Proper use of recursion in C - c

Question

I'm working on some basic programs for learning purposes. Struggling to find out logic in this kind of recursion fuction. How does the "loop" inside histogram function works? Is it possible to get rid of it and make it only main function? Any info is appreciate.
The task is to create horizontal histogram with given integers.
#include <stdio.h>
#include <string.h>
void histogram(int numbers[], int length, int n) {
int finished = 1;
for(int i = 0; i < length; i++){
if(numbers[i] - n > 0)
finished = 0;}
if(finished)
return;
else {
histogram(numbers, length, n +1);
int counter = 0;
for(int i = 0; i < length; i++) {
int number = numbers[i] -n;
if(number > 0)
printf("* ");
else
printf(" ");
}
printf("\n");
}
}
int main(void) {
int numbers[] = {1, 3, 1};
int length = sizeof(numbers) / sizeof(int);
histogram(numbers, length,0);
return 0;
}

Answer 1

Each iteration of the recursion is drawing a line of and * character, a horizontal slice of the histogram.
For n-th level the values numbers[i] that are larger or equal than n are marked by *, other become whitespaces.
Note that recursion is called before drawing anything. Thus the deepest level is drawn first:
For example:
numbers[] = {1, 2, 3, 1}
Level3: * \n as 1<3, 2<3, 3>=3, 1<3
Level2: ** \n as 1<2, 2>=2, 3>=2, 1<2
Level1:****\n as 1>=1, 2>=1, 3>=1, 1>=1
Level0:****\n as 1>=0, 2>=0, 3>=0, 1>=0
This recursion can rewritten as two nested loops.
Find maximal height. Set it max_number:
Iterate over heights from max_number to 0 inclusive.
For each height iterate over whole array printing * is numbers[i] >= height, otherwise print
Code:
#include <stdio.h>
void histogram(int numbers[], int length) {
int max_number = 0;
for (int i = 0; i < length; ++i)
if (numbers[i] > max_number)
max_number = numbers[i];
for (int height = max_number; height >= 0; --height) {
for (int i = 0; i < length; ++i)
if (numbers[i] >= height)
putchar('*');
else
putchar(' ');
putchar('\n');
}
}
int main() {
int A[] = {1,2,3,1};
histogram(A, 4);
return 0;
}
produces:
*
**
****
****
to make a horizontal histogram ... just switch the loops.
void horiz_histogram(int numbers[], int length) {
int max_number = 0;
for (int i = 0; i < length; ++i)
if (numbers[i] > max_number)
max_number = numbers[i];
for (int i = 0; i < length; ++i) {
for (int height = max_number; height >= 0; --height)
if (numbers[i] >= height)
putchar('*');
else
putchar(' ');
putchar('\n');
}
}
produces:
**
***
****
**

Answer 2

Imagine drawing a table wide as the length of the array of numbers and high as its maximum value:
// Pseudocode
width = length = sizeof(numbers) / sizeof(int) // = 3
height = max(numbers[] = {1, 3, 1}) // = 3
At each step histogram() checks if it has reached the top of the graph.
If so, it prints the top line and returns.
Otherwise it goes up one line and checks again.
This way histogram() prints the top line first and then the others "climbing down"