Problem:
0-1 Knapsack Problem II

You have N items that you want to put them into a knapsack. Item i has value vi and weight wi.

You want to find a subset of items to put such that:

The total value of the items is as large as possible.

The items have combined weight at most W, that is capacity of the knapsack.

Find the maximum total value of items in the knapsack.

Input

N W
v1 w1
v2 w2
:
vN wN

The first line consists of the integers N and W. In the following N lines, the value and weight of the i-th item are given.

Output

Print the maximum total values of the items in a line.

Constraints

1 ≤ N ≤ 100

1 ≤ vi ≤ 100

1 ≤ wi ≤ 10,000,000

1 ≤ W ≤ 1,000,000,000

Sample Input 1

4 5
4 2
5 2
2 1
8 3

Sample Output 1

13

Sample Input 2

2 20
5 9
4 10

Sample Output 2

9

Solution in C (judge verdict: Runtime Error)

#include<stdio.h>
#include<stdlib.h>
struct goods {
  int profit;
  int weight;
};
int **C;
struct goods *item;
int knapsack(int size, int limit);
int main(void)
{
  int i, n, w;
  scanf("%d%d", &n, &w);
  C = (int**)malloc(sizeof(int*) * (n + 1));
  item = (struct goods*)malloc(sizeof(struct goods) * (n + 1));
  for (i = 0; i <= n; i++) {
    C[i] = (int*)malloc(sizeof(int) * (w + 1));
    C[i][0] = 0;
    if (i) scanf("%d%d", &item[i].profit, &item[i].weight);
  }
  for (i = 0; i <= w; i++) C[0][i] = 0;
  printf("%d\n", knapsack(n, w));
  for (i = 0; i <= n; i++) free(C[i]);
  free(C);
  free(item);
}
int knapsack(int size, int limit)
{
  int i, j;
  for (i = 1; i <= size; i++) {
    for (j = 1; j <= limit; j++) {
      C[i][j] = C[i-1][j];
      if (item[i].weight > j) continue;
      if (item[i].profit + C[i-1][j-item[i].weight] > C[i-1][j]) {
        C[i][j] = item[i].profit + C[i-1][j-item[i].weight];
      }
    }
  }
  return C[size][limit];
}
/*#include<stdio.h>
#include<stdlib.h>
#include<limits.h>
struct knapsack {
  int profit;
  int weight;
};
struct knapsack *goods;
int maxprofit, n;
int cmp(const void *a, const void *b);
void backtrack(int phase, int p, int w);
int main (void)
{
  int i, limit;
  scanf("%d %d", &n, &limit);
  goods = (struct knapsack*)malloc(sizeof(struct knapsack) * (n + 1));
  for (i = 0; i < n; i++) scanf("%d %d", &goods[i].profit, &goods[i].weight);
  goods[n].profit = 0;
  goods[n].weight = INT_MAX;
  qsort(goods, n, sizeof(struct knapsack), cmp);
  backtrack(0, 0, limit);
  printf("%d\n", maxprofit);
  free(goods);
}
int cmp (const void *a, const void *b)
{
  struct knapsack ta = *(struct knapsack*)a, tb = *(struct knapsack*)b;
  if ((double)ta.profit / ta. weight < (double)tb.profit / tb.weight) return 1;
  else if ((double)ta.profit / ta. weight > (double)tb.profit / tb.weight) return -1;
  else return 0;
}
void backtrack(int phase, int p, int w)
{
  if (phase >= n) {
    if (p > maxprofit) maxprofit = p;
  } else {
    double z = 0.0, u = w;
    int i = phase + 1;
    if (goods[phase].weight <= w) {
      backtrack(phase + 1, p + goods[phase].profit, w - goods[phase].weight);
    }
    while (goods[i].weight <= u) {
      u -= goods[i].weight;
      z += goods[i].profit;
      i++;
    }
    z += u * goods[i].profit / goods[i].weight;
    if (z + p > maxprofit) {
      backtrack(phase + 1, p, w);
    }
  }
}
*/