Find the index with minimum score from a given array

Given an array A[] of size N(1 ≤ N ≤ 10⁵), consisting of positive integers, where the score of an index i in range [0, N – 1] is defined as:

Score[i] = A[i] * ((i + A[i] < N) ? Score(i + A[i]) : 1)

The task is to find the index with minimum score.

Examples:

Input: A[] = {1, 2, 3, 4, 5}
Output: 2
Explanation:

• Score[4] = 5 * 1 = 5
• Score[3]. = 4 * 1 = 4
• Score[2] = 3 * 1 = 3 (Minimum)
• Score[1] = 2 * Score[3] = 2 * 4 = 8
• Score[0] = 1 * Score[1] = 1 * 8 = 8

Input: A[] = {9, 8, 1, 2, 3, 6}
Output : 4

Approach: Follow the steps below to solve the problem 

1. Traverse the array in reverse, i.e. iterate from i = N – 1 to 0.
2. For every i, check if (A[i] + i) is less than N or not.
3. Update score[i] for index i as Score[i] = A[i] * ((i + A[i] < N) ? Score(i + A[i]) ? 1)
4. Print the index with minimum score.

Below is the implementation of above approach:

C++

// C++ program for the above approach

#include <bits/stdc++.h>

using namespace std;


//Function to find the index
//with minimum score
void Min_Score_Index(int N, vector<int> A){

    //Stores the score of current index
    vector<int> Score(N,0);

    //Traverse the array in reverse
    for (int i=N-1;i>=0;i--){

        if (A[i] + i < N)
            Score[i] = A[i] * Score[A[i] + i];
        else
            Score[i] = A[i];
    }

    //Update minimum score
    int min_value = INT_MAX;

    for(int i:Score) min_value = min(i,min_value);

    //Print the index with minimum score
    int ind = 0;

    for(int i=0;i<N;i++){
      if(Score[i]==min_value) ind = i;
    }

    cout<<(ind);
}



//Driver Code
int main(){
  int N = 5;
  vector<int> A ={1, 2, 3, 4, 5};

  Min_Score_Index(N, A);

}

Java

// Java program for the above approach
import java.util.*;
class GFG
{

// Function to find the index
// with minimum score
static void Min_Score_Index(int N, int []A)
{

    // Stores the score of current index
    int []Score = new int[N];

    // Traverse the array in reverse
    for (int i = N - 1; i >= 0; i--)
    {

        if (A[i] + i < N)
            Score[i] = A[i] * Score[A[i] + i];
        else
            Score[i] = A[i];
    }

    // Update minimum score
    int min_value = Integer.MAX_VALUE;
    for(int i:Score) min_value = Math.min(i, min_value);

    // Print the index with minimum score
    int ind = 0;
    for(int i = 0; i < N; i++)
    {
      if(Score[i] == min_value)
        ind = i;
    }
    System.out.print(ind);
}

// Driver Code
public static void main(String[] args)
{
  int N = 5;
  int []A ={1, 2, 3, 4, 5};
  Min_Score_Index(N, A);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python3 program for the above approach

# Function to find the index
# with minimum score
def Min_Score_Index(N, A):

    # Stores the score of current index
    Score = [0] * N

    # Traverse the array in reverse
    for i in range(N - 1, -1, -1):
        if A[i] + i < N:
            Score[i] = A[i] * Score[A[i] + i]
        else:
            Score[i] = A[i]

    # Update minimum score
    min_value = min(Score)

    # Print the index with minimum score
    ind = Score.index(min_value)
    print(ind)

# Driver Code
if __name__ == "__main__":
    N = 5
    A = [1, 2, 3, 4, 5]
    Min_Score_Index(N, A)

# This code is contributed by mohit kumar 29

C#

// C# program for the above approach
using System;

class GFG{

// Function to find the index
// with minimum score
static void Min_Score_Index(int N, int[] A)
{

    // Stores the score of current index
    int[] Score = new int[N];

    // Traverse the array in reverse
    for(int i = N - 1; i >= 0; i--)
    {
        if (A[i] + i < N)
            Score[i] = A[i] * Score[A[i] + i];
        else
            Score[i] = A[i];
    }

    // Update minimum score
    int min_value = Int32.MaxValue;
    foreach(int i in Score)
    {
        min_value = Math.Min(i, min_value);
    }

    // Print the index with minimum score
    int ind = 0;
    for(int i = 0; i < N; i++)
    {
        if (Score[i] == min_value)
            ind = i;
    }
    Console.WriteLine(ind);
}

// Driver Code
public static void Main()
{
    int N = 5;
    int[] A = { 1, 2, 3, 4, 5 };

    Min_Score_Index(N, A);
}
}

// This code is contributed by chitranayal

Javascript

<script>

// JavaScript program for the above approach


// Function to find the index
// with minimum score
function Min_Score_Index(N, A){

    // Stores the score of current index
    var Score = Array(N).fill(0);

    // Traverse the array in reverse
    for (var i=N-1;i>=0;i--){

        if (A[i] + i < N)
            Score[i] = A[i] * Score[A[i] + i];
        else
            Score[i] = A[i];
    }

    // Update minimum score
    var min_value = 1000000000;

    Score.forEach(i => {
        min_value = Math.min(i,min_value);
    });

    // Print the index with minimum score
    var ind = 0;

    for(var i=0;i<N;i++){
      if(Score[i]==min_value) ind = i;
    }

    document.write(ind);
}



// Driver Code

var N = 5;
var A =[1, 2, 3, 4, 5];
Min_Score_Index(N, A);

</script>

Output:

2

Time Complexity: O(N)
Auxiliary Space: O(N)