Every time I change the constant, the result is different - c++

Question

I want to code the 01 Knapsack problem with c++. Each time I change the value of a constant MAX to a different value, such as 100,90, or 80, the result is different. What's the cause? I'm using Visual Studio 2019.
The input is a text file, for example.
20
40 35 18 4 10 2 70 20 39 37 7 5 10 8 15 21 50 40 10 30
100 50 45 20 10 5 31 10 20 19 4 3 6 8 12 7 10 2 5 5
137
The first row is the number of objects, the second row is the price, the third row is the weight, and the last row is the size of the knapsack.
#include <stdio.h>
#include <time.h>
#define MAX 100
#define CLOCKS_PER_MS CLOCKS_PER_SEC/1000
int X_d[MAX] = { 0 }; //solution vector
int max(int a, int b) {
if (a >= b)
return a;
else
return b;
}
void dynamic(int n, int M, int p[], int w[]) {
int result;
int i, y, k;
int P[MAX][MAX] = { 0 };
clock_t start, finish;
start = clock();
for (i = 0; i <= n; i++) {
for (y = 0; y <= M; y++) {
if (i == 0 || y == 0)
P[i][y] = 0;
else if (w[i - 1] > y)
P[i][y] = P[i - 1][y];
else
P[i][y] = max(P[i - 1][y], p[i - 1] + P[i - 1][y - w[i - 1]]);
}
}
finish = clock();
result = P[n][M];
y = M;
for (i = n; i > 0 && result > 0; i--) {
if (result == P[i - 1][y]) {
continue;
}
else {
X_d[i - 1] = 1;
result = result - p[i - 1];
y = y - w[i - 1];
}
}
printf("\n(1) Dynamic Programming");
printf("\nThe maximum profit is $%d", P[n][M]);
printf("\nThe solution vetor X = ( ");
for (k = 0; k < n; k++)
printf("%d ", X_d[k]);
printf(")\n");
printf("The execution time is %f milliseconds.\n", (float)(finish - start) / CLOCKS_PER_MS);
}
int main() {
int i, j;
int num, M;
int p[MAX] = { 0 }, w[MAX] = { 0 };
FILE* fp = NULL;
fopen_s(&fp, "p2data6.txt", "r");
fscanf_s(fp, "%d", &num);
for (i = 0; i < num; i++)
fscanf_s(fp, "%d", &p[i]);
for (i = 0; i < num; i++)
fscanf_s(fp, "%d", &w[i]);
fscanf_s(fp, "%d", &M);
printf("n = %d\n", num);
printf("pi = ");
for (i = 0; i < num; i++)
printf("%3d ", p[i]);
printf("\nwi = ");
for (i = 0; i < num; i++)
printf("%3d ", w[i]);
printf("\npi/wi = ");
for (i = 0; i < num; i++)
printf("%f ", (double)p[i] / w[i]);
printf("\nM = %d\n", M);
dynamic(num, M, p, w);
return 0;
}

Answer 1

Geeks for Geeks has a very good explanation of this problem here:
To quote the Geeks for Geeks article by Sam007:
A simple solution is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.
1) Optimal Substructure:
To consider all subsets of items, there can be two cases for every item: (1) the item is included in the optimal subset, (2) not included in the optimal set.
Therefore, the maximum value that can be obtained from n items is max of following two values.
1) Maximum value obtained by n-1 items and W weight (excluding nth item).
2) Value of nth item plus maximum value obtained by n-1 items and W minus weight of the nth item (including nth item).
If weight of nth item is greater than W, then the nth item cannot be included and case 1> is the only possibility.
2) Overlapping Subproblems
Following is recursive implementation that simply follows the recursive structure mentioned above.