn fgl
+xrv: pxz lbp pnm
+ksr: czh rdv kgj hnz
+bpc: hzt hjj
+prq: fcm jlz
+hvx: vxz qmx tzx znj
+vvb: tns
+blb: rsd thd vxk
+njt: thv klh
+jff: jpp gpz mng ngg
+zzn: xsm nvg zsg glh
+xpm: clh skk
+klc: ddd
+crl: src pml
+lcr: jtl bvd
+hrl: zbv ndb gpl crz
+gxk: xfb
+hhm: cjg kgj cjl
+cfb: rxb cxn zff djg nzf mbn
+dzz: qpb btm fqv cjx
+fbk: qgn dpg tnh
+snm: qtm
+rkn: dtk hxv bgg cfl
+jln: qgk zhh qkr fmj
+kht: dgs gpl cln xtn nhr qfp
+htb: bnr ncb rlm jtr xhh
+bvf: tzx qlz ptl gpp
+xvp: hrf
+hdv: fht
+qqn: nvg kjs rrm
+fkz: mqd svg
+qqt: ntx gpm srg tpf fdr
+xxd: zxt fzg
+dsc: zng gpx zkk kjz
+smj: mss
+njs: rsc npj
+nmp: zkn xfb zhr
+zfv: hnz tzp vjb
+nvd: mmt ljm hqz vqm
+vgh: tzp fqv rtc mtj zds
+zsb: gpp
+rjz: lkl
+khl: qkp vml mjr gkh
+qkn: bbr mng pmc
+mxm: gsf zpt sdq rnc
+chh: prz jjq dqm shc qpt
+mnz: pdf
+znj: kqv
+dmj: zdz psv gzk vcv pfh
+lqb: bql jbt vmc
+dhq: kdr htk gtn fsc
+czq: jtl
+jfz: zrz
+rxb: rpb nhl
+vqg: rxz vcx cbn tjz
+gls: lmh qcb jsx ndf lbp
+jvf: fhg pdh
+lnr: gqp ktq smb plt
+sqm: gtn kmn sbk djg qhm vvb
+nbf: vkh dtb qhf xxd
+fpd: ltc szj shd
+cdz: xgl brq njv xmc
+rfg: jfp
+lxq: nfl cmp mtj bxb
+vkl: sbd qzj ddp
+zqp: szj txz qkr
+fxk: jlb htk mtf
+xpt: bhx
+bks: jrp zsm plt
+qmv: xgx jtd bpp ntx
+lgr: dgs tns jln grc
+gpl: fqm qcb xfp
+tgr: nxn qgn
+sbj: fcz pfh
+blm: hjg
+vcg: ggd cpx phr njc
+xjm: djb xjx zjr lxd vxk
+sjv: ndb fds vjp
+xgt: gcg srg
+qbj: qnm slp
+lmg: krx cjg ldk rrm
+zbx: qvj zng qvf
+qvj: dqd qkc vjf
+lmk: lkr ctf
+mqj: snm crh qdr
+bmr: gff vxx bkc
+rbb: gdj xhz jgr
+bxd: zht
+djk: ffz ssd pkv zxv
+nxq: gkd dzn rgr
+fds: gxp
+hkh: gsv mss
+kxx: rsc
+rvd: jqq kkj rrr
+lnp: mhx nqh xtc pmh
+jll: tsh dfl zmz
+rjp: cmp rhz nnd snc
+cfl: mhg
+ttd: crq ttr nnb dqd ncb nts
+psp: psf
+vpc: bvl krh lnn tnv rjs
+stm: rjz vdz gxk nzf
+nvv: mxg
+cjx: vxx pkv
+nnc: fbm xxl
+kkj: xkd
+xtv: vjf mxp
+vjl: hlx
+rdj: vnh mhs hdk gzj
+dvd: rgb kmk
+xhb: cdd mtq hhp bkx
+rtc: phr qxg lcm pcb hbt
+fzv: vmz mlx gcs gnx
+jkj: dds rvr gjz
+fpx: hmj vtp ldx nvv gdd
+gjr: qxx zck lqc bfb
+hrr: rfg kmf
+lmh: hnz rdd
+zmb: zdz gnz
+zpf: ntr
+xpf: vfm rvr
+zhh: rdd
+tft: qll pxs xkp mqj
+ddd: zjd dtk
+csd: tjb dxp jnb jhz
+jpx: kqd cmp mtv nrj
+vll: nqh src
+ttq: xnk sbj
+vsx: qsx
+ffz: tgr tht pml pck
+tqj: qtn
+ngg: npj
+qpv: lkd tkh
+chf: bnf rpt
+cxn: xfp qbn dvd zkn hkr
+kps: stb klh drh qqm gdj
+hjp: sqs gft hbq kbx
+clh: zdh
+jmz: bpz
+lrg: xgm jlx vjl klc
+htf: mzp
+rbg: ftt qsg rzp
+tgx: vbz
+bnc: kmg zmh pdf qjx
+fgn: vbv rsx fsv
+nvs: jbt
+dpl: jfz
+gcz: vvb ldp
+fqg: pzv
+bxr: qth
+fdz: dvd vqq gpm
+dsh: mts dpc pjj tfd
+jjc: ldh vjp
+jvs: kcc src tcr zvz
+lgt: cbj
+psd: shd kmk
+mjt: rmz xpn xqs
+nqj: qnt fzg vhp tbl
+fdf: sdv ldh
+gmr: jkg ggd zvp
+lng: fqn ggm bnx tmm
+pqn: vrm hls pdm
+tnr: dgm
+dcb: zfr tqx lrc ptl jjk fzg
+ngp: hbt xkd
+hxp: znr
+tqn: ndz tvf xpt ztk
+pbq: tgn tlh cqr
+pmz: vjn mzp dzn
+snf: vqt
+rhz: dfz lhj rdd
+prb: dbp fcz
+bgt: cpl tqk cqq
+xlt: ldb xfc ljj
+qdc: vgc vkh rsx spp
+jtr: brs hzz
+dpq: lkd thl rjz
+hmc: jjz rgb
+qqm: jlz cpt zcs
+mxp: xjc
+tjq: vmr xfp
+stz: dhb rsb
+zdm: bpv
+dzl: zff pnz njh zjl
+nkj: scs lll lzl vng
+trk: mbp cgb shh
+qlz: gcb
+mbk: rsx vxz rms
+zfr: zdh
+nts: rtk kxr
+qvm: pxz kkj fbm rrm
+bkx: jgp
+vmx: mvt dpq mqd dxx
+mch: xfp fgv vlv vmx jtl
+fph: svn zss pch
+ngv: nsj rdr mng hxt lnn
+bct: nvs fdr dfz qlf pbk pvh
+sdc: lfh czq fgv nnc
+lfh: glh xpp pck mnt
+kkk: vrv pvk bnc stz
+mzv: nxb
+bqp: nvs vlm plz
+dff: mvt
+gpp: xpn
+krt: vjf zbk
+qbf: fzq mtv dhs qdx xpp
+vxd: vcl psp flh
+hlt: nfl mmk rzl pxc gqg
+shc: kpq rlj bdh
+mjr: jlb
+kmg: pct gxx
+kmn: fkr cgb
+kmf: slt
+tct: zlv qvs jkg
+jhb: cjl zsm
+bqf: cpl ptz
+stg: xhj csc ghn
+dkl: qst ppx tlh
+klx: rdr
+vjq: dlt jxq xpm
+gvx: ppm qvf jch fhg mph
+xpb: zss gzb
+qrc: jvf klx gpz
+qmb: cll
+bjx: pzn qzm
+mpt: pct ndz hvj
+bdb: grs hzt hqv
+tzx: dpl
+zqx: kxr dxp hkh
+vvs: srd xjx flp dqh
+hfb: dfz hsr trk rgn
+qht: nvj hjd
+hhj: kxx vqt bsq vcv dbp
+plt: tkh
+mgr: hpt jvx xxs
+hqv: kxx pbd
+ggc: tcx cns bhx
+qmx: dfg gxx zlp
+fnt: zhh pxf lfr kgh
+pfc: gnk xnk zsj vbz
+cgn: kqd gcd
+gcs: ntr
+zlv: zgj hrf pvh npc ttg
+gcc: ggd
+ssr: zpf zbj bqz qch
+svn: rsc qtm
+lkg: fnq mrt
+rbd: dqj mtq vxd gtf
+shz: bqz xrb mxg
+cdd: ghn lfc ddq
+nzf: mqd
+bbr: jvf
+jpm: mkz zvg dcb smj
+vff: nvs qmb pqd mtf
+gvp: xgf klc spk
+nhq: nnn sbr tmz khm bpz
+tfd: ngj xdm
+rkj: dfl zqx svn dbv xln
+gbs: knj zrq
+btm: zfl
+nnd: jsh
+lnt: mtg tdj mrs hvh qxs
+jvx: snl
+scs: rsb pjm zbk llz
+qxh: mhx bgt
+gqv: zbk
+qnt: dlt bxj kpv qlz ttc
+tlb: nvg
+njd: mpx ckr
+qzn: mhj qzx bfb
+rnq: gbs znd pql
+brq: tdv jkn bsz
+djg: hqc
+hdk: gdd rtk
+mzc: xjc vsx
+kqd: ldb
+vnh: mpj vkh drh lxg pql
+qhm: pkv jmk jfv vrf
+xhj: rgn
+tqx: lsf
+htq: pkp vbz cpt qrc vsv
+nhd: pdl hzc mgj
+vkh: vnc zrq
+bqm: kjc zfr vng zrq
+gsv: jfz krx fnz
+zst: gdx ctb tzn
+vls: cpt
+psf: fbt
+lkk: gsl xdb lcm rqj
+rhr: lnm ccn rrl
+tjf: bgg bhx xpm hrq
+krh: mcm zkk vhf
+bsq: tqj
+pnr: gmk hvj nsj
+xmm: vxf czh gpt
+nvk: mrs
+nkz: cgb dzz bnx rjz
+tkh: cjg
+ftf: mkz smv brs jhx
+fqm: gxv
+gmt: gkn hzz
+lhx: zmv
+hmr: ldp mxn pzx xkc
+fxs: nts vqt mzc
+ghv: npb jgg hpt dbj
+fpq: jvp njs rlm nnn
+svf: hkr kcc mzv rjp xrv
+czr: kfr ffs dfg
+pnm: jnj
+gfb: gkd mqd
+rzl: bkp jtg lcr
+pqd: vts vxd
+mkc: jtd fdl npc lmj
+nzv: bql hgf dqm xmf
+dfz: bxd
+zqk: pfh qbs
+bql: lvt cpx
+zbv: ldp bmr mqd xkd
+tjg: pxf tlb psd xtd
+qgj: gtn
+btg: sfx jjz dkc mpl qfg
+xmh: gmk mjt mpj grs
+rqk: msg mfd ptl prx
+krc: srv lfh kcc
+sqs: cpl crl
+txr: ggd
+lqf: zjd qch jcg mjg
+gtf: ckl vmc pgp
+tfl: hfh rzq vbv mxk crq
+bkv: fnt zst nxn fqg
+mqs: pct zbx gnk krh ckv
+sbd: fmd
+qvh: fph kms zmv
+tvf: tlb
+mrr: ttg vzv gmr jgg zvz gcz
+dxp: kbc
+bzp: hhp tcz
+rqm: tpx gcc ntx xfs
+nms: qfb xhc
+knd: tfx tvf mbp xhp
+hkq: tnj npc sqc
+pgv: vbz
+vzh: gqv rhj vjc cgf
+ppv: vfm
+sbv: shd mvk tgr
+dhb: hbs zqv
+jpg: ngc
+rsq: zmx cjv bnr hvx
+lnm: hhp
+xxj: grs qsx
+gtv: bvc qpb qxc ndf
+rfc: htk mzp bpp qdx
+nvj: ljg drj tmv
+sxr: rdr zbj
+mcr: hzc dzj
+ldg: xhj kdr mtq rbf
+bxk: jzm njp dhb vdc
+nmq: lhx qch
+ktj: fkp mmt gcc
+dfs: jfp jkn qzm qbs qhf chg
+skh: ltp rtk vfx gmt
+bft: tdj rfg jcg jgr
+hxv: zzs ttc
+vrf: hpt fvb
+tbb: rqj cjx fkz mtv
+grj: pmh jfv hbd rxb
+svk: fbt nlg rhx jfr hmf
+nxg: cpl zff
+xnk: vcv jnb
diff --git a/2023/src/bin/day_25.rs b/2023/src/bin/day_25.rs
index b3a610b..7bd3751 100644
--- a/2023/src/bin/day_25.rs
+++ b/2023/src/bin/day_25.rs
@@ -1,19 +1,154 @@
-use nom::IResult;
-use std::fs;
+use nom::{
+    bytes::complete::tag,
+    character::complete::{alpha1, line_ending, space1},
+    combinator::map,
+    multi::separated_list1,
+    sequence::separated_pair,
+    IResult,
+};
+use std::{collections::BTreeMap, fs};
 
 fn main() -> Result<(), Box<dyn std::error::Error>> {
-    let input = fs::read_to_string("inputs/day_2.txt")?;
-    let parsed = Example::parser(&input).unwrap().1;
-    dbg!(&parsed);
+    let input = fs::read_to_string("inputs/day_25.txt")?;
+    let parsed = Circuit::parser(&input).unwrap().1;
+    let three_cut_partition_sizes = parsed.find_non_zero_three_cut_partition_sizes();
+    dbg!(&three_cut_partition_sizes);
+    dbg!(three_cut_partition_sizes.0 * three_cut_partition_sizes.1);
 
     Ok(())
 }
 
+#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
+struct VertexId(usize);
+
 #[derive(Debug)]
-struct Example;
+struct Circuit {
+    wires: Vec<Vec<VertexId>>,
+}
+
+#[derive(Debug, Clone, Eq)]
+struct Edge {
+    a: VertexId,
+    b: VertexId,
+}
+
+impl PartialEq for Edge {
+    fn eq(&self, other: &Self) -> bool {
+        (self.a == other.a && self.b == other.b) || (self.a == other.b && self.b == other.a)
+    }
+}
+
+impl Circuit {
+    fn parser(input: &str) -> IResult<&str, Self> {
+        map(
+            separated_list1(
+                line_ending,
+                separated_pair(
+                    map(alpha1, |s: &str| s.to_owned()),
+                    tag(": "),
+                    separated_list1(space1, map(alpha1, |s: &str| s.to_owned())),
+                ),
+            ),
+            |vertices| {
+                let mut vertex_id_mapping = BTreeMap::new();
+                let mut wires = Vec::new();
+
+                for (from, tos) in vertices {
+                    let from_id = vertex_id_mapping
+                        .entry(from)
+                        .or_insert_with(|| {
+                            let new_id = VertexId(wires.len());
+                            wires.push(Vec::new());
+                            new_id
+                        })
+                        .clone();
+                    for to in tos {
+                        let to_id = vertex_id_mapping
+                            .entry(to)
+                            .or_insert_with(|| {
+                                let new_id = VertexId(wires.len());
+                                wires.push(Vec::new());
+                                new_id
+                            })
+                            .clone();
+                        wires[from_id.0].push(to_id);
+                        wires[to_id.0].push(from_id);
+                    }
+                }
+                Circuit { wires }
+            },
+        )(input)
+    }
+
+    fn find_non_zero_three_cut_partition_sizes(&self) -> (usize, usize) {
+        let cut1s = self.edges_to_traverse_everything([]);
+        for (cut1i, cut1) in cut1s.iter().enumerate() {
+            let cut2s = self.edges_to_traverse_everything([cut1.clone()]);
+            for (cut2i, cut2) in cut2s.iter().enumerate() {
+                if cut1s[0..cut1i].contains(&cut2) {
+                    continue;
+                }
+                for cut3 in self.edges_to_traverse_everything([cut1.clone(), cut2.clone()]) {
+                    if cut1s[0..cut1i].contains(&cut3) || cut2s[0..cut2i].contains(&cut3) {
+                        // if (cut2, *) didn't work, then (*, cut2) also wouldn't work.
+                        continue;
+                    }
+                    let (size1, size2) = self.partition_sizes([cut1.clone(), cut2.clone(), cut3]);
+                    if size2 > 0 {
+                        return (size1, size2);
+                    }
+                }
+            }
+        }
+        panic!("No partitions with three cuts");
+    }
+
+    fn partition_sizes(&self, cuts: [Edge; 3]) -> (usize, usize) {
+        let mut visited = vec![false; self.wires.len()];
+        let mut frontier = Vec::new();
+
+        visited[0] = true;
+        frontier.push(VertexId(0));
+        let mut visited_count = 1;
+
+        while let Some(from) = frontier.pop() {
+            for to in &self.wires[from.0] {
+                let edge = Edge::new(from, *to);
+                if !cuts.contains(&edge) && !visited[to.0] {
+                    visited[to.0] = true;
+                    visited_count += 1;
+                    frontier.push(*to);
+                }
+            }
+        }
+
+        (visited_count, self.wires.len() - visited_count)
+    }
+
+    fn edges_to_traverse_everything<const N: usize>(&self, cuts: [Edge; N]) -> Vec<Edge> {
+        let mut visited = vec![false; self.wires.len()];
+        let mut frontier = Vec::new();
+
+        visited[0] = true;
+        frontier.push(VertexId(0));
+        let mut used_edges = Vec::new();
+
+        while let Some(from) = frontier.pop() {
+            for to in &self.wires[from.0] {
+                let edge = Edge::new(from, *to);
+                if !cuts.contains(&edge) && !visited[to.0] {
+                    visited[to.0] = true;
+                    used_edges.push(edge);
+                    frontier.push(*to);
+                }
+            }
+        }
+        used_edges
+    }
+}
 
-impl Example {
-    fn parser(_input: &str) -> IResult<&str, Self> {
-        todo!()
+impl Edge {
+    fn new(a: VertexId, b: VertexId) -> Edge {
+        Edge { a, b }
     }
 }