标签：style blog class code java c
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.
用回溯TLE，所以想用dp来做。
为了方便计算，从尾往前扫。dp[i][j]表示s3[i+j...n3-1]是不是s1[i...n1-1]和s2[j...n2-1]的interleaving。
如果s3[i+j]=s1[i]，那么s[i+j...n3-1]是不是interleaving，取决于s1[i+1...n1-1]和s2[j...n2-1]是不是合法的interleaving。
如果s[i+1]=s2[j]，同理，取决于取决于s1[i...n1-1]和s2[j+1...n2-1]是不是合法的interleaving。
以上只要有一种情况满足就可以了。
dp[i][j] = ((s3[i + j] == s1[i] && dp[i + 1][j]) || (s3[i + j] == s2[j] && dp[i][j + 1]));
关于初始值：
i=n1的时候，也就是s1=“”，空串和s2是不是一个合法的interleaving，s2后半段和s3后半段都相同的部分全部为true。j=n2同理。
当然也可以认为，dp[i][n2] = (s3[i + n2] == s1[i] && dp[i+1][n2]);dp[n1][i] = (s3[i + n1] == s2[i] && dp[n1][i + 1]);
1 class Solution { 2 public: 3 bool isInterleave(string s1, string s2, string s3) { 4 int n1 = s1.length(), n2 = s2.length(), n3 = s3.length(); 5 if (n1 + n2 != n3) return false; 6 7 vector<vector<bool> > dp(n1 + 1, vector<bool>(n2 + 1, false)); 8 dp[n1][n2] = true; 9 for (int i = n1 - 1; i >= 0; --i) { 10 dp[i][n2] = (s3[i + n2] == s1[i] && dp[i+1][n2]); 11 } 12 for (int i = n2 - 1; i >= 0; --i) { 13 dp[n1][i] = (s3[i + n1] == s2[i] && dp[n1][i + 1]); 14 } 15 16 for (int i = n1 - 1; i >= 0; --i) { 17 for (int j = n2 - 1; j >= 0; --j) { 18 dp[i][j] = ((s3[i + j] == s1[i] && dp[i + 1][j]) 19 || (s3[i + j] == s2[j] && dp[i][j + 1])); 20 } 21 } 22 23 24 return dp[0][0]; 25 } 26 };
因为只用到上一行当前位置和当前行后一个位置，所以二维dp可以再优化成一维。
1 class Solution { 2 public: 3 bool isInterleave(string s1, string s2, string s3) { 4 int n1 = s1.length(), n2 = s2.length(), n3 = s3.length(); 5 if (n1 + n2 != n3) return false; 6 7 vector<bool> dp(n2 + 1, false); 8 dp[n2] = true; 9 10 for (int i = n2 - 1; i >= 0; --i) { 11 dp[i] = (s3[i + n1] == s2[i] && dp[i + 1]); 12 } 13 14 for (int i = n1 - 1; i >= 0; --i) { 15 dp[n2] = (s3[i + n2] == s1[i] && dp[n2]); 16 for (int j = n2 - 1; j >= 0; --j) { 17 dp[j] = ((s3[i + j] == s1[i] && dp[j]) 18 || (s3[i + j] == s2[j] && dp[j + 1])); 19 } 20 } 21 22 23 return dp[0]; 24 } 25 };
Leetcode | Interleaving String,布布扣,bubuko.com
Leetcode | Interleaving String
标签：style blog class code java c
原文地址：http://www.cnblogs.com/linyx/p/3724348.html
