dp12 & 13

115. 不同的子序列

class Solution {
public:
    int numDistinct(string s, string t) {
        int result = 0;
        vector<vector<uint64_t>> dp(s.size() + 1, vector<uint64_t>(t.size() + 1, 0)); //防溢出
        if (s[0] == t[0]) dp[0][0] = 1;
        for (int i = 1; i <= s.size(); i++) {
                dp[i][0] = 1;
        }
        for (int i = 1; i <= s.size(); i++) {
            for (int j = 1; j <= t.size(); j++) {
                if (s[i - 1] == t[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1] + dp[i - 1][j];
                }
                else {
                    dp[i][j] = dp[i - 1][j];
                }
            }
        }
        return dp[s.size()][t.size()];
    }
};

583. 两个字符串的删除操作

class Solution {
public:
    int minDistance(string word1, string word2) {
        vector<vector<int>> dp(word1.size() + 1, vector<int>(word2.size() + 1, INT_MAX));
        for (int i = 0; i <= word1.size(); i++) {
            dp[i][0] = i;
        }
        for (int j = 0; j <= word2.size(); j++) {
            dp[0][j] = j;
        }
        for (int i = 1; i <= word1.size(); i++) {
            for (int j = 1; j <= word2.size(); j++) {
                if (word1[i - 1] == word2[j - 1]) { //别错
                    dp[i][j] = dp[i - 1][j - 1];
                }
                else
                    dp[i][j] = min(dp[i - 1][j] + 1, dp[i][j - 1] + 1);
                
            }
        }
        return dp[word1.size()][word2.size()];
    }
};

72. 编辑距离

class Solution {
public:
    int minDistance(string word1, string word2) {
        vector<vector<int>> dp(word1.size() + 1, vector<int>(word2.size() + 1));
        for (int i = 0; i <= word1.size(); i++) dp[i][0] = i;
        for (int j = 0; j <= word2.size(); j++) dp[0][j] = j;
        for (int i = 1; i <= word1.size(); i++) {
            for (int j = 1; j <= word2.size(); j++) {
                if (word1[i - 1] == word2[j - 1]) {
                    dp[i][j] = dp[i - 1][j - 1];
                }
                else {
                 
                    dp[i][j] = min(dp[i][j - 1] + 1, dp[i - 1][j] + 1); //删除/增加
                    dp[i][j] = min(dp[i][j], dp[i - 1][j - 1] + 1); //替换 
                  
                }
            }
        }
        return dp[word1.size()][word2.size()];
    }
};

647. 回文子串

class Solution {
public:
    int countSubstrings(string s) {
        vector<vector<bool>> dp(s.size(), vector<bool>(s.size(), false));
        int result = 0;
        for (int i = s.size() - 1; i >= 0; i--) {
            for (int j = i; j < s.size(); j++) {
                if (s[i] == s[j]) {
                    if (j - i <= 1) {
                        dp[i][j] = true;
                        result++;
                    }
                    else {
                        if (dp[i + 1][j - 1] == true) {
                            dp[i][j] = true;
                            result++;
                        }
                    }
                }
            }
        }
        return result;
    }
};

516. 最长回文子序列

class Solution {
public:
    int longestPalindromeSubseq(string s) {
        vector<vector<int>> dp(s.size(), vector<int>(s.size(), 0));
  
        int result = 0;
        for (int i = s.size() - 1; i >= 0; i--) {
            for (int j = i; j < s.size(); j++) {
                if (i == j) dp[i][j] = 1;
                else if (s[i] == s[j]) {
                    dp[i][j] = max(dp[i + 1][j - 1] + 2, dp[i][j]);
                }
                else {
                    dp[i][j] = max(dp[i][j - 1], dp[i + 1][j]);
                }
            }
        }
        return dp[0][s.size() - 1];

    }
};