Leetcode 416. 分割等和子集

0/1背包

物品是nums[i]，重量是nums[i]，价值也是nums[i]，背包体积是sum/2

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int n = nums.size();
        if (n < 2) return false;
        int sum = 0, Max = 0;

        for (int i = 0; i < n; i++) {
            sum += nums[i];
            Max =  max(Max, nums[i]);
        }

        int target = sum / 2;
        if (sum % 2 == 1 || Max > target) return false;

        vector<vector<int>> dp(n, vector<int>(target + 1, 0));

        // 初始化
        for (int j = nums[0]; j <= target; j++) 
            dp[0][j] = nums[0];
            
        for (int i = 1; i < n; i++) {
            for (int j = 1; j <= target; j++) {
                if (j >= nums[i])
                    dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - nums[i]] + nums[i]);
                else
                    dp[i][j] = dp[i - 1][j];
            }
        }
        if (dp[n -1][target] == target)
            return true;
        else
            return false;
    }
};

空间优化(滚动数组)

class Solution {
public:
    bool canPartition(vector<int>& nums) {
        int n = nums.size();
        if (n < 2) return false;
        int sum = 0, Max = 0;

        for (int i = 0; i < n; i++) {
            sum += nums[i];
            Max =  max(Max, nums[i]);
        }

        int target = sum / 2;
        if (sum % 2 == 1 || Max > target) return false;

        vector<int> dp(target + 1, 0);

        // 初始化
        for (int i = 0; i < n; i++) {
            for (int j = target; j >= nums[i]; j--) {
                    dp[j] = max(dp[j], dp[j - nums[i]] + nums[i]);
            }
        }
        if (dp[target] == target)
            return true;
        else
            return false;
    }
};