416. Partition Equal Subset Sum (Medium)

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: DP 46ms

Subset Sum Problem

Algorithm:

Firstly this algorithm can be viewed as knapsack problem where individual array elements are the weights and half the sum as total weight of the knapsack.

1.take a solution array as boolean array sol[] of size sum/2+1

1. For each array element,traverse the array and set sol [j] to be true if sol [j – value of array] is true

3.Let halfsumcloser be the closest reachable number to half the sum and partition are sum-halfsumcloser and halfsumcloser.

4.start from halfsum and decrease halfsumcloser once everytime until you find that sol[halfsumcloser] is true

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