# Find Maximum Index Product

### Problem Statement :

```You are given a N list of  numbers . For each element at position  (), we define  and  as:
= closest index j such that j < i and . If no such j exists then  = 0.
= closest index k such that k > i and . If no such k exists then  = 0.

We define  =  * . You need to find out the maximum  among all i.

Input Format

The first line contains an integer , the number of integers. The next line contains the  integers describing the list a[1..N].

Constraints

1  <=  N  <=  10^5
1  <= ai  <=  10^9

Output Format

Output the maximum IndexProduct among all indices from 1 to N.```

### Solution :

```                            ```Solution in C :

In   C++  :

#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;

int inp[100010];
int sta[100010][2];
int lef[100010];
int rig[100010];
int n;

void find(int *arr, int st, int ed, int d, int *out) {
int top = 1;
sta[0][0] = 2000000000;
sta[0][1] = 0;
for (int i=st; i!=ed; i+=d) {
while (sta[top-1][0] <= arr[i]) top--;
out[i] = sta[top-1][1];
sta[top][0] = arr[i];
sta[top++][1] = i+1;
}
return;
}
int main() {

scanf("%d", &n);
for (int i=0; i<n; i++)scanf("%d", &inp[i]);
find(inp, 0, n, 1, lef);
find(inp, n-1, -1, -1, rig);
long long ans = 0;
for (int i=0; i<n; i++) {
if ((long long)lef[i] * rig[i] > ans) ans = (long long)lef[i] * rig[i];
}
cout << ans << endl;
return 0;
}

In    Java  :

import java.awt.Point;
import java.io.BufferedOutputStream;
import java.io.IOException;
import java.util.ArrayList;

public class Solution {
public static void main(String[] args) throws IOException,
NumberFormatException {
BufferedOutputStream bos =
new BufferedOutputStream(System.out);
byte[] eolb = System.getProperty(
"line.separator").getBytes();

long[] arr = new long[n];
for (int i = 0; i < n; i++) {
arr[i] = Integer.parseInt(values[i]);
}

long[] leftArr = new long[n];
ArrayList<Point> states = new ArrayList<Point>();
for (int i = 1; i < n; i++) {
for (int j = states.size() - 1; j >= 0; j--) {
if (states.get(j).getX() > arr[i]) {
leftArr[i] = (int) states.get(j).getY();
states.add(new Point((int) arr[i], i + 1));
break;
} else {
states.remove(j);
if (states.size() == 0) {
states.add(new Point((int) arr[i], i + 1));
break;
}
}
}
}
states.clear();

long[] rightArr = new long[n];
states.add(new Point((int) arr[n - 1], n));
for (int i = n - 2; i >= 0; i--) {
for (int j = states.size() - 1; j >= 0; j--) {
if (states.get(j).getX() > arr[i]) {
rightArr[i] = (int) states.get(j).getY();
states.add(new Point((int) arr[i], i + 1));
break;
} else {
states.remove(j);
if (states.size() == 0) {
states.add(new Point((int) arr[i], i + 1));
break;
}
}
}
}

long ans = -1;
for (int i = 0; i < n; i++) {
ans = Math.max(ans,
(long) leftArr[i] * rightArr[i]);
}
bos.write(String.valueOf(ans).getBytes());
bos.write(eolb);
bos.flush();

}
}

In   C  :

#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>

int main() {

long int n, left=0, right=0, i, j, a[100000], out, max=0;

scanf("%ld", &n);
for(i=0;i<n;i++)
{
scanf("%ld", &a[i]);
}
for(i=n-1;i>=1;i--)
{
/*    for(j=i-1;j>=0;j--)
{
if(a[j]>a[i])
{
left=j+1;
break;
}
}
for(j=i+1;j<=n-1;j++)
{
if(a[j]>a[i])
{
right=j+1;
break;
}
}*/
if(a[i]<a[i+1]&&a[i]<a[i-1])
{
max=i*(i+2);
break;
}

/*out=left*right;
if(out>max)
max=out;
left=0;
right=0;*/

}
printf("%ld", max);
return 0;
}

In   Python3  :

def lefts(L):
left = [];
maxes = [];
for i in range(len(L)):
while maxes and L[maxes[-1]] <= L[i]:
maxes.pop();
if not maxes: left.append(-1);
else: left.append(maxes[-1]);
maxes.append(i); #maxes = [i];
return left;

def rights(L):
right = [];
maxes = [];
for i in range(len(L)-1, -1, -1):
while maxes and L[maxes[-1]] <= L[i]:
maxes.pop();
if not maxes: right.append(-1);
else: right.append(maxes[-1]);
maxes.append(i); #maxes = [i];
right.reverse();
return right;

def indexProduct(L):
left = lefts(L);
right = rights(L);
products = ((left[i] + 1) * (right[i] + 1) for i in range(len(L)));
return max(products);

if __name__ == "__main__":
input();
L = [int(n) for n in input().split()];
print(indexProduct(L));```
```

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