Code & Func

第33天。

今天的题目是Minimum ASCII Delete Sum for Two Strings:

一道动态规划的问题，而且挺常规的。这道题的动规方程如下：

$$ dp[i, j] = \left{ \begin{aligned} \sum_{k=0}^{j} s2[k] & ,& i == 0 \ \sum_{k=0}^{i} s1[k] & ,& j == 0 \ dp[i-1, j-1] & ,& s1[i] == s2[j] \ min{dp[i-1][j] + s1[i], dp[i][j-1] + s2[j] } & ,& s1[i] == s2[j] \end{aligned} \right. $$

其中d[i, j]表示字符串s1[0, i)和字符串s2[0, j)的最小删除ASCII之和。根据动规方程可以写出如下代码：

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int minimumDeleteSum(string s1, string s2) {
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    vector<int> dp(s2.size() + 1);
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    dp[0] = 0;
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    for(int i = 1;i < dp.size(); i++) {
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        dp[i] = dp[i-1] + s2[i-1];
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    }
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    int prev;
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    for(int i = 0;i < s1.size(); i++) {
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        prev = dp[0];
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        dp[0] += s1[i];
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        for(int j = 1;j <= s2.size(); j++) {
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            if (s1[i] == s2[j-1]) {
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                swap(prev, dp[j]);
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            } else {
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                prev = dp[j];
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                dp[j] = min(dp[j] + s1[i], dp[j-1] + s2[j-1]);
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            }
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        }
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    }
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    return dp[s2.size()];
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}