#### Strange behaviour of integer overflow

I created the following code for finding the answer to the coin problem. This involves finding minimum number of coins of given k denominations (where each such coins are in infinite supply) to form a target sum n. In particular I have investigated the case where `k=5`, denominations = `{2,3,4,5,6}` and target sum `n=100`.

Code:

``````#include<iostream>
#include<algorithm>
using namespace std;

int coins[5] = {2,3,4,5,6};
int values[101];
int n=100;
int k=5;
int INF = INT_MAX;

int main()
{
for (int x=1;x<=n;x++)
{
values[x] = INF;
for (int j=1;j<=k;j++)
{
if (x-coins[j-1]>=0)
{
values[x] = min(values[x],values[x-coins[j-1]]+1);
}
}
}
cout<<values[100];

return 0;
}
``````

The output to this code that I received is `-2147483632`. Clearly some kind of overflow must be occurring so I decided to output `INF+1`. And I got `INT_MIN` as the answer. But I had also remembered that often while outputting some numbers beyond the int range there was no such problem.

I decided to output `1e11` and to my surprise the answer was still `1e11`. Why is this happening, please help.

Source: Windows Questions C++