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