416. Partition Equal Subset Sum
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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.
Approach #1: DP. [C++]
class Solution { public: bool canPartition(vector<int>& nums) { int sum = std::accumulate(nums.begin(), nums.end(), 0); if (sum % 2 != 0) return false; vector<int> dp(sum+1, 0); dp[0] = 1; for (int num : nums) { for (int i = sum; i >= 0; --i) if (dp[i]) dp[i+num] = 1; if (dp[sum/2]) return true; } return false; } };
Analysis:
dp[i][j] : whether we can sum to j using first i numbers.
dp[i][j] = true if dp[i-1][j-num]
check dp[n-1][sum/2]
init dp[-1][0] = true
Time complexity: O(n^2*sum) -> O(n*sum)
Space complexity: O(sum)
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Leetcode 416. Partition Equal Subset Sum