Número de números decimales de longitud k, que son estrictamente monótonos

Llamamos a un número decimal monótono si: Escribe un programa que toma un número positivo n en la entrada y devuelve una cantidad de números decimales de longitud n que son estrictamente monótonos. El número no puede comenzar con 0. Ejemplos:

Input : 2
Output : 36
Numbers are 12, 13, ... 19, 23
24, ... 29, .... 89.

Input : 3
Output : 84

Las explicaciones de este problema siguen las mismas reglas que se aplican en: Número de números decimales de longitud k, que son monótonos La única diferencia es que ahora no podemos tomar duplicados, por lo que los valores calculados previamente son los de la diagonal superior izquierda y la izquierda. 

// CPP program to count numbers of k
// digits that are strictly monotone.
#include <cstring>
#include <iostream>
 
int static const DP_s = 9;
 
int getNumStrictMonotone(int len)
{
    // DP[i][j] is going to store monotone
    // numbers of length i+1 considering
    // j+1 digits (1, 2, 3, ..9)
    int DP[len][DP_s];
    memset(DP, 0, sizeof(DP));
  
    // Unit length numbers
    for (int i = 0; i < DP_s; ++i)
        DP[0][i] = i + 1;   
 
    // Building dp[] in bottom up
    for (int i = 1; i < len; ++i)
        for (int j = 1; j < DP_s; ++j)
            DP[i][j] = DP[i - 1][j - 1] + DP[i][j - 1];       
     
    return DP[len - 1][DP_s - 1];
}
 
// Driver code
int main()
{
    std::cout << getNumStrictMonotone(2);
    return 0;
}

// Java program to count numbers of k
// digits that are strictly monotone.
import java.io.*;
import java.util.*;
 
class GFG {
 
    static int DP_s = 9;
     
    static int getNumStrictMonotone(int len)
    {
        // DP[i][j] is going to store monotone
        // numbers of length i+1 considering
        // j+1 digits (1, 2, 3, ..9)
        int[][] DP = new int[len][DP_s];
     
        // Unit length numbers
        for (int i = 0; i < DP_s; ++i)
        DP[0][i] = i + 1;
     
        // Building dp[] in bottom up
        for (int i = 1; i < len; ++i)
             for (int j = 1; j < DP_s; ++j)
                DP[i][j] = DP[i - 1][j - 1]
                             + DP[i][j - 1];
     
        return DP[len - 1][DP_s - 1];
    }
    public static void main(String[] args)
    {
        int n = 2;
        System.out.println(getNumStrictMonotone(n));
    }
}
 
// This code is contributed by Gitanjali.

# Python3 program to count numbers of k
# digits that are strictly monotone.
 
DP_s = 9
 
def getNumStrictMonotone(ln):
     
    # DP[i][j] is going to store monotone
    # numbers of length i+1 considering
    # j+1 digits (1, 2, 3, ..9)
    DP = [[0] * DP_s for _ in range(ln)]
 
    # Unit length numbers
    for i in range(DP_s):
        DP[0][i] = i + 1
 
    # Building dp[] in bottom up
    for i in range(1, ln):
         
        for j in range(1, DP_s):
             
            DP[i][j] = DP[i - 1][j - 1] + DP[i][j - 1]    
     
    return DP[ln - 1][DP_s - 1]
 
# Driver code
print(getNumStrictMonotone(2))
 
 
# This code is contributed by Ansu Kumari.

// C# program to count numbers of k
// digits that are strictly monotone.
using System;
 
class GFG {
 
    static int DP_s = 9;
     
    static int getNumStrictMonotone(int len)
    {
        // DP[i][j] is going to store monotone
        // numbers of length i+1 considering
        // j+1 digits (1, 2, 3, ..9)
        int[,] DP = new int[len,DP_s];
     
        // Unit length numbers
        for (int i = 0; i < DP_s; ++i)
        DP[0,i] = i + 1;
     
        // Building dp[] in bottom up
        for (int i = 1; i < len; ++i)
            for (int j = 1; j < DP_s; ++j)
                DP[i,j] = DP[i - 1,j - 1]
                            + DP[i,j - 1];
     
        return DP[len - 1,DP_s - 1];
    }
     
    // Driver code
    public static void Main()
    {
        int n = 2;
        Console.WriteLine(getNumStrictMonotone(n));
    }
}
 
// This code is contributed by vt_m.

<?php
// PHP program to count
// numbers of k digits
// that are strictly
// monotone.
$DP_s = 9;
 
function getNumStrictMonotone($len)
{
    global $DP_s;
     
    // DP[i][j] is going to
    // store monotone numbers
    // of length i+1 considering
    // j+1 digits (1, 2, 3, ..9)
    $DP = array(array());
    for($i = 0; $i < $len; $i++)
    {
        for($j = 0; $j < $DP_s; $j++)
            $DP[$i][$j] = 0;
    }
     
    // Unit length numbers
    for ($i = 0; $i < $DP_s; ++$i)
        $DP[0][$i] = $i + 1;
 
    // Building dp[]
    // in bottom up
    for ($i = 1; $i < $len; ++$i)
        for ($j = 1; $j < $DP_s; ++$j)
            $DP[$i][$j] = $DP[$i - 1][$j - 1] +
                          $DP[$i][$j - 1];    
     
    return $DP[$len - 1][$DP_s - 1];
}
 
// Driver code
echo (getNumStrictMonotone(2));
 
// This code is contributed by
// Manish Shaw(manishshaw1)
?>

<script>
 
// JavaScript program to count numbers of k
// digits that are strictly monotone.
const DP_s = 9;
 
function getNumStrictMonotone(len)
{
    // DP[i][j] is going to store monotone
    // numbers of length i+1 considering
    // j+1 digits (1, 2, 3, ..9)
    let DP = new Array(len);
    for(let i = 0; i < len; i++){
        DP[i] = new Array(DP_s).fill(0);
    }
 
    // Unit length numbers
    for (let i = 0; i < DP_s; ++i)
        DP[0][i] = i + 1;   
 
    // Building dp[] in bottom up
    for (let i = 1; i < len; ++i)
        for (let j = 1; j < DP_s; ++j)
            DP[i][j] = DP[i - 1][j - 1] + DP[i][j - 1];       
     
    return DP[len - 1][DP_s - 1];
}
 
// Driver code
document.write(getNumStrictMonotone(2));
 
// This code is contributed by shinjanpatra
 
</script>

Producción :

36