# Length of Smallest Subsequence such that sum of elements is greater than equal to K

Given an array **arr[]** of size N and a number K, the task is to find the length of the smallest subsequence such that the sum of the subsequence is greater than or equal to number K.**Example:**

Input:arr[] = {2, 3, 1, 5, 6, 3, 7, 9, 14, 10, 2, 5}, K = 35Output:4

Smallest subsequence with the sum greater than or equal to the given sum K is {7, 9, 14, 10}Input:arr[] = {1, 2, 2, 2, 3, 4, 5, 4, 7, 6, 5, 12}, K = 70Output:-1

Subsequence with sum greater than equal to the given sum is not possible.Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the

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**Approach:**

- This problem can be solved with the help of priority queue
- Traverse input array and insert every array element into priority queue.
- Initialize variables that holds the sum of picked element from priority queue and the variable to get the count of picked element from priority queue to 0
- Pop the elements out from the priority queue until the priority queue is not empty
- Add the element into the
**sum** - Increase the count because the element is picked to contribute to the total sum
- Check if the
**sum**is greater than the given number**K**, If yes then stop checking and output the count.

- Add the element into the

Below is the implementation of above approach.

## C++

`// C++ implementation to find length of smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K` `int` `lengthOfSmallestSubsequence(` `int` `K, vector<` `int` `> v)` `{` ` ` `// Initialize priority queue` ` ` `priority_queue<` `int` `> pq;` ` ` `// Loop to insert all elements into` ` ` `// the priority queue` ` ` `for` `(` `int` `i = 0; i < v.size(); i++) {` ` ` `pq.push(v[i]);` ` ` `}` ` ` `int` `sum = 0, count = 0;` ` ` `// Loop to find the smallest` ` ` `// subsequence such that sum of elements` ` ` `// is greater than equal to given number K` ` ` `while` `(!pq.empty() && sum < K) {` ` ` `sum += pq.top();` ` ` `pq.pop();` ` ` `count++;` ` ` `}` ` ` `// If sum is less then K` ` ` `// then return -1 else return count.` ` ` `if` `(sum < K) {` ` ` `return` `-1;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `int` `main()` `{` ` ` `vector<` `int` `> v{ 2, 3, 1, 5,` ` ` `6, 3, 7, 9,` ` ` `14, 10, 2, 5 };` ` ` `int` `K = 35;` ` ` `cout << lengthOfSmallestSubsequence(K, v);` ` ` `return` `0;` `}` |

## Java

`// Java implementation to find length of smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K` `import` `java.util.*;` `class` `GFG` `{` `// Function to find the smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K` `static` `int` `lengthOfSmallestSubsequence(` `int` `K, ` `int` `[]v)` `{` ` ` `// Initialize priority queue` ` ` `Queue<Integer> pq =` ` ` `new` `PriorityQueue<Integer>(Collections.reverseOrder());` ` ` `// Loop to insert all elements into` ` ` `// the priority queue` ` ` `for` `(` `int` `i = ` `0` `; i < v.length; i++)` ` ` `{` ` ` `pq.add(v[i]);` ` ` `}` ` ` `int` `sum = ` `0` `, count = ` `0` `;` ` ` `// Loop to find the smallest` ` ` `// subsequence such that sum of elements` ` ` `// is greater than equal to given number K` ` ` `while` `(!pq.isEmpty() && sum < K)` ` ` `{` ` ` `sum += pq.peek();` ` ` `pq.remove();` ` ` `count++;` ` ` `}` ` ` ` ` `// If sum is less then K` ` ` `// then return -1 else return count.` ` ` `if` `(sum < K)` ` ` `{` ` ` `return` `-` `1` `;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `[]v = { ` `2` `, ` `3` `, ` `1` `, ` `5` `,` ` ` `6` `, ` `3` `, ` `7` `, ` `9` `,` ` ` `14` `, ` `10` `, ` `2` `, ` `5` `};` ` ` `int` `K = ` `35` `;` ` ` `System.out.print(lengthOfSmallestSubsequence(K, v));` `}` `}` `// This code is contributed by Rajput-Ji` |

## Python3

`# Python3 implementation to find length of smallest` `# subsequence such that sum of elements` `# is greater than equal to given number K` `# Function to find the smallest` `# subsequence such that sum of elements` `# is greater than equal to given number K` `def` `lengthOfSmallestSubsequence(K, v):` ` ` ` ` `# Initialize priority queue` ` ` `pq ` `=` `[]` ` ` `# Loop to insert all elements into` ` ` `# the priority queue` ` ` `for` `i ` `in` `v:` ` ` `pq.append(i)` ` ` `pq.sort()` ` ` `sum` `=` `0` ` ` `count ` `=` `0` ` ` `# Loop to find the smallest` ` ` `# subsequence such that sum of elements` ` ` `# is greater than equal to given number K` ` ` `while` `(` `len` `(pq) > ` `0` `and` `sum` `< K):` ` ` `sum` `+` `=` `pq[` `-` `1` `]` ` ` `del` `pq[` `-` `1` `]` ` ` `count ` `+` `=` `1` ` ` ` ` `# If sum is less then K` ` ` `# then return -1 else return count.` ` ` `if` `(` `sum` `< K):` ` ` `return` `-` `1` ` ` `return` `count` `# Driver code` `v ` `=` `[` `2` `, ` `3` `, ` `1` `, ` `5` `,` ` ` `6` `, ` `3` `, ` `7` `, ` `9` `,` ` ` `14` `, ` `10` `, ` `2` `, ` `5` `]` `K ` `=` `35` `print` `(lengthOfSmallestSubsequence(K, v))` `# This code is contributed by mohit kumar 29` |

## C#

`// C# implementation to find length of smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K using System;` `using` `System;` `using` `System.Collections.Generic;` `using` `System.Linq;` `class` `GFG` `{` ` ` `// Function to find the smallest` ` ` `// subsequence such that sum of elements` ` ` `// is greater than equal to given number K` ` ` `static` `int` `lengthOfSmallestSubsequence(` `int` `K, ` `int` `[]v)` ` ` `{` ` ` `// Initialize List` ` ` `List<` `int` `> pq = ` `new` `List<` `int` `>();` ` ` `// Loop to insert all elements into` ` ` `// the List` ` ` `for` `(` `int` `i = 0; i < v.Length; i++) ` ` ` `{` ` ` `pq.Add(v[i]);` ` ` `}` ` ` `// Sort list in reverse order` ` ` `pq.Sort();` ` ` `pq.Reverse();` ` ` `int` `sum = 0;` ` ` `int` `count = 0;` ` ` `// Loop to find the smallest` ` ` `// subsequence such that sum of elements` ` ` `// is greater than equal to given number K` ` ` `while` `(pq.Count > 0 && sum < K)` ` ` `{` ` ` `sum += pq[0];` ` ` `pq.RemoveAt(0);` ` ` `count++;` ` ` `}` ` ` `// If sum is less then K` ` ` `// then return -1 else return count.` ` ` `if` `(sum < K)` ` ` `{` ` ` `return` `-1;` ` ` `}` ` ` `return` `count;` ` ` `}` ` ` `// Driver code` ` ` `static` `public` `void` `Main ()` ` ` `{` ` ` `int` `[]v = { 2, 3, 1, 5,6, 3, 7, 9, 14, 10, 2, 5 };` ` ` `int` `K = 35;` ` ` `Console.WriteLine(lengthOfSmallestSubsequence(K, v));` ` ` `}` `}` `// This code is contributed by avanitrachhadiya2155` |

## Javascript

`<script>` `// JavaScript implementation to find length of smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K using System;` `// Function to find the smallest` `// subsequence such that sum of elements` `// is greater than equal to given number K` `function` `lengthOfSmallestSubsequence(K, v) {` ` ` `// Initialize List` ` ` `let pq = ` `new` `Array();` ` ` `// Loop to insert all elements into` ` ` `// the List` ` ` `for` `(let i = 0; i < v.length; i++) {` ` ` `pq.push(v[i]);` ` ` `}` ` ` `// Sort list in reverse order` ` ` `pq.sort((a, b) => b - a);` ` ` `let sum = 0;` ` ` `let count = 0;` ` ` `// Loop to find the smallest` ` ` `// subsequence such that sum of elements` ` ` `// is greater than equal to given number K` ` ` `while` `(pq.length > 0 && sum < K) {` ` ` `sum += pq[0];` ` ` `pq.splice(0, 1);` ` ` `count++;` ` ` `}` ` ` `// If sum is less then K` ` ` `// then return -1 else return count.` ` ` `if` `(sum < K) {` ` ` `return` `-1;` ` ` `}` ` ` `return` `count;` `}` `// Driver code` `let v = [2, 3, 1, 5, 6, 3, 7, 9, 14, 10, 2, 5];` `let K = 35;` `document.write(lengthOfSmallestSubsequence(K, v));` `// This code is contributed by gfgking` `</script>` |

**Output:**

4