Find the subsequence with given sum in a superincreasing sequence

A sequence of positive real numbers S1, S2, S3, …, SN is called a superincreasing sequence if every element of the sequence is greater than the sum of all the previous elements in the sequence. For example, 1, 3, 6, 13, 27, 52 is such subsequence.
Now, given a superincreasing sequence S and the sum of a subsequence of this sequence, the task is to find the subsequence.

Examples:

Input: S[] = {17, 25, 46, 94, 201, 400}, sum = 272
Output: 25 46 201
25 + 46 + 201 = 272

Input: S[] = {1, 2, 4, 8, 16}, sum = 12
Output: 4 8

Approach: This problem can be solved using the greedy technique. Starting from the last element of the array till the first element, there are two cases:



  1. sum < arr[i]: In this case, the current element cannot be a part of the required subsequence as after including it, the sum of the subsequence will exceed the given sum. So discard the current element.
  2. sum ≥ arr[i]: In this case, the current element has to be included in the required subsequence. This is because if the current element is not included then the sum of the previous elements in the array will be smaller than the current element (as it is a superincreasing sequence) which will in turn be smaller than the required sum. So take the current element and update the sum as sum = sum – arr[i].

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to find the required subsequence
void findSubSeq(int arr[], int n, int sum)
{
  
    for (int i = n - 1; i >= 0; i--) {
  
        // Current element cannot be a part
        // of the required subsequence
        if (sum < arr[i])
            arr[i] = -1;
  
        // Include current element in
        // the requried subsequence
        // So update the sum
        else
            sum -= arr[i];
    }
  
    // Print the elements of the
    // required subsequence
    for (int i = 0; i < n; i++) {
  
        // If the current element was
        // included in the subsequence
        if (arr[i] != -1)
            cout << arr[i] << " ";
    }
}
  
// Driver code
int main()
{
    int arr[] = { 17, 25, 46, 94, 201, 400 };
    int n = sizeof(arr) / sizeof(int);
    int sum = 272;
  
    findSubSeq(arr, n, sum);
  
    return 0;
}

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Java

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// Java implementation of the approach 
class GFG 
{
      
    // Function to find the required subsequence 
    static void findSubSeq(int arr[], int n, int sum) 
    
        for (int i = n - 1; i >= 0; i--)
        
      
            // Current element cannot be a part 
            // of the required subsequence 
            if (sum < arr[i]) 
                arr[i] = -1
      
            // Include current element in 
            // the requried subsequence 
            // So update the sum 
            else
                sum -= arr[i]; 
        
      
        // Print the elements of the 
        // required subsequence 
        for (int i = 0; i < n; i++) 
        
      
            // If the current element was 
            // included in the subsequence 
            if (arr[i] != -1
                System.out.print(arr[i] + " "); 
        
    
      
    // Driver code 
    public static void main (String[] args) 
    
        int arr[] = { 17, 25, 46, 94, 201, 400 }; 
        int n = arr.length; 
        int sum = 272
      
        findSubSeq(arr, n, sum); 
    
}
  
// This code is contributed by AnkitRai01

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Python3

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# Python3 implementation of the approach 
  
# Function to find the required subsequence 
def findSubSeq(arr, n, sum) : 
  
    for i in range(n - 1, -1, -1) :
  
        # Current element cannot be a part 
        # of the required subsequence 
        if (sum < arr[i]) :
            arr[i] = -1
  
        # Include current element in 
        # the requried subsequence 
        # So update the sum 
        else :
            sum -= arr[i]; 
  
    # Print the elements of the 
    # required subsequence 
    for i in range(n) :
  
        # If the current element was 
        # included in the subsequence 
        if (arr[i] != -1) :
            print(arr[i], end = " "); 
  
# Driver code 
if __name__ == "__main__"
  
    arr = [ 17, 25, 46, 94, 201, 400 ]; 
    n = len(arr); 
    sum = 272
  
    findSubSeq(arr, n, sum); 
  
# This code is contributed by kanugargng

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C#

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// C# implementation of the approach
using System;
      
class GFG 
{
      
    // Function to find the required subsequence 
    static void findSubSeq(int []arr, 
                           int n, int sum) 
    
        for (int i = n - 1; i >= 0; i--)
        
      
            // Current element cannot be a part 
            // of the required subsequence 
            if (sum < arr[i]) 
                arr[i] = -1; 
      
            // Include current element in 
            // the requried subsequence 
            // So update the sum 
            else
                sum -= arr[i]; 
        
      
        // Print the elements of the 
        // required subsequence 
        for (int i = 0; i < n; i++) 
        
      
            // If the current element was 
            // included in the subsequence 
            if (arr[i] != -1) 
                Console.Write(arr[i] + " "); 
        
    
      
    // Driver code 
    public static void Main (String[] args) 
    
        int []arr = { 17, 25, 46, 94, 201, 400 }; 
        int n = arr.Length; 
        int sum = 272; 
      
        findSubSeq(arr, n, sum); 
    
}
  
// This code is contributed by PrinciRaj1992

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Output:

25 46 201

Time Complexity: O(n)

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