Maximum people a person can see while standing in a line in both direction

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Given an array height[] which represents the height of N people standing in a line. A person i can see a person j if height[j] < height[i] and there is no person k standing in between them such that height[k] ≥ height[i]. Find the maximum number of people a person can see.

Note: A person can see any other person irrespective of whether they are standing in his front or back.

Examples:

Input: heights[] = {6, 2, 5, 4, 5, 1, 6}.
Output: 6
Explanation:
Person 1 (height = 6) can see five other people at following positions (2, 3, 4, 5. 6) in addition to himself, i.e. total 6.
Person 2 (height: 2) can see only himself.
Person 3 (height = 5) is able to see people 2nd, 3rd, and 4th person.
Only Person 4 (height = 4) can see himself.
Person 5 (height = 5) can see people 4th, 5th, and 6th.
Person 6 (height =1) can only see himself.
Person 7 (height = 6) can see 2nd, 3rd, 4th, 5th, 6th, and 7th people.
A maximum of six people can be seen by Person 1, 7th

Input: heights[] = {1, 3, 6, 4 }
Output: 3

Naive Approach: A simple solution is to iterate through the given array and for every idx in the row:

Maintain a left pointer (leftptr) which points to idx-1 and a right pointer (rightptr) which points to idx+1.
Move the left pointer in the left direction until you find a person whose height is greater than or equal to height[idx].
Move the right pointer in the right direction until you find a person whose height is greater than or equal to the height [idx].
The difference between the indices of the right and left pointer gives us the number of people the ith person can see and update the Ans as max(Ans, rightptr – leftptr-1).

Below is the implementation of the above idea.

C++

// C++ code to implement the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the leftmost index
// of the person whose height is
// greater the height of person idx.
int leftindex(vector<int> heights,
              int idx, int n)
{
 
    int h = heights[idx];
    for (int i = idx - 1; i >= 0; i--) {
 
        // If height of person i is
        // greater than or equal to
        // current person of height h
        // then the current person(idx)
        // cannot see him
        if (heights[i] >= h)
            return i;
    }
    // If a person can see all other people
    // who are standing on his left
    return -1;
}
 
// Function to find the rightmost index
// of the person whose height is
// greater the height of person idx.
int rightindex(vector<int> heights,
               int idx, int n)
{
    int h = heights[idx];
    for (int i = idx + 1; i < n; i++) {
 
        // If height of person i is
        // greater than or equal to
        // current person of height h
        // then the current person(idx)
        // cannot see him
        if (heights[i] >= h)
            return i;
    }
    // If a person can see all other people
    // who are standing on his right
    return n;
}
 
// Function to find maximum number of people
// a person can see
int max_people(vector<int> heights, int n)
{
    // Ans stores the maximum of people
    // a person can see
    int ans = 0;
    for (int i = 0; i < n; i++) {
 
        // Leftptr stores the leftmost index
        // of the person which
        // the current person cannot see
        int leftptr
            = leftindex(heights, i, n);
 
        // Rightptr stores the rightmost index
        // of the person which
        // the current person cannot see
        int rightptr
            = rightindex(heights, i, n);
 
        // Maximum number of people
        // a person can see
        ans = max(ans,
                  rightptr - leftptr - 1);
    }
    return ans;
}
 
// Driver code
int main()
{
    int N = 7;
    vector<int> heights{ 6, 2, 5, 4, 5, 1, 6 };
 
    // Function call
    cout << max_people(heights, N) << endl;
    return 0;
}

Java

// JAVA code to implement the above approach
import java.util.*;
class GFG
{
 
  // Function to find the leftmost index
  // of the person whose height is
  // greater the height of person idx.
  public static int leftindex(int[] heights, int idx,
                              int n)
  {
 
    int h = heights[idx];
    for (int i = idx - 1; i >= 0; i--) {
 
      // If height of person i is
      // greater than or equal to
      // current person of height h
      // then the current person(idx)
      // cannot see him
      if (heights[i] >= h)
        return i;
    }
    // If a person can see all other people
    // who are standing on his left
    return -1;
  }
 
  // Function to find the rightmost index
  // of the person whose height is
  // greater the height of person idx.
  public static int rightindex(int[] heights, int idx,
                               int n)
  {
    int h = heights[idx];
    for (int i = idx + 1; i < n; i++) {
 
      // If height of person i is
      // greater than or equal to
      // current person of height h
      // then the current person(idx)
      // cannot see him
      if (heights[i] >= h)
        return i;
    }
 
    // If a person can see all other people
    // who are standing on his right
    return n;
  }
 
  // Function to find maximum number of people
  // a person can see
  public static int max_people(int[] heights, int n)
  {
 
    // Ans stores the maximum of people
    // a person can see
    int ans = 0;
    for (int i = 0; i < n; i++) {
 
      // Leftptr stores the leftmost index
      // of the person which
      // the current person cannot see
      int leftptr = leftindex(heights, i, n);
 
      // Rightptr stores the rightmost index
      // of the person which
      // the current person cannot see
      int rightptr = rightindex(heights, i, n);
 
      // Maximum number of people
      // a person can see
      ans = Math.max(ans, rightptr - leftptr - 1);
    }
    return ans;
  }
 
  // Driver code
  public static void main(String[] args)
  {
    int N = 7;
    int[] heights = new int[] { 6, 2, 5, 4, 5, 1, 6 };
 
    // Function call
    System.out.println(max_people(heights, N));
  }
}
 
// This code is contributed by Taranpreet

Python3

# Python code to implement the above approach
 
# Function to find the leftmost index
# of the person whose height is
# greater the height of person idx.
def leftindex(heights, idx,  n):
    h = heights[idx]
    for i in range(idx - 1, -1, -1):
 
        # If height of person i is
        # greater than or equal to
        # current person of height h
        # then the current person(idx)
        # cannot see him
        if heights[i] >= h:
            return i
 
    # If a person can see all other people
    # who are standing on his left
    return -1
 
# Function to find the rightmost index
# of the person whose height is
# greater the height of person idx.
def rightindex(heights, idx,  n):
 
    h = heights[idx]
    for i in range(idx + 1, n):
       
        # If height of person i is
        # greater than or equal to
        # current person of height h
        # then the current person(idx)
        # cannot see him
        if (heights[i] >= h):
            return i
 
    # If a person can see all other people
    # who are standing on his right
    return n
 
# Function to find maximum number of people
# a person can see
def max_people(heights,  n):
 
    # Ans stores the maximum of people
    # a person can see
    ans = 0
    for i in range(n):
       
        # Leftptr stores the leftmost index
        # of the person which
        # the current person cannot see
        leftptr = leftindex(heights, i, n)
         
        # Rightptr stores the rightmost index
        # of the person which
        # the current person cannot see
        rightptr = rightindex(heights, i, n)
 
        # Maximum number of people
        # a person can see
        ans = max(ans, rightptr - leftptr - 1)
 
    return ans
 
# Driver code
N = 7
heights=[6, 2, 5, 4, 5, 1, 6]
 
# Function call
print(max_people(heights, N))
 
# This code is contributed by rohitsingh07052.

C#

// C# code to implement the above approach
using System;
class GFG
{
 
  // Function to find the leftmost index
  // of the person whose height is
  // greater the height of person idx.
  static int leftindex(int[] heights, int idx,
                       int n)
  {
 
    int h = heights[idx];
    for (int i = idx - 1; i >= 0; i--) {
 
      // If height of person i is
      // greater than or equal to
      // current person of height h
      // then the current person(idx)
      // cannot see him
      if (heights[i] >= h)
        return i;
    }
    // If a person can see all other people
    // who are standing on his left
    return -1;
  }
 
  // Function to find the rightmost index
  // of the person whose height is
  // greater the height of person idx.
  static int rightindex(int[] heights, int idx,
                        int n)
  {
    int h = heights[idx];
    for (int i = idx + 1; i < n; i++) {
 
      // If height of person i is
      // greater than or equal to
      // current person of height h
      // then the current person(idx)
      // cannot see him
      if (heights[i] >= h)
        return i;
    }
 
    // If a person can see all other people
    // who are standing on his right
    return n;
  }
 
  // Function to find maximum number of people
  // a person can see
  static int max_people(int[] heights, int n)
  {
 
    // Ans stores the maximum of people
    // a person can see
    int ans = 0;
    for (int i = 0; i < n; i++) {
 
      // Leftptr stores the leftmost index
      // of the person which
      // the current person cannot see
      int leftptr = leftindex(heights, i, n);
 
      // Rightptr stores the rightmost index
      // of the person which
      // the current person cannot see
      int rightptr = rightindex(heights, i, n);
 
      // Maximum number of people
      // a person can see
      ans = Math.Max(ans, rightptr - leftptr - 1);
    }
    return ans;
  }
 
  // Driver code
  public static void Main()
  {
    int N = 7;
    int[] heights = new int[] { 6, 2, 5, 4, 5, 1, 6 };
 
    // Function call
    Console.WriteLine(max_people(heights, N));
  }
}
 
// This code is contributed by Samim Hossain Mondal.

Javascript

<script>
    // JavaScript code to implement the above approach
 
    // Function to find the leftmost index
    // of the person whose height is
    // greater the height of person idx.
    const leftindex = (heights, idx, n) => {
 
        let h = heights[idx];
        for (let i = idx - 1; i >= 0; i--) {
 
            // If height of person i is
            // greater than or equal to
            // current person of height h
            // then the current person(idx)
            // cannot see him
            if (heights[i] >= h)
                return i;
        }
        // If a person can see all other people
        // who are standing on his left
        return -1;
    }
 
    // Function to find the rightmost index
    // of the person whose height is
    // greater the height of person idx.
    const rightindex = (heights, idx, n) => {
        let h = heights[idx];
        for (let i = idx + 1; i < n; i++) {
 
            // If height of person i is
            // greater than or equal to
            // current person of height h
            // then the current person(idx)
            // cannot see him
            if (heights[i] >= h)
                return i;
        }
        // If a person can see all other people
        // who are standing on his right
        return n;
    }
 
    // Function to find maximum number of people
    // a person can see
    const max_people = (heights, n) => {
        // Ans stores the maximum of people
        // a person can see
        let ans = 0;
        for (let i = 0; i < n; i++) {
 
            // Leftptr stores the leftmost index
            // of the person which
            // the current person cannot see
            let leftptr
                = leftindex(heights, i, n);
 
            // Rightptr stores the rightmost index
            // of the person which
            // the current person cannot see
            let rightptr
                = rightindex(heights, i, n);
 
            // Maximum number of people
            // a person can see
            ans = Math.max(ans,
                rightptr - leftptr - 1);
        }
        return ans;
    }
 
    // Driver code
 
    let N = 7;
    let heights = [6, 2, 5, 4, 5, 1, 6];
 
    // Function call
    document.write(max_people(heights, N));
 
// This code is contributed by rakeshsahni
 
</script>

Output

Time Complexity: O(N²)
Auxiliary Space: O(N)

Efficient Approach: This problem can be solved using stacks. For every person in the row, we are trying to find the index of the next taller person on right and next taller person on the left.

Create an array r_heights of size N to store the index of the next greater person(right).
To find the position of the next greater person on the right:
push the last index of the array to the stack.
For each index ranging from N-1 to 0:
keep popping the indices from the stack until you find an index whose height is greater than or equal to the current person’s height or until the stack is empty.
If the stack is not empty update r_heights[i] value to match to the top of stack else r_heights[i]=N.
Push the current index to the stack.
Iterate from 0 to N to find the index of the next greater person on the left side for each person in the row.
For every person in the row the number of people he can see is r_heigths[i]-l_heights[i]-1. Update the Ans as max(Ans, r_heigths[i]-l_heigths[i]-1)

Below is the implementation of above approach:

C++

// C++ code to implement the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to store the index
// of next taller person on left
void leftindex(vector<int> heights,
               vector<int>& l_heights,
               int n)
{
    stack<int> st;
 
    for (int i = 0; i < n; i++) {
        // While the top value of the stack
        // is lesser than the
        // current person's height
        while (st.empty() == false
               && heights[st.top()]
                      < heights[i])
            st.pop();
 
        // If the stack is empty
        l_heights[i]
            = (st.empty() == false)
                  ? st.top()
                  : (-1);
        st.push(i);
    }
 
    return;
}
 
// Function to store the index of
// next taller person on right
void rightindex(vector<int>& heights,
                vector<int>& r_heights,
                int n)
{
    // Stack to store the next
    // taller person on its right
    stack<int> st;
 
    for (int i = n - 1; i >= 0; i--) {
 
        // If the top value of the stack
        // is lesser than the current height
        while (st.empty() == false
               && heights[st.top()]
                      < heights[i])
            st.pop();
 
        // If the stack is empty
        r_heights[i]
            = (st.empty() == false)
                  ? st.top()
                  : n;
        st.push(i);
    }
    return;
}
 
// Function to find the maximum number
// of people a person can see
int max_people(vector<int> heights, int n)
{
    // To store the answer
    int ans = 0;
 
    vector<int> r_heights(n), l_heights(n);
    leftindex(heights, l_heights, n);
    rightindex(heights, r_heights, n);
    for (int i = 0; i < n; i++) {
 
        // Contains the leftmost index
        // of the person which
        // current person cannot see
        int l_index = l_heights[i];
 
        // Contains the rightmost index
        // of the person which
        // the current person cannot see
        int r_index = r_heights[i];
 
        // Calculate the maximum answer
        ans = max(ans, r_index - l_index - 1);
    }
    return ans;
}
 
// Driver code
int main()
{
    int N = 7;
    vector<int> heights{ 6, 2, 5, 4, 5, 1, 6 };
 
    // Function call
    cout << max_people(heights, N) << endl;
    return 0;
}

Java

// Java code to implement the above approach
import java.io.*;
import java.util.*;
 
class GFG {
    // Function to store the index
    // of next taller person on left
    public static void leftindex(int heights[],
                                 int l_heights[], int n)
    {
        Stack<Integer> st = new Stack<Integer>();
 
        for (int i = 0; i < n; i++) {
            // While the top value of the stack
            // is lesser than the
            // current person's height
            while (st.empty() == false
                   && heights[st.peek()] < heights[i])
                st.pop();
 
            // If the stack is empty
            l_heights[i]
                = (st.empty() == false) ? st.peek() : (-1);
            st.push(i);
        }
 
        return;
    }
 
    // Function to store the index of
    // next taller person on right
    public static void rightindex(int heights[],
                                  int r_heights[], int n)
    {
        // Stack to store the next
        // taller person on its right
        Stack<Integer> st = new Stack<Integer>();
 
        for (int i = n - 1; i >= 0; i--) {
 
            // If the top value of the stack
            // is lesser than the current height
            while (st.empty() == false
                   && heights[st.peek()] < heights[i])
                st.pop();
 
            // If the stack is empty
            r_heights[i]
                = (st.empty() == false) ? st.peek() : n;
            st.push(i);
        }
        return;
    }
 
    // Function to find the maximum number
    // of people a person can see
    public static int max_people(int heights[], int n)
    {
        // To store the answer
        int ans = 0;
 
        int r_heights[] = new int[n];
        int l_heights[] = new int[n];
        leftindex(heights, l_heights, n);
        rightindex(heights, r_heights, n);
        for (int i = 0; i < n; i++) {
 
            // Contains the leftmost index
            // of the person which
            // current person cannot see
            int l_index = l_heights[i];
 
            // Contains the rightmost index
            // of the person which
            // the current person cannot see
            int r_index = r_heights[i];
 
            // Calculate the maximum answer
            ans = Math.max(ans, r_index - l_index - 1);
        }
        return ans;
    }
    public static void main(String[] args)
    {
        int N = 7;
        int heights[] = { 6, 2, 5, 4, 5, 1, 6 };
 
        // Function call
        System.out.println(max_people(heights, N));
    }
}
 
// This code is contributed by Rohit Pradhan

Python3

# Python code to implement the above approach
 
# Function to store the index
# of next taller person on left
def leftindex(heights, l_heights, n):
    st = []
    for i in range(n):
       
        # While the top value of the stack
        # is lesser than the
        # current person's height
        while (st != [] and heights[st[-1]] < heights[i]):
            st.pop()
             
        # If the stack is empty
        if st:
            l_heights[i] = st[-1]
        else:
              l_heights[i] = -1
        st.append(i)
    return l_heights
 
# Function to store the index of
# next taller person on right
def rightindex(heights, r_heights, n):
   
    # Stack to store the next
    # taller person on its right
    st = []
 
    for i in range(n - 1, -1, -1):
       
        # If the top value of the stack
        # is lesser than the current height
        while (st != [] and heights[st[-1]] < heights[i]):
            st.pop()
             
        # If the stack is empty
        if st:
              r_heights[i] = st[-1]
        else:
              r_heights[i] = n
        st.append(i)
     
    return r_heights
 
# Function to find the maximum number
# of people a person can see
def max_people( heights,  n):
   
      # To store the answer
    ans = 0
    r_heights=[0 for i in range(n)]
    l_heights= [0 for i in range(n)]
    l_heights = leftindex(heights, l_heights, n)
    r_heights = rightindex(heights, r_heights, n)
    for i in range(n):
       
        # Contains the leftmost index
        # of the person which
        # current person cannot see
        l_index = l_heights[i]
         
        # Contains the rightmost index
        # of the person which
        # the current person cannot see
        r_index = r_heights[i]
         
        # Calculate the maximum answer
        ans = max(ans, r_index - l_index - 1)
    return ans
 
# Driver code
N = 7
heights = [6, 2, 5, 4, 5, 1, 6 ]
 
# Function call
print(max_people(heights, N))
 
# This code is contributed by rohitsingh07052.

C#

// C# code to implement the above approach
using System;
using System.Collections;
 
public class GFG {
 
  // Function to store the index
  // of next taller person on left
  public static void leftindex(int[] heights,
                               int[] l_heights, int n)
  {
    Stack st = new Stack();
 
    for (int i = 0; i < n; i++) {
      // While the top value of the stack
      // is lesser than the
      // current person's height
      while (st.Count != 0
             && heights[(int)st.Peek()] < heights[i])
        st.Pop();
 
      // If the stack is empty
      l_heights[i]
        = (st.Count != 0) ? (int)st.Peek() : (-1);
      st.Push(i);
    }
 
    return;
  }
 
  // Function to store the index of
  // next taller person on right
  public static void rightindex(int[] heights,
                                int[] r_heights, int n)
  {
    // Stack to store the next
    // taller person on its right
    Stack st = new Stack();
 
    for (int i = n - 1; i >= 0; i--) {
 
      // If the top value of the stack
      // is lesser than the current height
      while (st.Count != 0
             && heights[(int)st.Peek()] < heights[i])
        st.Pop();
 
      // If the stack is empty
      r_heights[i]
        = (st.Count != 0) ? (int)st.Peek() : n;
      st.Push(i);
    }
    return;
  }
 
  // Function to find the maximum number
  // of people a person can see
  public static int max_people(int[] heights, int n)
  {
    // To store the answer
    int ans = 0;
 
    int[] r_heights = new int[n];
    int[] l_heights = new int[n];
    leftindex(heights, l_heights, n);
    rightindex(heights, r_heights, n);
    for (int i = 0; i < n; i++) {
 
      // Contains the leftmost index
      // of the person which
      // current person cannot see
      int l_index = l_heights[i];
 
      // Contains the rightmost index
      // of the person which
      // the current person cannot see
      int r_index = r_heights[i];
 
      // Calculate the maximum answer
      ans = Math.Max(ans, r_index - l_index - 1);
    }
    return ans;
  }
 
  static public void Main()
  {
 
    // Code
    int N = 7;
    int[] heights = { 6, 2, 5, 4, 5, 1, 6 };
 
    // Function call
    Console.WriteLine(max_people(heights, N));
  }
}
 
// This code is contributed by lokeshmvs21.

Javascript

<script>
 
// Javascript code to implement the above approach
 
// Function to store the index
// of next taller person on left
function leftindex(heights, l_heights, n){
    let st = []
    for(let i=0;i<n;i++){
       
        // While the top value of the stack
        // is lesser than the
        // current person's height
        while (st != [] && heights[st[st.length-1]] < heights[i])
            st.pop()
             
        // If the stack is empty
        if(st.length > 0)
            l_heights[i] = st[st.length-1]
        else
            l_heights[i] = -1
        st.push(i)
    }
    return l_heights
}
 
// Function to store the index of
// next taller person on right
function rightindex(heights, r_heights, n){
   
    // Stack to store the next
    // taller person on its right
    st = []
 
    for(let i= n-1;i>=0;i--){
       
        // If the top value of the stack
        // is lesser than the current height
        while (st != [] && heights[st[st.length-1]] < heights[i])
            st.pop()
             
        // If the stack is empty
        if(st.length > 0)
            r_heights[i] = st[st.length-1]
        else
              r_heights[i] = n
        st.push(i)
    }
     
    return r_heights
}
 
// Function to find the maximum number
// of people a person can see
function max_people( heights,  n){
   
      // To store the answer
    let ans = 0
    let r_heights=new Array(n).fill(0)
    let l_heights= new Array(n).fill(0)
    l_heights = leftindex(heights, l_heights, n)
    r_heights = rightindex(heights, r_heights, n)
    for(let i=0;i<n;i++){
       
        // Contains the leftmost index
        // of the person which
        // current person cannot see
        let l_index = l_heights[i]
         
        // Contains the rightmost index
        // of the person which
        // the current person cannot see
        let r_index = r_heights[i]
         
        // Calculate the maximum answer
        ans = Math.max(ans, r_index - l_index - 1)
    }
    return ans
}
 
// Driver code
let N = 7
let heights = [6, 2, 5, 4, 5, 1, 6 ]
 
// Function call
document.write(max_people(heights, N))
 
// This code is contributed by shinjanpatra
 
</script>

Output

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

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