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| 1 | +/* |
| 2 | + * @lc app=leetcode id=416 lang=cpp |
| 3 | + * |
| 4 | + * [416] Partition Equal Subset Sum |
| 5 | + */ |
| 6 | + |
| 7 | +// @lc code=start |
| 8 | +class Solution { |
| 9 | +public: |
| 10 | + // 回溯法 超时 |
| 11 | + // bool canPartition(vector<int>& nums) { |
| 12 | + // int pack1 = nums[0]; |
| 13 | + // int pack2 = 0; |
| 14 | + // return traceback(nums, pack1, pack2, 1); |
| 15 | + // } |
| 16 | + |
| 17 | + |
| 18 | + // bool traceback(const vector<int>& nums, int pack1, int pack2, int i) { |
| 19 | + // if (i >= nums.size()) |
| 20 | + // return pack1 == pack2; |
| 21 | + // bool left = traceback(nums, pack1 + nums[i], pack2, i+1); |
| 22 | + // if (left) |
| 23 | + // return true; |
| 24 | + // bool right = traceback(nums, pack1, pack2 + nums[i], i+1); |
| 25 | + // if (right) |
| 26 | + // return true; |
| 27 | + // return false; |
| 28 | + // } |
| 29 | + |
| 30 | + |
| 31 | + |
| 32 | + bool canPartition(vector<int>& nums) { |
| 33 | + int sum = 0; |
| 34 | + int n = nums.size(); |
| 35 | + for (int i = 0; i < n; i++) |
| 36 | + { |
| 37 | + sum += nums[i]; |
| 38 | + } |
| 39 | + if (sum % 2 != 0) // 不为偶数,定不可二分相同 |
| 40 | + { |
| 41 | + return false; |
| 42 | + } |
| 43 | + int target = sum / 2; |
| 44 | + vector<vector<bool>> dp(n, vector<bool>(target + 1, false)); // dp[i][j] 前i个物品, |
| 45 | + for (int i = 0; i < n; i++) |
| 46 | + { |
| 47 | + // 背包容量为 0 说明装满 |
| 48 | + dp[i][0] = true; |
| 49 | + } |
| 50 | + for (int i = 1; i < n; i++) |
| 51 | + { |
| 52 | + for (int j = 0; j < target + 1; j++) |
| 53 | + { |
| 54 | + if (j - nums[i] < 0) |
| 55 | + { |
| 56 | + dp[i][j] = dp[i-1][j]; |
| 57 | + } else |
| 58 | + dp[i][j] = dp[i-1][j] || dp[i-1][j - nums[i]]; |
| 59 | + } |
| 60 | + } |
| 61 | + return dp[n-1][target]; |
| 62 | + } |
| 63 | + |
| 64 | +}; |
| 65 | +// @lc code=end |
| 66 | + |
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