Partition Equal Subset Sum.cpp

[leetcode]416-Partition Equal Subset Sum

链接：https://leetcode.com/problems/partition-equal-subset-sum/description/

Question

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:

1. Each of the array element will not exceed 100.
2. 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.

Solution

class Solution {
public:
  bool canPartition(vector<int>& nums) {
    int sum = 0;
    int size = nums.size();
    for (int i = 0; i < size; i++)
      sum += nums[i];
    if (sum % 2 == 1) return false;
    vector<vector<bool> > dp;
    dp.resize(size+1);
    for (int i = 0; i <= size; i++) dp[i].resize(sum, false);

    dp[0][0] = true;
    for (int i = 1; i <= size; i++) {
      for (int j = 0; j <= sum; j++) {
        if (j >= nums[i-1]) dp[i][j] = dp[i-1][j-nums[i-1]] || dp[i-1][j];
        else dp[i][j] = dp[i-1][j];
        if (j == sum/2 && dp[i][j] == true)
          return true;
      }
    }
    return false;
  }
};

思路：dp[i][j]表示是否可能前i个数中的总和为j，为true就是有可能，为false就是没有可能。状态转移很简单，每次要不选择nums[j]，要不干脆不选，看看有没有可能。如果在中间直接有机会等于sum/2就说明成功了。