AlgorithmJourney/LeetCode/LeetCode416.java at main · HenryJi529/AlgorithmJourney · GitHub

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
public class LeetCode416 {
    public static void main(String[] args) {
        // 输入：nums = [1,5,11,5]
        // 输出：true
        System.out.println(new Solution416_2().canPartition(new int[] { 1, 5, 11, 5 }));

        // 输入：nums = [1,2,3,5]
        // 输出：false
        System.out.println(new Solution416_2().canPartition(new int[] { 1, 2, 3, 5 }));
    }
}

/**
 * 针对NP问题，采用时间复杂度与元素大小相关的动态规划
 */
class Solution416_1 {
    public boolean canPartition(int[] nums) {
        int n = nums.length;
        if (n < 2) {
            return false;
        }
        int sum = 0, maxNum = 0;
        for (int num : nums) {
            sum += num;
            maxNum = Math.max(maxNum, num);
        }
        if (sum % 2 != 0) {
            return false;
        }
        int target = sum / 2;
        if (maxNum > target) {
            return false;
        }
        boolean[][] dp = new boolean[n][target + 1];
        for (int i = 0; i < n; i++) {
            dp[i][0] = true;
        }
        dp[0][nums[0]] = true;
        for (int i = 1; i < n; i++) {
            int num = nums[i];
            for (int j = 1; j <= target; j++) {
                if (j >= num) {
                    dp[i][j] = dp[i - 1][j] | dp[i - 1][j - num];
                } else {
                    dp[i][j] = dp[i - 1][j];
                }
            }
        }
        return dp[n - 1][target];
    }
}

class Solution416_2 {
    public boolean canPartition(int[] nums) {
        int n = nums.length;
        if (n < 2) {
            return false;
        }
        int sum = 0, maxNum = 0;
        for (int num : nums) {
            sum += num;
            maxNum = Math.max(maxNum, num);
        }
        if (sum % 2 != 0) {
            return false;
        }
        int target = sum / 2;
        if (maxNum > target) {
            return false;
        }
        boolean[] dp = new boolean[target + 1];
        dp[0] = true;
        for (int i = 0; i < n; i++) {
            int num = nums[i];
            // NOTE: 这里需要倒序，因为如果正序一轮中靠前的记录会影响靠后的记录
            for (int j = target; j >= num; --j) {
                dp[j] |= dp[j - num];
            }
        }
        return dp[target];
    }
}