Given n items with size A[i], an integer m denotes the size of a backpack. How full you can fill this backpack?
You can not divide any item into small pieces.
If we have 4 items with size [2, 3, 5, 7], the backpack size is 11, we can select 2, 3 and 5, so that the max size we can fill this backpack is 10. If the backpack size is 12. we can select [2, 3, 7] so that we can fulfill the backpack.
You function should return the max size we can fill in the given backpack.
Analysis:
DP.
boolean d[i][j]: From the first i items, can we select some items so that their weight equals to j.
d[i][j] = d[i-1][j] || d[i-1][j-A[i-1]].
d[0][0] = true;
We can use 1D array to perform the DP.
d[j] = d[j] || d[j-A[i-1]].
NOTE: for 1D array, the j must be decreased from m to 0 rather increasing from 0 to m!
Solution:
1 public class Solution { 2 /** 3 * @param m: An integer m denotes the size of a backpack 4 * @param A: Given n items with size A[i] 5 * @return: The maximum size 6 */ 7 public int backPack(int m, int[] A) { 8 if (A.length==0) return 0; 9 10 int len = A.length; 11 boolean[] size = new boolean[m+1]; 12 Arrays.fill(size,false); 13 size[0] = true; 14 for (int i=1;i<=len;i++) 15 for (int j=m;j>=0;j--){ 16 if (j-A[i-1]>=0 && size[j-A[i-1]]) 17 size[j] = size[j-A[i-1]]; 18 } 19 20 for (int i=m; i>=0;i--) 21 if (size[i]) return i; 22 23 return 0; 24 } 25 }