# Chef and Interesting Subsequences Codechef Solution

#### ByBrokenprogrammers

Dec 16, 2022

Hello Programmers In this post, you will know how to solve the Chef and Interesting Subsequences Codechef Solution.

One more thing to add, don’t directly look for the solutions, first try to solve the problems of Codechef by yourself. If you find any difficulty after trying several times, then you can look for solutions.

### Problem

Chef has a sequence A1,A2,…,ANA1,A2,…,AN. This sequence has exactly 2N2N subsequences. Chef considers a subsequence of AA interesting if its size is exactly KK and the sum of all its elements is minimum possible, i.e. there is no subsequence with size KK which has a smaller sum.

Help Chef find the number of interesting subsequences of the sequence AA.

### Input

• The first line of the input contains a single integer TT denoting the number of test cases. The description of TT test cases follows.
• The first line of each test case contains two space-separated integers NN and KK.
• The second line contains NN space-separated integers A1,A2,…,ANA1,A2,…,AN.

### Output

For each test case, print a single line containing one integer ― the number of interesting subsequences.

### Constraints

• 1≤T≤101≤T≤10
• 1≤K≤N≤501≤K≤N≤50
• 1≤Ai≤1001≤Ai≤100 for each valid ii

Subtask #2 (70 points): original constraints

```1
4 2
1 2 3 4
```

```1
```

### Explanation

Example case 1: There are six subsequences with length 22: (1,2)(1,2), (1,3)(1,3), (1,4)(1,4), (2,3)(2,3), (2,4)(2,4) and (3,4)(3,4). The minimum sum is 33 and the only subsequence with this sum is (1,2)(1,2).

### Chef and Interesting Subsequences CodeChef Solution in JAVA

```import java.util.*;
class HelloWorld {
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
int T = in.nextInt();
while(T-- > 0) {
int N = in.nextInt();
int K = in.nextInt();
int[] arr = new int[N];
Map<Integer, Integer> map = new HashMap<>();
for(int i=0; i<N; i++) {
arr[i] = in.nextInt();
map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
}
Arrays.sort(arr);
int m = arr[K-1];
int n = 1;
for(int i=K-2; i>=0 && arr[i] == m; i--) n++;
long count = binomialCoeff(map.get(m), n);
System.out.println(count);
}
}
static long binomialCoeff(int n, int k)
{
long C[][] = new long[n + 1][k + 1];
int i, j;
for (i = 0; i <= n; i++) {
for (j = 0; j <= Math.min(i, k); j++) {
// Base Cases
if (j == 0 || j == i)
C[i][j] = 1;
else
C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
}
}
return C[n][k];
}
}
```

### Chef and Interesting Subsequences CodeChef Solutions in CPP

```#include<bits/stdc++.h>
using namespace std;
long long C(long n, long r) {
long long p = 1, k = 1;
if (n - r < r) r = n - r;
if (n != 0) {
while(r > 0) {
p = p * n;
k = k * r;
long long m = __gcd(p,k);
p = p / m;
k = k / m;
n--;
r--;
}
}else p = 1;
return p;
}
int main() {
long t;
cin >> t;
for (long x = 0; x < t; x++) {
long n,k;
cin >> n >> k;
long long a[n];
for (long j = 0; j < n; j++) {
cin >> a[j];
}
sort(a,a+n);
long long mx = 0;
for (long i = 0; i < k; i++) {
mx = max(mx,a[i]);
}
long long slm = 0;
for (long j = 0; j < n; j++) {
if (a[j] == mx) slm++;
}
long long sm = 0;
for (long i = 0; i < k; i++) {
if (a[i] == mx) sm++;
}
cout << C(slm,sm) << endl;
}
return 0;
}```

### Chef and Interesting Subsequences CodeChef Solutions in Python

```t = int(input())
for i in range(t):
n, k = map(int, input().split())
l = sorted(list(map(int, input().split())))
x = l.count(l[k - 1])
y = l[:k].count(l[k - 1])
a = 1
b = 1
for j in range(x - y + 1, x + 1):
a *= j
for z in range(1, y + 1):
b *= z
print(a // b)```

Disclaimer: The above Problem (Chef and Interesting Subsequences) is generated by CodeChef but the solution is provided by BrokenProgrammers. This tutorial is only for Educational and Learning purpose.

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