Given an array a[1..N]. For each element at position i (1 <= i <= N). Where
- L(i) is defined as closest index j such that j < i and a[j] > a[i]. If no such j exists then L(i) = 0.
- R(i) is defined as closest index k such that k > i and a[k] > a[i]. If no such k exists then R(i) = 0.
LRProduct(i) = L(i)*R(i) .
We need to find an index with maximum LRProduct
Examples:
Input : 1 1 1 1 0 1 1 1 1 1
Output : 24
For {1, 1, 1, 1, 0, 1, 1, 1, 1, 1} all element are same except 0. So only for zero their exist greater element and for others it will be zero. for zero, on left 4th element is closest and greater than zero and on right 6th element is closest and greater. so maximum
product will be 4*6 = 24.Input : 5 4 3 4 5
Output : 8
For {5, 4, 3, 4, 5}, L[] = {0, 1, 2, 1, 0} and R[]
= {0, 5, 4, 5, 0},
LRProduct = {0, 5, 8, 5, 0} and max in this is 8.
Note: Taking starting index as 1 for finding LRproduct.
This problem is based on Next Greater Element.
From the current position, we need to find the closest greater element on its left and right side.
So to find next greater element, we used stack one from left and one from right.simply we are checking which element is greater and storing their index at specified position.
1- if stack is empty, push current index.
2- if stack is not empty
….a) if current element is greater than top element then store the index of current element on index of top element.
Do this, once traversing array element from left and once from right and form the left and right array, then, multiply them to find max product value.
// C++ program to find the max // LRproduct[i] among all i #include <bits/stdc++.h> using namespace std;
#define MAX 1000 // function to find just next greater // element in left side vector< int > nextGreaterInLeft( int a[], int n)
{ vector< int > left_index(MAX, 0);
stack< int > s;
for ( int i = n - 1; i >= 0; i--) {
// checking if current element is greater than top
while (!s.empty() && a[i] > a[s.top() - 1]) {
int r = s.top();
s.pop();
// on index of top store the current element
// index which is just greater than top element
left_index[r - 1] = i + 1;
}
// else push the current element in stack
s.push(i + 1);
}
return left_index;
} // function to find just next greater element // in right side vector< int > nextGreaterInRight( int a[], int n)
{ vector< int > right_index(MAX, 0);
stack< int > s;
for ( int i = 0; i < n; ++i) {
// checking if current element is greater than top
while (!s.empty() && a[i] > a[s.top() - 1]) {
int r = s.top();
s.pop();
// on index of top store the current element
// index which is just greater than top element
// stored index should be start with 1
right_index[r - 1] = i + 1;
}
// else push the current element in stack
s.push(i + 1);
}
return right_index;
} // Function to find maximum LR product int LRProduct( int arr[], int n)
{ // for each element storing the index of just
// greater element in left side
vector< int > left = nextGreaterInLeft(arr, n);
// for each element storing the index of just
// greater element in right side
vector< int > right = nextGreaterInRight(arr, n);
int ans = -1;
for ( int i = 1; i <= n; i++) {
// finding the max index product
ans = max(ans, left[i] * right[i]);
}
return ans;
} // Drivers code int main()
{ int arr[] = { 5, 4, 3, 4, 5 };
int n = sizeof (arr) / sizeof (arr[1]);
cout << LRProduct(arr, n);
return 0;
} |
// Java program to find the // max LRproduct[i] among all i import java.io.*;
import java.util.*;
class GFG
{ static int MAX = 1000 ;
// function to find just next
// greater element in left side
static int [] nextGreaterInLeft( int []a,
int n)
{
int []left_index = new int [MAX];
Stack<Integer> s = new Stack<Integer>();
for ( int i = n - 1 ; i >= 0 ; i--)
{
// checking if current
// element is greater than top
while (s.size() != 0 &&
a[i] > a[s.peek() - 1 ])
{
int r = s.peek();
s.pop();
// on index of top store
// the current element
// index which is just
// greater than top element
left_index[r - 1 ] = i + 1 ;
}
// else push the current
// element in stack
s.push(i + 1 );
}
return left_index;
}
// function to find just next
// greater element in right side
static int [] nextGreaterInRight( int []a,
int n)
{
int []right_index = new int [MAX];
Stack<Integer> s = new Stack<Integer>();
for ( int i = 0 ; i < n; ++i) {
// checking if current element
// is greater than top
while (s.size() != 0 &&
a[i] > a[s.peek() - 1 ])
{
int r = s.peek();
s.pop();
// on index of top store
// the current element index
// which is just greater than
// top element stored index
// should be start with 1
right_index[r - 1 ] = i + 1 ;
}
// else push the current
// element in stack
s.push(i + 1 );
}
return right_index;
}
// Function to find
// maximum LR product
static int LRProduct( int []arr, int n)
{
// for each element storing
// the index of just greater
// element in left side
int []left = nextGreaterInLeft(arr, n);
// for each element storing
// the index of just greater
// element in right side
int []right = nextGreaterInRight(arr, n);
int ans = - 1 ;
for ( int i = 1 ; i <= n; i++)
{
// finding the max
// index product
ans = Math.max(ans, left[i] *
right[i]);
}
return ans;
}
// Driver code
public static void main(String args[])
{
int []arr = new int []{ 5 , 4 , 3 , 4 , 5 };
int n = arr.length;
System.out.print(LRProduct(arr, n));
}
} // This code is contributed by // Manish Shaw(manishshaw1) |
# Python3 program to find the # max LRproduct[i] among all i # Method to find the next greater # value in left side def nextGreaterInLeft(a):
left_index = [ 0 ] * len (a)
s = []
for i in range ( len (a)):
# Checking if current
# element is greater than top
while len (s) ! = 0 and a[i] > = a[s[ - 1 ]]:
# Pop the element till we can't
# get the larger value then
# the current value
s.pop()
if len (s) ! = 0 :
left_index[i] = s[ - 1 ]
else :
left_index[i] = 0
# Else push the element in the stack
s.append(i)
return left_index
# Method to find the next # greater value in right def nextGreaterInRight(a):
right_index = [ 0 ] * len (a)
s = []
for i in range ( len (a) - 1 , - 1 , - 1 ):
# Checking if current element
# is greater than top
while len (s) ! = 0 and a[i] > = a[s[ - 1 ]]:
# Pop the element till we can't
# get the larger value then
# the current value
s.pop()
if len (s) ! = 0 :
right_index[i] = s[ - 1 ]
else :
right_index[i] = 0
# Else push the element in the stack
s.append(i)
return right_index
def LRProduct(arr):
# For each element storing
# the index of just greater
# element in left side
left = nextGreaterInLeft(arr)
# For each element storing
# the index of just greater
# element in right side
right = nextGreaterInRight(arr)
ans = - 1
# As we know the answer will
# belong to the range from
# 1st index to second last index.
# Because for 1st index left
# will be 0 and for last
# index right will be 0
for i in range ( 1 , len (left) - 1 ):
if left[i] = = 0 or right[i] = = 0 :
# Finding the max index product
ans = max (ans, 0 )
else :
temp = (left[i] + 1 ) * (right[i] + 1 )
# Finding the max index product
ans = max (ans, temp)
return ans
# Driver Code arr = [ 5 , 4 , 3 , 4 , 5 ]
print (LRProduct(arr))
# This code is contributed by Mohit Pathneja |
// C# program to find the max LRproduct[i] // among all i using System;
using System.Collections.Generic;
class GFG {
static int MAX = 1000;
// function to find just next greater
// element in left side
static int [] nextGreaterInLeft( int []a, int n)
{
int []left_index = new int [MAX];
Stack< int > s = new Stack< int >();
for ( int i = n - 1; i >= 0; i--) {
// checking if current element is
// greater than top
while (s.Count != 0 && a[i] > a[s.Peek() - 1])
{
int r = s.Peek();
s.Pop();
// on index of top store the current
// element index which is just greater
// than top element
left_index[r - 1] = i + 1;
}
// else push the current element in stack
s.Push(i + 1);
}
return left_index;
}
// function to find just next greater element
// in right side
static int [] nextGreaterInRight( int []a, int n)
{
int []right_index = new int [MAX];
Stack< int > s = new Stack< int >();
for ( int i = 0; i < n; ++i) {
// checking if current element is
// greater than top
while (s.Count != 0 && a[i] > a[s.Peek() - 1])
{
int r = s.Peek();
s.Pop();
// on index of top store the current
// element index which is just greater
// than top element stored index should
// be start with 1
right_index[r - 1] = i + 1;
}
// else push the current element in stack
s.Push(i + 1);
}
return right_index;
}
// Function to find maximum LR product
static int LRProduct( int []arr, int n)
{
// for each element storing the index of just
// greater element in left side
int []left = nextGreaterInLeft(arr, n);
// for each element storing the index of just
// greater element in right side
int []right = nextGreaterInRight(arr, n);
int ans = -1;
for ( int i = 1; i <= n; i++) {
// finding the max index product
ans = Math.Max(ans, left[i] * right[i]);
}
return ans;
}
// Drivers code
static void Main()
{
int []arr = new int []{ 5, 4, 3, 4, 5 };
int n = arr.Length;
Console.Write(LRProduct(arr, n));
}
} // This code is contributed by Manish Shaw |
<script> // Javascript program to find the max LRproduct[i] among all i
let MAX = 1000;
// function to find just next greater
// element in left side
function nextGreaterInLeft(a, n)
{
let left_index = new Array(MAX);
left_index.fill(0);
let s = [];
for (let i = n - 1; i >= 0; i--) {
// checking if current element is
// greater than top
while (s.length != 0 && a[i] > a[s[s.length - 1] - 1])
{
let r = s[s.length - 1];
s.pop();
// on index of top store the current
// element index which is just greater
// than top element
left_index[r - 1] = i + 1;
}
// else push the current element in stack
s.push(i + 1);
}
return left_index;
}
// function to find just next greater element
// in right side
function nextGreaterInRight(a, n)
{
let right_index = new Array(MAX);
right_index.fill(0);
let s = [];
for (let i = 0; i < n; ++i) {
// checking if current element is
// greater than top
while (s.length != 0 && a[i] > a[s[s.length - 1] - 1])
{
let r = s[s.length - 1];
s.pop();
// on index of top store the current
// element index which is just greater
// than top element stored index should
// be start with 1
right_index[r - 1] = i + 1;
}
// else push the current element in stack
s.push(i + 1);
}
return right_index;
}
// Function to find maximum LR product
function LRProduct(arr, n)
{
// for each element storing the index of just
// greater element in left side
let left = nextGreaterInLeft(arr, n);
// for each element storing the index of just
// greater element in right side
let right = nextGreaterInRight(arr, n);
let ans = -1;
for (let i = 1; i <= n; i++) {
// finding the max index product
ans = Math.max(ans, left[i] * right[i]);
}
return ans;
}
let arr = [ 5, 4, 3, 4, 5 ];
let n = arr.length;
document.write(LRProduct(arr, n));
// This code is contributed by suresh07.
</script> |
8
Complexity Analysis:
Time Complexity: O(n)
Space Complexity: O(n)
Method 2: Reducing the space used by using only one array to store both left and right max.
Approach:
Prerequisite: https://www.geeksforgeeks.org/next-greater-element/amp/
- To find the next greater element to left, we used a stack from the left, and the same stack is used for multiplying the right greatest element index with the left greatest element index.
- Function maxProduct( ) is used for returning the max product by iterating the resultant array.
// C++ program to find max LR product #include <bits/stdc++.h> using namespace std;
stack< int > mystack;
// To find greater element to left void nextGreaterToLeft( int arr[], int res[], int N) {
mystack.push(0);
res[0] = 0;
// iterate through the array
for ( int i = 1; i < N; i++) {
while (mystack.size() > 0 && arr[mystack.top()] <= arr[i])
mystack.pop();
// place the index to the left in the resultant array
res[i] = (mystack.size() == 0) ? 0 : mystack.top()+1;
mystack.push(i);
}
} //// To find greater element to right void nextGreaterToRight( int arr[], int res[], int N) {
mystack = stack< int >();
int n = N;
mystack.push(n-1);
res[n-1] *= 0;
// iterate through the array in the reverse order
for ( int i=n - 2 ; i >= 0; i--) {
while (mystack.size() > 0 && arr[mystack.top()] <= arr[i])
mystack.pop();
//multiply the index to the right with the index to the left
//in the resultant array
res[i] = (mystack.size() == 0) ? res[i]*0 : res[i]*(mystack.top()+1);
mystack.push(i);
}
} //function to return the max value in the resultant array int maxProduct( int arr[], int res[], int N) {
nextGreaterToLeft(arr,res, N); //to find left max
nextGreaterToRight(arr,res, N); //to find right max
int Max = res[0];
for ( int i = 1; i < N; i++){
Max = max(Max, res[i]);
}
return Max;
} int main()
{ int arr[] = {5, 4, 3, 4, 5};
int N = sizeof (arr) / sizeof (arr[0]);
int res[N];
int maxprod = maxProduct(arr, res, N);
cout << maxprod << endl;
return 0;
} // This code is contributed by decode2207. |
//java program to find max LR product import java.util.*;
public class GFG {
Stack<Integer> mystack = new Stack<>();
//To find greater element to left
void nextGreaterToLeft( int [] arr, int [] res) {
mystack.push( 0 );
res[ 0 ] = 0 ;
//iterate through the array
for ( int i= 1 ;i<arr.length;i++) {
while (!mystack.isEmpty() && arr[mystack.peek()] <= arr[i])
mystack.pop();
//place the index to the left in the resultant array
res[i] = (mystack.isEmpty()) ? 0 : mystack.peek()+ 1 ;
mystack.push(i);
}
}
////To find greater element to right
void nextGreaterToRight( int [] arr, int [] res) {
mystack.clear();
int n = arr.length;
mystack.push(n- 1 );
res[n- 1 ] *= 0 ;
//iterate through the array in the reverse order
for ( int i=n- 2 ;i>= 0 ;i--) {
while (!mystack.isEmpty() && arr[mystack.peek()] <= arr[i])
mystack.pop();
//multiply the index to the right with the index to the left
//in the resultant array
res[i] = (mystack.isEmpty()) ? res[i]* 0 : res[i]*(mystack.peek()+ 1 );
mystack.push(i);
}
}
//function to return the max value in the resultant array
int maxProduct( int [] arr, int [] res) {
nextGreaterToLeft(arr,res); //to find left max
nextGreaterToRight(arr,res); //to find right max
int max = res[ 0 ];
for ( int i = 1 ;i<res.length;i++){
max = Math.max(max, res[i]);
}
return max;
}
//Driver function
public static void main(String args[]) {
GFG obj = new GFG();
int arr[] = { 5 , 4 , 3 , 4 , 5 };
int res[] = new int [arr.length];
int maxprod = obj.maxProduct(arr, res);
System.out.println(maxprod);
}
} //this method is contributed by Likhita AVL |
# Python3 program to find max LR product mystack = []
# To find greater element to left def nextGreaterToLeft(arr, res):
mystack.append( 0 )
res[ 0 ] = 0
# iterate through the array
for i in range ( 1 , len (arr)):
while ( len (mystack) > 0 and arr[mystack[ - 1 ]] < = arr[i]):
mystack.pop()
# place the index to the left in the resultant array
if ( len (mystack) = = 0 ):
res[i] = 0
else :
res[i] = mystack[ - 1 ] + 1
mystack.append(i)
# To find greater element to right def nextGreaterToRight(arr, res):
mystack = []
n = len (arr)
mystack.append(n - 1 )
res[n - 1 ] * = 0
# iterate through the array in the reverse order
for i in range (n - 2 , - 1 , - 1 ):
while ( len (mystack) > 0 and arr[mystack[ - 1 ]] < = arr[i]):
mystack.pop()
# multiply the index to the right with the index to the left
# in the resultant array
if ( len (mystack) = = 0 ):
res[i] = res[i] * 0
else :
res[i] = res[i] * (mystack[ - 1 ] + 1 )
mystack.append(i)
# function to return the max value in the resultant array def maxProduct(arr, res):
nextGreaterToLeft(arr,res) #to find left max
nextGreaterToRight(arr,res) #to find right max
Max = res[ 0 ]
for i in range ( 1 , len (res)):
Max = max ( Max , res[i])
return Max
# Driver code
arr = [ 5 , 4 , 3 , 4 , 5 ]
res = [ 0 ] * ( len (arr))
maxprod = maxProduct(arr, res)
print (maxprod)
# This code is contributed by mukesh07. |
// C# program to find max LR product using System;
using System.Collections;
class GFG {
static Stack mystack = new Stack();
//To find greater element to left
static void nextGreaterToLeft( int [] arr, int [] res) {
mystack.Push(0);
res[0] = 0;
//iterate through the array
for ( int i=1;i<arr.Length;i++) {
while (mystack.Count > 0 && arr[( int )mystack.Peek()] <= arr[i])
mystack.Pop();
//place the index to the left in the resultant array
res[i] = (mystack.Count == 0) ? 0 : ( int )mystack.Peek()+1;
mystack.Push(i);
}
}
////To find greater element to right
static void nextGreaterToRight( int [] arr, int [] res) {
mystack = new Stack();
int n = arr.Length;
mystack.Push(n-1);
res[n-1] *= 0;
//iterate through the array in the reverse order
for ( int i = n - 2; i >= 0; i--) {
while (mystack.Count == 0 && arr[( int )mystack.Peek()] <= arr[i])
mystack.Pop();
//multiply the index to the right with the index to the left
//in the resultant array
res[i] = (mystack.Count == 0) ? res[i]*0 : res[i]*(( int )mystack.Peek()+1);
mystack.Push(i);
}
}
//function to return the max value in the resultant array
static int maxProduct( int [] arr, int [] res) {
nextGreaterToLeft(arr, res); //to find left max
nextGreaterToRight(arr, res); //to find right max
int max = res[0];
for ( int i = 1; i < res.Length; i++){
max = Math.Max(max, res[i]);
}
return max;
}
static void Main() {
int [] arr = {5, 4, 3, 4, 5};
int [] res = new int [arr.Length];
int maxprod = maxProduct(arr, res);
Console.WriteLine(maxprod);
}
} // This code is contributed by divyeshrabadiya07. |
<script> // Javascript program to find max LR product
let mystack = [];
// To find greater element to left
function nextGreaterToLeft(arr, res) {
mystack.push(0);
res[0] = 0;
// iterate through the array
for (let i = 1; i < arr.length; i++) {
while (mystack.length > 0 && arr[mystack[mystack.length - 1]] <= arr[i])
mystack.pop();
// place the index to the left in the resultant array
res[i] = (mystack.length == 0) ? 0 : mystack[mystack.length - 1]+1;
mystack.push(i);
}
}
//// To find greater element to right
function nextGreaterToRight(arr, res) {
mystack = [];
let n = arr.length;
mystack.push(n-1);
res[n-1] *= 0;
// iterate through the array in the reverse order
for (let i = n - 2; i >= 0; i--) {
while (mystack.length > 0 && arr[mystack[mystack.length - 1]] <= arr[i])
mystack.pop();
// multiply the index to the right with the index to the left
// in the resultant array
res[i] = (mystack.length == 0) ? res[i]*0 : res[i]*(mystack[mystack.length - 1]+1);
mystack.push(i);
}
}
// function to return the max value in the resultant array
function maxProduct(arr, res) {
nextGreaterToLeft(arr,res); //to find left max
nextGreaterToRight(arr,res); //to find right max
let max = res[0];
for (let i = 1;i<res.length;i++){
max = Math.max(max, res[i]);
}
return max;
}
let arr = [5, 4, 3, 4, 5];
let res = new Array(arr.length);
let maxprod = maxProduct(arr, res);
document.write(maxprod);
// This code is contributed by divyesh072019.
</script> |
8
Complexity Analysis:
Time Complexity: O(n)
Space Complexity: O(n)