LC.P300[最长递增子序列]

方法一：记忆化搜索

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class Solution {
    int[] nums, cache;

    public int lengthOfLIS(int[] nums) {
        this.nums = nums;
        int n = nums.length;
        cache = new int[n];
        int ans = 0;
        for (int i = 0; i < n; ++i) {
            ans = Math.max(ans, dfs(i));
        }
        return ans;
    }

    private int dfs(int i) {
        if (cache[i] > 0) return cache[i];
        for (int j = 0; j < i; ++j) {
            if (nums[j] < nums[i]) cache[i] = Math.max(cache[i], dfs(j));
        }
        return ++cache[i];
    }
}
  • 时间复杂度：$O(n^2)$
  • 空间复杂度：$O(n)$

方法二：1:1翻译成递推

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class Solution {
    public int lengthOfLIS(int[] nums) {
        int n = nums.length, ans = 0;
        int[] f = new int[n];
        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < i; ++j) {
                if (nums[j] < nums[i]) f[i] = Math.max(f[i], f[j]);
            }
            ans = Math.max(ans, ++f[i]);
        }
        return ans;
    }
}
  • 时间复杂度：$O(n^2)$
  • 空间复杂度：$O(n)$