416. Partition Equal Subset Sum(第十六周)

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.

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum % 2 == 1) return false;
        int record = sum / 2;
        vector<bool> dp(recorf + 1, false);
        dp[0] = true;
        for (int i = 0; i < nums.size(); ++i) {
            for (int j = record; j >= nums[i]; --j) {
                dp[j] = dp[j] || dp[j - nums[i]];
            }
        }
        return dp.back();
    }
};
class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int sum = accumulate(nums.begin(), nums.end(), 0);
        if (sum % 2 == 1) return false;
        int record = sum / 2;
        vector<bool> dp(recorf + 1, false);
        dp[0] = true;
        for (int i = 0; i < nums.size(); ++i) {
            for (int j = record; j >= nums[i]; --j) {
                dp[j] = dp[j] || dp[j - nums[i]];
            }
        }
        return dp.back();
    }
};

Write a C program to partitions a hypergraph G = (V, E) into 2 partitions. The Assignment Write a computer program that takes a netlist represented by a weighted hypergraph and partitions it into two partitions. Each node is associated with an area value and each edge has an edge cost. Your program should minimize the total cost of the cut set, while satisfying the area constraint that the total area of partition 1 should satisfy the balance criteria as described in the class. That is, if the area sum of all the nodes is A, then the area of partition 1 should be greater than or equal to ra-tio_factor *A – amax and less than or equal to ratio_factor *A + amax, where amax is the maximum value among all cell areas. The program should prompt the user for the value of ratio_factor. Assumptions and Requirements of the Implementation 1. Your program should not have any limitation on the maximum number of nodes and the edges of the hypergraph. Each hyperedge could connect any subset of nodes in the hypergraph. 2. Each node area is a non-negative integer, and each edge cost is a non-negative floating- point value. 3. All the ids are 0-based. Namely, the id of the first element is 0, instead of 1. 4. The output of each partition should include the list of node ids, sorted in the ascending order. 5. The partition with the smaller minimum node id is listed first in the output. 6. Use balance criteria as the tiebreaker when there are multiple cell moves giving the max-imum gain, as described in the class. 7. Use the input and output formats given in the Sample Test Cases section. Sample Test Cases Test1: Please enter the number of nodes: 4 Please enter each of the 4 nodes with its id and the node area: 0 1 1 1 2 1 3 1 Please enter the number of edges: 3 Please enter each of the 3 edges with the number of connected nodes and their node ids, followed by the edge cost: 2 0 1 1 2 1 2 3 2 2 3 1 Please enter the percentage of the ratio factor: 50 The node ids of the partition 0 are 0 The node ids of the partition 1 are 1, 2, 3 The total cut cost is 1 Test2: Please enter the number of nodes: 4 Please enter each of the 4 nodes with its id and the node area: 0 1 1 4 2 2 3 1 Please enter the number of edges: 3 Please enter each of the 3 edges with the number of connected nodes and their node ids, followed by the edge cost: 3 0 1 2 5 3 0 2 3 3 3 0 1 3 4 Please enter the percentage of ratio factor: 50 The node ids of the partition 0 are 3 The node ids of the partition 1 are 0, 1, 2 The total cut cost is 7
07-08
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