Minimize the total number of teddies to be distributed

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Given N number of students sitting in a line and each of them is having marks they got scored in the exam. The task is to distribute teddy as they satisfy given conditions

All students must have at least 1 teddy
If two students sit next to each other then the one with the higher marks must get more teddies.

So, the task is to minimize the total number of teddies.
Examples:

Input: n = 3, marks = [ 1, 2, 2 ]
Output: 4
Here 1, 2, 2 is the marks. 
Note that when two students have equal marks 
they are allowed to have a different number of teddies. 
Hence optimal distribution will be 1, 2, 1.

Input: n = 6, marks = [ 1, 4, 5, 2, 2, 1 ]
Output: 10

Approach: The approach is to use the dynamic programming to solve given problem:

Initialize the table of size n.
Run loop for n times.
If left adjacent student is having higher marks review and change all the table values assigned before as solution until assigned table values as a solution are found wrong according to given constraints.
If right adjacent student is having higher marks add one in solution for left adjacent and assign to solution for right one.

Below is the implementation of the above approach:

C++

// C++ implementation of the
// above approach
#include<bits/stdc++.h>
using namespace std;
 
long long fun(int marks[],int n)
{
    // Initializing one tablet 
    // for each student
    long long dp[n], temp;
    fill(dp, dp + n, 1);
     
    for(int i = 0; i < n - 1; i++)
    {
        // if left adjacent is having 
        // higher marks review and change 
        // all the dp values assigned before
        // until assigned dp values are found 
        // wrong according to given constrains
        if (marks[i] > marks[i + 1])
        { 
            temp = i;
            while (true)
            {
                if ((marks[temp] > marks[temp + 1]) && 
                                         temp >= 0)
                {
                    if (dp[temp] > dp[temp + 1])
                    {
                        temp -= 1;
                        continue;
                    }
                    else
                    {
                        dp[temp] = dp[temp + 1] + 1;
                        temp -= 1;
                    }
                }                     
                else
                    break; 
            } 
        }
         
        // if right adjacent is having higher
        // marks add one in dp of left adjacent
        // and assign to right one
        else if( marks[i] < marks[i + 1])
            dp[i + 1] = dp[i] + 1;
    }
 
    int sum = 0;
 
    for(int i = 0; i < n; i++)
    sum += dp[i];
 
    return sum;
}
 
// Driver Code
int main()
{
    // n number of students
    int n = 6;
     
    // marks of students
    int marks[6] = { 1, 4, 5, 2, 2, 1};
     
    // solution of problem
    cout << fun(marks, n);
     
    return 0;
}
 
// This code is contributed by ash264

Java

// Java implementation of the 
// above approach 
 
public class GFG {
 
    static long fun(int marks[],int n) 
    { 
        // Initializing one tablet  
        // for each student 
        long dp[] = new long[n] ;
        int temp; 
         
        for (int i = 0;i < n;i ++)
            dp[i] = 1 ; 
           
        for(int i = 0; i < n - 1; i++) 
        { 
            // if left adjacent is having  
            // higher marks review and change  
            // all the dp values assigned before 
            // until assigned dp values are found  
            // wrong according to given constrains 
            if (marks[i] > marks[i + 1]) 
            {  
                temp = i; 
                while (true) 
                { 
                    if ((marks[temp] > marks[temp + 1]) &&  
                                             temp >= 0) 
                    { 
                        if (dp[temp] > dp[temp + 1]) 
                        { 
                            temp -= 1; 
                            continue; 
                        } 
                        else
                        { 
                            dp[temp] = dp[temp + 1] + 1; 
                            temp -= 1; 
                        } 
                    }                     
                    else
                        break;  
                }  
            } 
               
            // if right adjacent is having higher 
            // marks add one in dp of left adjacent 
            // and assign to right one 
            else if( marks[i] < marks[i + 1]) 
                dp[i + 1] = dp[i] + 1; 
        } 
       
        int sum = 0; 
       
        for(int i = 0; i < n; i++) 
        sum += dp[i]; 
       
        return sum; 
    } 
     
    public static void main(String args[])
    {
        // n number of students 
        int n = 6; 
           
        // marks of students 
        int marks[] = { 1, 4, 5, 2, 2, 1}; 
           
        // solution of problem 
        System.out.println(fun(marks, n)); 
    }
    // This code is contributed by ANKITRAI1
}

Python 3

# Python implementation of the above approach
 
def fun(marks, n):
    # Initializing one tablet for each student
    dp = [ 1 for i in range(0, n) ]
 
    for i in range(0, n-1):
 
        # if left adjacent is having higher marks
        # review and change all the dp values assigned before
        # until assigned dp values are found wrong 
        # according to given constrains
        if marks[i] > marks[i + 1]:
            temp = i
            while True:
                if marks[temp] > marks[temp + 1] and temp >= 0:
                    if dp[temp] > dp[temp + 1]:
                        temp -= 1
                        continue
                    else:
                        dp[temp] = dp[temp + 1] + 1
                        temp -= 1                       
                else:
                    break   
 
        # if right adjacent is having higher marks
        # add one in dp of left adjacent and assign to right one
        elif marks[i] < marks[i + 1]:
            dp[i + 1] = dp[i] + 1
 
    return(sum(dp))
 
 
 
# driver code
 
# n number of students
n = 6
 
# marks of students
marks = [ 1, 4, 5, 2, 2, 1]
 
# solution of problem
print(fun(marks, n))

C#

// C# implementation of the 
// above approach 
using System; 
   
class GFG 
{ 
    public static long fun(int[] marks,int n) 
    { 
        // Initializing one tablet  
        // for each student 
        long[] dp = new long[n];
        long temp; 
         
        for(int i = 0; i < n; i++)
            dp[i] = 1;
           
        for(int i = 0; i < n - 1; i++) 
        { 
            // if left adjacent is having  
            // higher marks review and change  
            // all the dp values assigned before 
            // until assigned dp values are found  
            // wrong according to given constrains 
            if (marks[i] > marks[i + 1]) 
            {  
                temp = i; 
                while (true) 
                { 
                    if ((marks[temp] > marks[temp + 1]) &&  
                                             temp >= 0) 
                    { 
                        if (dp[temp] > dp[temp + 1]) 
                        { 
                            temp -= 1; 
                            continue; 
                        } 
                        else
                        { 
                            dp[temp] = dp[temp + 1] + 1; 
                            temp -= 1; 
                        } 
                    }                      
                    else
                        break;  
                }  
            } 
               
            // if right adjacent is having higher 
            // marks add one in dp of left adjacent 
            // and assign to right one 
            else if( marks[i] < marks[i + 1]) 
                dp[i + 1] = dp[i] + 1; 
        } 
       
        long sum = 0; 
       
        for(int i = 0; i < n; i++) 
            sum += dp[i]; 
       
        return sum; 
    } 
       
    // Driver Code 
    static void Main() 
    { 
        // n number of students 
        int n = 6; 
           
        // marks of students 
        int[] marks = new int[]{ 1, 4, 5, 2, 2, 1}; 
           
        // solution of problem 
        Console.Write( fun(marks, n) );  
    }
    //This code is contributed by DrRoot_
}

Javascript

<script>
    // Javascript implementation of the above approach 
     
    function fun(marks, n) 
    { 
        // Initializing one tablet  
        // for each student 
        let dp = new Array(n);
        let temp; 
           
        for(let i = 0; i < n; i++)
            dp[i] = 1;
             
        for(let i = 0; i < n - 1; i++) 
        { 
            // if left adjacent is having  
            // higher marks review and change  
            // all the dp values assigned before 
            // until assigned dp values are found  
            // wrong according to given constrains 
            if (marks[i] > marks[i + 1]) 
            {  
                temp = i; 
                while (true) 
                { 
                    if ((marks[temp] > marks[temp + 1]) &&  
                                             temp >= 0) 
                    { 
                        if (dp[temp] > dp[temp + 1]) 
                        { 
                            temp -= 1; 
                            continue; 
                        } 
                        else
                        { 
                            dp[temp] = dp[temp + 1] + 1; 
                            temp -= 1; 
                        } 
                    }                      
                    else
                        break;  
                }  
            } 
                 
            // if right adjacent is having higher 
            // marks add one in dp of left adjacent 
            // and assign to right one 
            else if( marks[i] < marks[i + 1]) 
                dp[i + 1] = dp[i] + 1; 
        } 
         
        let sum = 0; 
         
        for(let i = 0; i < n; i++) 
            sum += dp[i]; 
         
        return sum; 
    } 
     
    // n number of students 
    let n = 6; 
 
    // marks of students 
    let marks = [ 1, 4, 5, 2, 2, 1]; 
 
    // solution of problem 
    document.write( fun(marks, n) );  
 
// This code is contributed by divyesh072019.
</script>

Output:

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