0-1 Knapsack for large weights - c++

Question

I am trying to solve the 0-1 Knapsack for the large weights problem. Constraints for the problem are :
*All values in input are integers.
$$1 \leq N \leq 100$$
$$1 \leq W \leq 10^9$$
$$1 \leq w_i \leq W$$
$$1 \leq v_i \leq 10^3*$$
Below is the code which I have written with comments.
#include <vector>
#include <algorithm>
#include <climits>
using namespace std;
const int V = 1e5;
const int N = 100;
int main() {
int n, w, inp1, inp2, max_val = -1;
vector<pair<int, int>> arr;
cin >> n >> w; // n - no of items, w - total weight that the knapsack can hold
for(int i = 0; i < n; i++){
cin >> inp1 >> inp2; // ith input : w_i v_i
arr.push_back({inp1, inp2});
max_val = max(max_val, inp2); // storing maximum value of an item from the inputs
}
unsigned long long int dp[N + 1][V + 1]; // dp[i][j] = min weight that can be obtained from items 0..(i - 1) having total value atmost j
for(int i = 0; i <= n; i++){
for(int j = 0; j <= (max_val * n); j++){
if(i == 0 || j == 0)
dp[i][j] = ULLONG_MAX;
else if(j >= arr[i].second)
dp[i][j] = min(dp[i - 1][j], dp[i - 1][j - arr[i - 1].second] + arr[i - 1].first);
else
dp[i][j] = dp[i - 1][j];
}
}
for(int i = 0; i <= n; i++){
for(int j = 0; j <= (max_val * n); j++)
cout << dp[i][j] << " ";
cout << endl;
}
int i;
for(i = (max_val * n); i >= 1; i--){
if(dp[n][i] != ULLONG_MAX && dp[n][i] <= w)
break;
}
cout << i;
return 0;
}
But I am not getting correct answer for all inputs. For example, for input
3 8
3 30
4 50
5 60
I am getting 180 as answer, whereas 90 is the accurate answer. Please help me fix it.

Answer 1

You are using 2-D array when weight can be 10^9,
And the complexity of your code is O(n*w).
So that will give TLE in other cases.
Use unordered_map for memoization.