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# Backpack

## 题目描述

Given n items with size Ai, an integer m denotes the size of a backpack. How full you can fill this backpack?
Example
Example 1:
Input: [3,4,8,5], backpack size=10
Output: 9
Example 2:
Input: [2,3,5,7], backpack size=12
Output: 12
Challenge
O(n x m) time and O(m) memory.
O(n x m) memory is also acceptable if you do not know how to optimize memory.

## 代码

public class Solution {
public int backpack (int m, int[] A) {
if (A == null || A.length < 0) {
return 0;
}
int[] f = new int[m + 1];
for (int i = 0; i < A.length; i++) {
for (int j = m; i > 0; j--) {
if (j >= A[i]) {
f[j] = Math.max(f[j], f[j - A[i]] + A[i]);
}
}
}
return f[m];
}
}
public class Solution {
public int backpack (int m, int[] A) {
if (A == null || A.length < 0) {
return 0;
}
int[][] f = new int[A.length + 1][m + 1];
for (int i = 1; i < A.length; i++) {
for (int j = 0; i <= m; j++) {
if (j >= A[i]) {
f[i][j] = Math.max(f[i - 1][j], f[i - 1][j - A[i] + A[i]);
} else {
f[i][j] = f[i - 1][j];
}
}
}
return f[A.length][m];
}
}