Problem p02316 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <algorithm>
#include <bitset>
#include <cmath>
#include <complex>
#include <cstdio>
#include <fstream>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <tuple>
#include <utility>
#include <vector>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;
typedef vector<ll> V;
typedef complex<double> Point;

#define PI acos(-1.0)
#define EPS 1e-10
const ll INF = 1e12;
const ll MOD = 1e9 + 7;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define rep(i, N) for (int i = 0; i < (N); i++)
#define ALL(s) (s).begin(), (s).end()
#define EQ(a, b) (abs((a) - (b)) < EPS)
#define EQV(a, b) (EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()))
#define fi first
#define se second
#define N_SIZE (1LL << 20)
#define NIL -1
#define MAX_N 100100

ll sq(ll num) { return num * num; }
ll mod_pow(ll x, ll n) {
  if (n == 0)
    return 1;
  if (n == 1)
    return x % MOD;
  ll res = sq(mod_pow(x, n / 2));
  res %= MOD;
  if (n % 2 == 1) {
    res *= x;
    res %= MOD;
  }
  return res;
}
ll mod_add(ll a, ll b) { return (a + b) % MOD; }
ll mod_sub(ll a, ll b) { return (a - b + MOD) % MOD; }
ll mod_mul(ll a, ll b) { return a * b % MOD; }

int n, W;
int w[100], v[100];
int dp[101][10100];
// dp[i+1][j]:i???????????§???????????§?????????j??\\??????????????¨?????????????????????????????§???

int main() {
  cin >> n >> W;
  for (int i = 0; i < n; i++)
    cin >> v[i] >> w[i];
  // for (int i = 0; i < n; i++) {
  //	for (int j = 0; j <= W; j++) {
  //		for (int k = 0; k*w[i] <= j; k++) {
  //			dp[i + 1][j] = max(dp[i + 1][j], dp[i][j - k*w[i]] +
  //k*v[i]);
  //		}
  //	}
  // }

  for (int i = 0; i < n; i++) {
    for (int j = 0; j <= W; j++) {
      if (j < w[i]) {
        dp[i + 1][j] = dp[i][j];
      } else {
        dp[i + 1][j] = max(dp[i][j], dp[i + 1][j - w[i]] + v[i]);
      }
    }
  }

  // rep(i, n + 1) {
  //	rep(j, W + 1) {
  //		printf("%3d", dp[i][j]);
  //	}
  //	cout << endl;
  // }
  cout << dp[n][W] << endl;
}

Error: TLE

Fixed submission:

#include <algorithm>
#include <bitset>
#include <cmath>
#include <complex>
#include <cstdio>
#include <fstream>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <time.h>
#include <tuple>
#include <utility>
#include <vector>

using namespace std;

typedef long long ll;
typedef pair<ll, ll> P;
typedef vector<ll> V;
typedef complex<double> Point;

#define PI acos(-1.0)
#define EPS 1e-10
const ll INF = 1e12;
const ll MOD = 1e9 + 7;

#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define rep(i, N) for (int i = 0; i < (N); i++)
#define ALL(s) (s).begin(), (s).end()
#define EQ(a, b) (abs((a) - (b)) < EPS)
#define EQV(a, b) (EQ((a).real(), (b).real()) && EQ((a).imag(), (b).imag()))
#define fi first
#define se second
#define N_SIZE (1LL << 20)
#define NIL -1
#define MAX_N 100100

ll sq(ll num) { return num * num; }
ll mod_pow(ll x, ll n) {
  if (n == 0)
    return 1;
  if (n == 1)
    return x % MOD;
  ll res = sq(mod_pow(x, n / 2));
  res %= MOD;
  if (n % 2 == 1) {
    res *= x;
    res %= MOD;
  }
  return res;
}
ll mod_add(ll a, ll b) { return (a + b) % MOD; }
ll mod_sub(ll a, ll b) { return (a - b + MOD) % MOD; }
ll mod_mul(ll a, ll b) { return a * b % MOD; }

int n, W;
int w[100], v[100];
int dp[101][10100];
// dp[i+1][j]:i???????????§???????????§?????????j??\\??????????????¨?????????????????????????????§???

int main() {
  cin >> n >> W;
  for (int i = 0; i < n; i++)
    cin >> v[i] >> w[i];
  for (int i = 0; i < n; i++) {
    for (int j = 0; j <= W; j++) {
      for (int k = 0; k * w[i] <= j; k++) {
        dp[i + 1][j] = max(dp[i + 1][j], dp[i][j - k * w[i]] + k * v[i]);
      }
    }
  }
  // for (int i = 0; i < n; i++) {
  //	for (int j = 0; j <= W; j++) {
  //		if (j < w[i]) {
  //			dp[i + 1][j] = dp[i][j];
  //		}
  //		else {
  //			dp[i + 1][j] = max(dp[i][j], dp[i][j - w[i]] + v[i]);
  //		}
  //	}
  // }
  // rep(i, n + 1) {
  //	rep(j, W + 1) {
  //		printf("%3d", dp[i][j]);
  //	}
  //	cout << endl;
  // }
  cout << dp[n][W] << endl;
}