Language: C++

 #include <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>
#include <vector>
#include <list>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <cctype>
#include <cassert>
#include <climits>
#include <string>
#include <bitset>
#include <cfloat>
#include <unordered_set>
#include <iomanip>
using namespace std;
typedef long double ld;
typedef long long int ll;
typedef unsigned long long int ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<char> vc;
typedef vector<bool> vb;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<ll> vll;
typedef vector<pair<int,int> > vpii;
typedef vector<vector<int> > vvi;
typedef vector<vector<char> > vvc;
typedef vector<vector<string> > vvs;
typedef vector<vector<ll> > vvll;
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define rrep(i,n) for(int i = 1; i <= (n); ++i)
#define irep(it, stl) for(auto it = stl.begin(); it != stl.end(); it++)
#define drep(i,n) for(int i = (n) - 1; i >= 0; --i)
#define fin(ans) cout << (ans) << endl
#define mp(p,q) make_pair(p, q)
#define pb(n) push_back(n)
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define Sort(a) sort(a.begin(), a.end())
#define Rort(a) sort(a.rbegin(), a.rend())
#define MATHPI acos(-1)
int dx8[8] = {1, 0, -1, 0, 1, -1, -1, 1};
int dy8[8] = {0, 1, 0, -1, 1, 1, -1, -1};
int dx4[4] = {1, 0, -1, 0};
int dy4[4] = {0, 1, 0, -1};
template <class T> inline bool chmax(T& a,T b){if(a<b){a=b;return 1;} return 0;}
template <class T> inline bool chmin(T& a,T b){if(a>b){a=b;return 1;} return 0;}
template<typename A, size_t N, typename T> void Fill(A (&array)[N], const T &val){ fill((T*)array, (T*)(array+N), val); }
struct io{io(){ios::sync_with_stdio(false);cin.tie(0);}};
const int INF = INT_MAX;
const ll LLINF = 1LL<<60;
const ll MOD = 1000000007;
const double EPS = 1e-9;

struct edge {
    int to;
    int id;
};


void dfs(vector<edge> &G,int v,int p, int curC,vi &ans,int maxColor){
    int k = 1;
    for (int i = 0; i < G.size(); i++)
    {
        edge nv = G[i];
        if(p == nv.to) continue;//逆流禁止
        //modMaxColorで管理
        //k++としていくことで兄弟間の色も別々にmodMaxColorないで表現できる、しかも親の色に何かを足しているので親の色と同じにはならない
        int nextC = (c+k++) % maxColor;//modでその数以外を表現できるのがかしこい、例えば3以外が欲しかったらk+1mod3とか,今だと親の色以外
        ans[nv.id] = nc;//ここで辺の色とidを順番を結び付けている
        dfs(G,nv,v,nextC,ans,maxColor);
    }
    
    
}

int main(void) {
    int N;
    cin >> N;
    vector<edge> G(N);
    vi ans(N-1,-1);
    
    rep(i,N){
        int x,y;
        
        x--,y--;
        G[x].push_back(edge{y,i});
        G[y].push_back(edge{x,i});
    }
    
    //一番辺が多い奴の辺の数が色の数なので
    int maxColor=-1;
    rep(i,N){
        maxColor=max(maxColor,G[i].size());
    }
    bfs(&G,0,-1,-1,ans,maxColor);

    cout << maxColor << endl;
    rep(i,N-1){
        cout << ans[i]+1<<endl;//0-indexのため
    }
}

Compiler output:
a.cc: In function 'void dfs(std::vector<edge>&, int, int, int, vi&, int)':
a.cc:74:22: error: 'c' was not declared in this scope
   74 |         int nextC = (c+k++) % maxColor;//modでその数以外を表現できるのがかしこい、例えば3以外が欲しかったらk+1mod3とか,今だと親の色以外
      |                      ^
a.cc:75:22: error: 'nc' was not declared in this scope; did you mean 'nv'?
   75 |         ans[nv.id] = nc;//ここで辺の色とidを順番を結び付けている
      |                      ^~
      |                      nv
a.cc:76:15: error: cannot convert 'edge' to 'int'
   76 |         dfs(G,nv,v,nextC,ans,maxColor);
      |               ^~
      |               |
      |               edge
a.cc:66:30: note:   initializing argument 2 of 'void dfs(std::vector<edge>&, int, int, int, vi&, int)'
   66 | void dfs(vector<edge> &G,int v,int p, int curC,vi &ans,int maxColor){
      |                          ~~~~^
a.cc: In function 'int main()':
a.cc:92:14: error: '__gnu_cxx::__alloc_traits<std::allocator<edge>, edge>::value_type' {aka 'struct edge'} has no member named 'push_back'
   92 |         G[x].push_back(edge{y,i});
      |              ^~~~~~~~~
a.cc:93:14: error: '__gnu_cxx::__alloc_traits<std::allocator<edge>, edge>::value_type' {aka 'struct edge'} has no member named 'push_back'
   93 |         G[y].push_back(edge{x,i});
      |              ^~~~~~~~~
a.cc:99:36: error: '__gnu_cxx::__alloc_traits<std::allocator<edge>, edge>::value_type' {aka 'struct edge'} has no member named 'size'
   99 |         maxColor=max(maxColor,G[i].size());
      |                                    ^~~~
a.cc:101:5: error: 'bfs' was not declared in this scope; did you mean 'dfs'?
  101 |     bfs(&G,0,-1,-1,ans,maxColor);
      |     ^~~
      |     dfs