Node Marking Codechef Solution

Node Marking Solution Problem Code: NDMRK

You are given an integer KK and a tree of size NN, rooted at node 11. In one operation, you can either select a node of the tree and color its entire subtree or create a new (uncolored) copy of the given tree. Find the minimum number of operations required so that the total number of colored nodes among all trees is exactly KK.


  • The first line contains an integer TT, denoting the number of test cases. Then TT test cases follow.
  • For each test case, the first line contains two integers NN and KK, the size of the given tree and the number of nodes to be colored, respectively.
  • The next line contains N−1N−1 integers p2,…,pnp2,…,pn, where pipi is the parent of node ii.


For each testcase, output a single integer: the minimum number of operations required to color exactly KK total nodes.


  • 1≤T≤4001≤T≤400
  • 1≤N≤5⋅1041≤N≤5⋅104
  • 1≤K≤1031≤K≤103
  • 1≤pi≤N1≤pi≤N
  • The input describes a valid tree rooted at node 11
  • The sum of N⋅KN⋅K over all test cases does not exceed 107107


  • Subtask 1 (10 points): The tree is a simple path
  • Subtask 2 (35 points): 1≤N,K≤2001≤N,K≤200 and the sum of N⋅KN⋅K does not exceed 4⋅1044⋅104
  • Subtask 3 (55 points): Original constraints

Sample Input

3 5
1 1
4 6
1 2 2

Sample Output



For the first test case:

  • Operation 11: The subtree of node 11 is colored (coloring a total of 33 nodes).
  • Operation 22: A new copy of tree is generated.
  • Operation 33: The subtree of node 22 of the new tree is colored.
  • Operation 44: The subtree of node 33 of the new tree is colored.

For the second test case:

  • Operation 11: The subtree of node 22 is colored (coloring a total of 33 nodes).
  • Operation 22: A new copy of tree is generated.
  • Operation 33: The subtree of node 22 is colored (coloring a total of 33 more nodes).


#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/detail/standard_policies.hpp>
#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")

using namespace __gnu_pbds;
using namespace std;
typedef tree<int,null_type,less<int>,rb_tree_tag, tree_order_statistics_node_update> indexed_set;

#define ll long long int
#define fo(i,n) for(i=0;i<n;i++)
#define f0(i,k,n) for(i=k;i<n;i++)
#define fr(i,k,n) for(i=k-1;i>=n;i--)
#define Fo(i,k,n) for(i=k;k<n?i<n:i>n;k<n?i+=1:i-=1)
#define si(x) scanf("%d",&x)
#define sl(x) scanf("%lld",&x)
#define ss(s) scanf("%s",s)
#define pi(x) printf("%d\n",x)
#define pl(x) printf("%lld\n",x)
#define ps(s) printf("%s\n",s)
#define setbits(x) __builtin_popcountll(x)
#define endl '\n'
#define deb(x) cout << #x << "=" << x << endl
#define deb2(x,y) cout << #x << "=" << x << "," << #y << "=" << y <<endl
#define pb push_back
#define mk make_tuple
#define F first
#define S second
#define lb lower_bound
#define ub upper_bound 
#define MI INT_MIN
#define MX INT_MAX
#define gcd(x,y) __gcd(x,y)
#define all(x) x.begin(), x.end()
#define clr(x) memset(x, 0, sizeof(x))
#define sortall(x) sort(all(x))
#define tr(it,a) for(auto it = a.begin(); it != a.end(); it++)
#define PI 3.145926535897932384626
#define inf 1e18
#define sp(x,y) fixed<<setprecision(x)<<y   
#define fast() ios_base::sync_with_stdio(false);cin.tie(NULL)
typedef priority_queue<int, vector<int>,greater<int> > pqri;
typedef priority_queue<ll, vector<ll>,greater<ll> > pqrl;
typedef priority_queue<int> pqi;
typedef priority_queue<int> pql;
typedef pair <int,int> pii;
typedef pair <ll,ll> pll;
typedef vector <int> vi;
typedef vector <ll> vl;
typedef vector <pii> vpii;
typedef vector <pll> vpll;
typedef vector <vi> vvi;
typedef vector <vl> vvl;
typedef stack <int> sti;
typedef stack <ll> stl;
typedef queue <int> qi;
typedef queue <ll> ql;
typedef map<int,int> mpi;
typedef map<ll,ll> mpl;

const int mod = 1'000'000'007;
const int N = 3e5, M=N;

int p=1;

ll pw(ll n,ll a)
    ll ans = 1;
        ans = (n*ans)%mod;
        n = (n*n)%mod;
    return ans;
ll modInv(ll n, ll p) 
    return pw(n, p - 2); 

bool prime[10000001];
int call[10000001];
void Sieve(int n)
    memset(prime, true, sizeof(prime));
    for (int p = 2; p * p <= n; p++)
        if (prime[p] == true)
            for (ll i = p * p; i <= n; i += p)
                prime[i] = false;

    for(ll i=2;i<=n;i++)
    else call[i]=call[i-1];

void google(){
    ll i,j,k,m,n,x,y,z,mi,mx,count=0,ans=0;
    cout<<"Case #"<<p<<": "<<ans<<endl;
void solve(){
    ll i,j,k,m,n,x,y,z,mi,mx,count=0,ans=0,sum=0;


int main() {
    // Sieve(10000000);
    int t = 1;
    while(t--) {

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