# Exercise - Minimum Deletions in a String to make it a Palindrome

## 解法一 - DP

``````using namespace std;

#include <iostream>
#include <string>
#include <vector>

class MDSP {

public:
int findMinimumDeletions(const string &st) {
// subtracting the length of Longest Palindromic Subsequence from the length of
// the input string to get minimum number of deletions
return st.length() - findLPSLength(st);
}

int findLPSLength(const string &st) {
// dp[i][j] stores the length of LPS from index 'i' to index 'j'
vector<vector<int>> dp(st.length(), vector<int>(st.length()));

// every sequence with one element is a palindrome of length 1
for (int i = 0; i < st.length(); i++) {
dp[i][i] = 1;
}

for (int startIndex = st.length() - 1; startIndex >= 0; startIndex--) {
for (int endIndex = startIndex + 1; endIndex < st.length(); endIndex++) {
// case 1: elements at the beginning and the end are the same
if (st[startIndex] == st[endIndex]) {
dp[startIndex][endIndex] = 2 + dp[startIndex + 1][endIndex - 1];
} else { // case 2: skip one element either from the beginning or the end
dp[startIndex][endIndex] =
max(dp[startIndex + 1][endIndex], dp[startIndex][endIndex - 1]);
}
}
}
return dp[0][st.length() - 1];
}
};

int main(int argc, char *argv[]) {
MDSP *mdsp = new MDSP();
cout << mdsp->findMinimumDeletions("abdbca") << endl;
cout << mdsp->findMinimumDeletions("cddpd") << endl;
cout << mdsp->findMinimumDeletions("pqr") << endl;

delete mdsp;
}
``````