LeetCode ： 416. Partition Equal Subset Sum 数组拆分成两个相等子集 0-1背包问题

电玩女神 2021-06-24 16:10 248阅读 0赞

**试题**  
Given a non-empty array containing only positive integers, find if the array can be partitioned into two subsets such that the sum of elements in both subsets is equal.

Note:

Each of the array element will not exceed 100.  
The array size will not exceed 200.

Example 1:

Input: \[1, 5, 11, 5\]

Output: true

Explanation: The array can be partitioned as \[1, 5, 5\] and \[11\].

Example 2:

Input: \[1, 2, 3, 5\]

Output: false

Explanation: The array cannot be partitioned into equal sum subsets.  
**代码**  
看成0-1背包问题：能否用当前的数组组合出值为W的子集。

class Solution {
        public boolean canPartition(int[] nums) {
            int sum = 0;
            for(int num:nums){
                sum += num;
            }
            if(sum%2==1) return false;
            int W = sum/2;
            
            boolean[] dp = new boolean[W+1];
            dp[0] = true; // 初始值考虑的是dp[i-num]情况，当i==num时应该为true。
            
            for(int num:nums){
                for(int i=W; i>=num; i--){
                    dp[i] = dp[i] || dp[i-num]; //如果不加num时dp[i]已经为true，那么说明从开始到num这么多数是可以组合出和为dp[i]的，反之，加入num，就看dp[i-num]加上num能否组合出。
                }
            }
            return dp[W];
        }
    }