# A excellent solution but I cannot understand

• bool isInterleave(string s1, string s2, string s3) {
if (s1.size() + s2.size() != s3.size())
return false;
if (s1.size() < s2.size())
s1.swap(s2);
vector<bool>  dp(s1.size() + 1);
dp[0] = true;
for (size_t j = 0; j <= s2.size(); ++j)
for (size_t i = 1; i <= s1.size(); ++i)
dp[i] = ((dp[i - 1] && s1[i - 1] == s3[i + j - 1])
|| (j > 0 && dp[i] && s2[j - 1] == s3[i + j - 1]));
return dp[s1.size()];

}

this code was found in the discussion before, but I got confused! I cannot understand why it need to swap s1 and s2 too get large size dp[]? acturally, the value in dp might be wrong, for example, when i = 0, j=2, the temprary result in dp always get dp[0] = ture, which means the usual dp method's dp[2][0] = true. this is incorrect, when using the transmitting function to get following result, the following result may also be incorrect. but why the final result is still correct?

• The original dp formula is

dp[i][j] =  (dp[i - 1][j] AND s1[i - 1] = s3[i + j - 1])
OR (j > 0 AND dp[i][j-1] AND s2[j - 1] = s3[i + j - 1]))

Look into this formula, dp[i][j] only counts on dp[i - 1][j] and dp[i][j - 1].

The code in your post is using it.

// To avoid confusion, I change i, j to u, v
dp[v]   //  It is same as dp[i][j] . Pay attention, here is dp[v] instead of dp[u]
= ((dp[v] && s1[u - 1] == s3[u + v - 1])      //   It is same as (dp[i - 1][j] AND s1[i - 1] = s3[i + j - 1]). Here the dp[v] is still dp[u - 1][v] indeed.
||
(v > 0 && dp[v - 1] && s2[v - 1] == s3[u + v - 1]));  // It is same as (j > 0 AND dp[i][j-1] AND s2[j - 1] = s3[i + j - 1]))

Above all, it can explain why the size of dp should always pick the larger one.

• Thank you for your reply. I understand the formula, and I know what you explained above except the final point: "Above all, it can explain why the size of dp should always pick the larger one." Why pick the larger one? What is wrong if I choose the smaller one?

• what confused me is : first, why choose the larger one as dp's dimension? second, why didn't calculate the dp[0]'s value at the beginning of the inner for loop? If dp[0] always true, I think this is wrong and would cause wrong answer, but this code got accepted by OJ, so, why is it right?

• I got the answer, this code is wrong, and the author means to get litter memory.

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