美文网首页动态规划
115. Distinct Subsequences

115. Distinct Subsequences

作者: Jeanz | 来源:发表于2017-07-27 03:14 被阅读20次

    Given a string S and a string T, count the number of distinct subsequences of S which equals T.

    A subsequence of a string is a new string which is formed from the original string by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, "ACE" is a subsequence of "ABCDE" while "AEC" is not).

    Here is an example:
    S = "rabbbit", T = "rabbit"

    Return 3.

    一刷
    用dp来求解。构造二维数组dp[s.length()+1][t.length()+1], dp[i][0]=1;(当t为[]时),如果s.charAt(i-1) == t.charAt(j-1), dp[i][j] = dp[i-1][j-1] + dp[i-1][j], 如果不等, dp[i][j] = dp[i-1][j]

    public class Solution {
        public int numDistinct(String s, String t) {
            if(s == null || t == null) return 0;
            int[][] dp = new int[s.length() + 1][t.length() + 1];
            
            for(int i=0; i<=s.length(); i++){
                dp[i][0] = 1;
            }
            
            for(int i=1; i<=s.length(); i++){
                for(int j=1; j<=t.length(); j++){
                    dp[i][j] = dp[i-1][j];
                    if(s.charAt(i-1) == t.charAt(j-1))
                        dp[i][j] += dp[i-1][j-1];
                }
            }
            
            return dp[s.length()][t.length()];
        }
    }
    

    二刷
    空间复杂度O(m)
    由于我们仅用到了dp[i-1][j-1], dp[i-1][j],考虑用一维数组替换二维数组
    对于i, j, 未修改dp[j]时,此时dp[j]表示dp[i-1][j], 对于下一个j, 表示为dp[i-1][j-1]

    public class Solution {
        public int numDistinct(String s, String t) {
            int n = s.length(), m = t.length();
            int[] cur = new int[m+1];
            cur[0] = 1;
            for(int i=1; i<=n; i++){
                int prev = 1;
                for(int j=1; j<=m; j++){
                    int temp = cur[j];
                    if(s.charAt(i-1) == t.charAt(j-1)) cur[j] += prev;
                    prev = temp;
                }
            }
            return cur[m];
        }
    }
    

    相关文章

      网友评论

        本文标题:115. Distinct Subsequences

        本文链接:https://www.haomeiwen.com/subject/nvpakxtx.html