Having trouble implementing pseudocode for Subset Sum - c++

Question

so I am trying to implement the following pseudocode but it will not work as it is supposed to. Here is the problem description in the slide, "Given an integer bound, "W", and a collection of "n" items, each with a positive integer weight "wi", find a subset S of items that: maximizes Sigma sub i where i is an element of S "wi" while keeping this sum less than or equal or to W. I will attach the following slides for where I am getting the problem description and pseudocode from. The problem with my implementation is that it will only find the total max value and not the value that is less than or equal to the weight. So for example, if I had Weight 10 (W = 10) and items 3 (n = 3) with item weights 1, 4, & 8 then the following answer should be 9; however, my solution gives 12. Here are the slides (*Please not, where it says w[j] it is meant to be w[i] - the slide had a typo):
Here is my code that implements the pseudocode:
#include <stdio.h>
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
int max(int a, int b, int c) {
if (a >= b)
return a;
else
return b;
}
int optimal_weight(int W, const vector<int> &wt, int n){
vector<vector<int> > M;
M.resize(n+1);
for(int i = 0; i < n+1; ++i){
M[i].resize(W+1);
}
for(int w = 0; w < W+1; w++){
M[0][w] = 0;
}
for(int i = 1; i < n+1; i++){
M[i][0] = 0;
}
for(int i = 1; i < n+1; i++){
for(int w = 0; w < W+1; w++){
if(wt[i] > w){
M[i][w] = M[i-1][w];
}
M[i][w] = max(M[i-1][w], wt[i] + M[i-1][W-wt[i]], W);
}
}
for (int i = 0; i <= n; i++)
{
for (int j = 0; j <= W; j++)
printf ("%4d", M[i][j]);
printf("\n");
}
return M[n][W];
}
int main()
{
//int val[] = {1, 1, 1};
int W;
int n;
cin >> W >> n;
vector<int> wt(n);
for(int i = 0; i < n; i++){
cin >> wt[i];
}
cout << optimal_weight(W, wt, n) << endl;
}
Thank you for any help!

Answer 1

I figured it out! Here is my solution:
#include <iostream>
#include <vector>
using namespace std;
using std::vector;
int optimal_weight(int W, const vector<int> &wt) {
//write your code here
int n = wt.size();
vector<vector<int> > matrix;
matrix.resize(W+1);
for(int i = 0; i < W+1; i++){
matrix[i].resize(n);
}
for(int j = 0; j < n; j++){
matrix[0][j] = 0;
}
for(int w = 0; w < W + 1; w++){
matrix[w][0] = 0;
}
for(int i = 1; i < n; i++){
for(int w = 1; w < W+1; w++){
matrix[w][i] = matrix[w][i-1];
if(wt[i] <= w){
//cout << wt[i] << endl;
int val = matrix[w-wt[i]][i-1] + wt[i];
if(matrix[w][i] < val){
matrix[w][i] = val;
}
}
}
}
return matrix[W][n-1];
}
int main() {
int n, W;
std::cin >> W >> n;
vector<int> wt(n+1);
for (int i = 1; i < n+1; i++) {
wt[0]=0;
std::cin >> wt[i];
}
std::cout << optimal_weight(W, wt) << '\n';
}