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
- Traverse the array in reverse, i.e. iterate from i = N – 1 to 0.
- For every i, check if (A[i] + i) is less than N or not.
- Update score[i] for index i as Score[i] = A[i] * ((i + A[i] < N) ? Score(i + A[i]) ? 1)
- 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 scorevoid 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 Codeint main(){ int N = 5; vector<int> A ={1, 2, 3, 4, 5}; Min_Score_Index(N, A);} |
Java
// Java program for the above approachimport java.util.*;class GFG{// Function to find the index// with minimum scorestatic 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 Codepublic 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 scoredef 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 Codeif __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 approachusing System;class GFG{// Function to find the index// with minimum scorestatic 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 Codepublic 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 scorefunction 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 Codevar 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)
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