How do I find errors in a recursive function? - c++

Question

I'm trying to find the smallest of the biggest sum of each column of every possible permutations of a given 2D array NxN, where the values in each row can shift towards the left. For example, the array
4 6
3 7
would have 4 possibles permutations:
4 6 6 4 4 6 6 4
3 7 3 7 7 3 7 3
The biggest sum of each permutation is respectively, 13, 11, 11, 13. Thus the smallest of the biggest sums is 11. I have written a recursive function that should work, but for some reason, it only works for arrays that are smaller than 6x6... I'm new at programming, and just recently learned about recursion, any help or counsel on how to think recursively and to debug code would be greatly appreciated...
For the array 4x4
7410 1371 2665 3195
4775 4130 6499 3414
300 2092 4009 7638
5351 210 7225 7207
The answer is 18349, and my code gives me the correct answer.
However, for the array 6x6
5219 842 7793 2098 5109 2621
1372 3253 3804 5652 810 1620
4894 6792 1784 4335 4772 6656
3203 1070 4716 5335 1157 6855
5529 2767 2205 408 7516 7454
375 7036 2597 5288 937 2893
The answer should be 23733, but I've got 24176. How is this possible?
Here's my code:
#include <iostream>
using namespace std;
#define MAX_N 1000
int n, matrix[MAX_N][MAX_N], shift[MAX_N] = {0}, minSum = 100000000;
void possibTree(int position){
//Base case
if(position == n){
for (int i = 0; i < n; i++) {
// Temporary array to store the values in the row that just shifted towards the left
int temp[MAX_N] = {0};
for (int j = 0; j < n; j++) {
if(j - shift[i] < 0)
temp[n+(j-shift[i])] = matrix[i][j];
else
temp[j-shift[i]] = matrix[i][j];
}
for (int k = 0; k < n; k++)
matrix[i][k] = temp[k];
}
int max = 0;
for (int i = 0; i < n; i++) {
int temp = 0;
for (int j = 0; j < n; j++) {
temp += matrix[j][i];
}
if(temp > max)
max = temp;
}
if(minSum > max)
minSum = max;
return;
}
for (int i = 0; i < n; i++) {
shift[position] = i;
possibTree(position+1);
}
return;
}
int main() {
while(cin >> n){
memset(matrix, 0, sizeof(matrix));
memset(shift, 0, sizeof(shift));
if(n == -1) // The user enters "-1" to end the loop and terminate the program.
return 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cin >> matrix[i][j];
}
}
possibTree(0);
cout << minSum << endl;
minSum = 100000000;
}
return 0;
}

Answer 1

Ok I believe I understand my mistake, I have to reset the matrix to its original state at the end of each base case, when the matrices are small, the code is still capable of finding all the possible biggest sums, but when the matrices got bigger, some of the possibilities weren't generated. Here's my code:
#include <iostream>
using namespace std;
#define MAX_N 1000
int n, matrix[MAX_N][MAX_N], OrigMatrix[MAX_N][MAX_N], shift[MAX_N] = {0}, minSum = 100000000;
void possibTree(int position){
//Base case
if(position == n){
for (int i = 0; i < n; i++) {
// Temporary array to store the values in the row that just shifted towards the left
int temp[MAX_N] = {0};
for (int j = 0; j < n; j++) {
if(j - shift[i] < 0)
temp[n+(j-shift[i])] = matrix[i][j];
else
temp[j-shift[i]] = matrix[i][j];
}
for (int k = 0; k < n; k++)
matrix[i][k] = temp[k];
}
int max = 0;
for (int i = 0; i < n; i++) {
int temp = 0;
for (int j = 0; j < n; j++) {
temp += matrix[j][i];
}
if(temp > max)
max = temp;
}
if(minSum > max)
minSum = max;
//EDITS
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
matrix[i][j] = OrigMatrix[i][j];
}
}
return;
}
for (int i = 0; i < n; i++) {
shift[position] = i;
possibTree(position+1);
}
return;
}
int main() {
while(cin >> n){
memset(matrix, 0, sizeof(matrix));
memset(shift, 0, sizeof(shift));
if(n == -1) // The user enters "-1" to end the loop and terminate the program.
return 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cin >> matrix[i][j];
}
}
//EDITS
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
OrigMatrix[i][j] = matrix[i][j];
}
}
possibTree(0);
cout << minSum << endl;
minSum = 100000000;
}
return 0;
}