Add lcs

docs/dp/longest_common_subsequence.md

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+---
+title: Longest Common Subsequence (最長共通部分列)
+documentation_of: //dp/longest_common_subsequence.hpp
+---

dp/longest_common_subsequence.hpp

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+#pragma once
+
+#include <vector>
+#include <string>
+
+template <class T> std::vector<T> longest_common_subsequence(std::vector<T>& a, std::vector<T>& b) {
+    const int n = (int)(a.size()), m = (int)(b.size());
+    // -INF
+    constexpr int e = -1000000000;
+    std::vector dp(n + 1, std::vector<int>(m + 1, e));
+    std::vector pd(n + 1, std::vector<int>(m + 1, -1));
+    // initialize
+    for (int i = 0; i < n + 1; i++) dp[i][0] = 0;
+    for (int j = 0; j < m + 1; j++) dp[0][j] = 0;
+    // dp
+    for (int i = 0; i < n; i++) {
+        for (int j = 0; j < m; j++) {
+            if (a[i] == b[j]) {
+                if (dp[i + 1][j + 1] < dp[i][j] + 1) {
+                    dp[i + 1][j + 1] = dp[i][j] + 1;
+                    pd[i + 1][j + 1] = 0;
+                }
+            } else {
+                if (dp[i + 1][j + 1] < dp[i + 1][j]) {
+                    dp[i + 1][j + 1] = dp[i + 1][j];
+                    pd[i + 1][j + 1] = 1;
+                }
+                if (dp[i + 1][j + 1] < dp[i][j + 1]) {
+                    dp[i + 1][j + 1] = dp[i][j + 1];
+                    pd[i + 1][j + 1] = 2;
+                }
+            }
+        }
+    }
+    // 復元
+    std::vector<T> res;
+    res.reserve(dp[n][m]);
+    int i = n, j = m;
+    while (pd[i][j] != -1) {
+        if (pd[i][j] == 0) {
+            i--, j--;
+            res.push_back(a[i]);
+        } else if (pd[i][j] == 1) {
+            j--;
+        } else {
+            // pd[i][j] == 2
+            i--;
+        }
+    }
+    std::reverse(res.begin(), res.end());
+    return res;
+}
+
+std::string longest_common_subsequence(std::string& s, std::string& t) {
+    const int n = (int)(s.size()), m = (int)(t.size());
+    std::vector<int> a(n), b(m);
+    for (int i = 0; i < n; i++) a[i] = s[i];
+    for (int j = 0; j < m; j++) b[j] = t[j];
+    auto lcs = longest_common_subsequence(a, b);
+    const int k = (int)(lcs.size());
+    std::string res;
+    res.reserve(k);
+    for (int i = 0; i < k; i++) res += lcs[i];
+    return res;
+}

verify/aoj_alds1/aoj_alds1_10_c.test.cpp

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+#define PROBLEM "https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_10_C"
+
+#include <bits/stdc++.h>
+#include "dp/longest_common_subsequence.hpp"
+
+int main() {
+    int N;
+    std::cin >> N;
+    for (int i = 0; i < N; i++) {
+        std::string s, t;
+        std::cin >> s >> t;
+        std::cout << longest_common_subsequence(s, t).size() << '\n';
+    }
+    return 0;
+}