Segmentation fault in recursive program - c++

Question

I am doing the coin problem, the problem says that,
Given a set of coin values coins = {c1, c2,..., ck} and a target sum
of money n, our task is to form the sum n using as few coins as
possible.
suppose you have 9 dollars and you have set of {6,5,1} so, the minimum no. of sum/change for 9 dollars would be ( 6+1+1+1=9) i.e. 4.
i tried doing it recursively using this formula :
solve(x) = min( solve(x−6)+1, solve(x−5)+1, solve(x−1)+1 )
,but I don't know why I'm getting Segmentation fault in my code.
There are plenty of codes available online, but I want to know what am I doing wrong here, I'm new to recursion please help me, The code goes here:
//my code
#include<bits/stdc++.h>
using namespace std;
int solve (int x, int a[], int n)
{
if (x < 0)
{
return INT_MAX;
}
if (x == 0)
{
return 0;
}
int best = INT_MAX;
for (int i = 0; i < n; i++)
{
best = min (best, solve (x - a[i], a, n) + 1);
}
return best;
}
int main ()
{
int a[] = { 6, 5, 1 };
int x = 9;
int n = 3;
cout << solve (x, a, n);
return 0;
}

Answer 1

The code which have been took from: https://www.geeksforgeeks.org/find-minimum-number-of-coins-that-make-a-change/
#include <iostream>
using namespace std;
int minCoins(int coins[], int m, int amount) {
if (amount == 0) return 0;
int res = INT_MAX;
for (int i = 0; i < m; i++) {
if (coins[i] <= amount) {
int sub_res = minCoins(coins, m, amount - coins[i]);
if (sub_res != INT_MAX && sub_res + 1 < res) { // avoid overflow
res = sub_res + 1;
}
}
}
return res;
}
int main() {
int coins[] = { 6, 5, 1 };
int amount = 9;
cout << "Min coins is "
<< minCoins(coins, sizeof(coins) / sizeof(coins[0]), amount)
<< endl;
return 0;
}
About the problem:
Your Segmentation fault comes from the line:
best = min (best, solve (x - i, a, n) + 1);
The reason is: x-i will always gives you the same value so if you are run the program without debugging, your program crashing. So don't try to debug it because it will takes a lot of time to see this crashing.
For starters change to: best = min (best, solve (x - a[i], a, n) + 1);.
After fixing the section 1, the if case: if (x < 0) return INT_MAX; will causes problem and will return always the same value, which is: -INT_MAX. So you need to check the "if cases" again.
The algorithm you try to implement is not correct, see the pseudo-code of this algorithm:
minchange(M):
if M = 0:
return 0
v <- infinity
for c in denominations <= M:
v <- min { minchange(M - c) + 1, v }
return v
Better use: sizeof(a) / sizeof(a[0]) instead of int n = 3.