leetcode Interleaving String-优快云博客

本文链接：https://blog.youkuaiyun.com/taoqick/article/details/15659829

本文探讨了如何判断一个字符串是否可以通过两个给定字符串交错组成。通过深度优先搜索（DFS）和动态规划（DP）两种方法实现，并针对DP方法进行了优化。

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Interleaving String

Total Accepted: 2080 Total Submissions: 12038 My Submissions

Given s1, s2, s3, find whether s3 is formed by the interleaving of s1 and s2.

For example,
Given:
s1 = "aabcc",
s2 = "dbbca",

When s3 = "aadbbcbcac", return true.
When s3 = "aadbbbaccc", return false.

First, I wrote a DFS program using a stack, however, TLE

class Solution {
 public:
  bool isInterleave(string s1, string s2, string s3) {
    int i = 0, j = 0, k = 0;
    stack<int> s3stack, s2stack;
    if (s1.length() + s2.length() != s3.length())
      return false;
    
    for (k = 0; k < s3.length(); ++k) {
      if (i < s1.length() && s3[k] == s1[i]) {
        if (j < s2.length() && s3[k] == s2[j]) {
          s3stack.push(k);
          s2stack.push(j);
        }
        ++i;
      }
      else {
        if (j < s2.length() && s3[k] == s2[j])
          ++j;
        else {
          if (s3stack.empty())
            return false;
          k = s3stack.top();
          s3stack.pop();
          j = s2stack.top();
          s2stack.pop();
          i = k -j;
          ++j;
        }
      }
    }
    if (i == s1.length() && j == s2.length())
      return true;
    else
      return false;
  }
};

After reading the solution from other people, I wrote a DP program, however, I can't simplify the DP matrix to dp[k][i] though many statuses are redundant.. So the following is the code:

class Solution {
 public:
  bool isInterleave(string s1, string s2, string s3) {
    int i = 0, j = 0, k = 0;
    if (s1.length() + s2.length() != s3.length())
      return false;

    vector<vector<vector<bool>>> dp(s3.length()+1, vector<vector<bool>> (s1.length()+1, vector<bool> (s2.length()+1, false)));
    for (i = 0; i <= s1.length(); ++i)
      for (j = 0; j <=s2.length(); ++j)
        dp[0][i][j] = true;
    int less = s1.length() < s2.length() ? s1.length() : s2.length();    
    for (k = 0; k <= less; ++k)
      dp[k][0][k] = dp[k][k][0] = true;
      
    for (k = 1; k <= s3.length(); ++k) {
      int s1len = s1.length(), s2len = s2.length();
      int start = max(0,k-s2len);
      int end = min(k,s1len);
      for (i = start; i <= end; ++i)
        dp[k][i][k-i] = ((i>=1 && dp[k-1][i-1][k-i] && s3[k-1] == s1[i-1]) || (i<=k-1 && dp[k-1][i][k-i-1] && s3[k-1] == s2[k-i-1])) ? true : false;   
    }
    return dp[s3.length()][s1.length()][s2.length()];
  }
};

I made several mistakes:

1. The boundry: it's different for i>=1 and i <= k-1

2. You'd better use a variable to store s1.length() and s2.length(), the following code is wrong:

int start = (((k-s2.length()) > 0) ? (k-s2.length()) : 0);

but

int s2len = s2.length();
int start = (((k-s2len) > 0) ? (k-s2len) : 0);

is right.

So don't use s.length() for the operation

vector<vector<vector<bool>>> dp(s3.length()+1, vector<vector<bool>> (s1.length()+1, vector<bool> (s2.length()+1, false)));