标签：output iostream string closed cli stdout play display bsp
给定序列$X，Y$，求最长公共子序列。
设$dp[i][j]$表示前$i$个$x$和前$j$个$y$的最长公共子序列。
$dp[i][j]=max(dp[i][j],dp[i-1][j],dp[i][j-1])$ 当前最长由前一个转移过来
$if(x[i]==y[j]) dp[i][j]=max(dp[i][j],dp[i-1][j-1]+1)$ 如果当前两位相等，最长序列长度$+1$
1 for (int i = 0; i <= len1; ++i) dp[i][0] = 0; 2 for (int i = 0; i <= len2; ++i) dp[0][i] = 0; 3 for (int i = 1; i <= len1; ++i) { 4 for (int j = 1; j <= len2; ++j) { 5 if (x[i] == y[j]) { 6 dp[i][j] = dp[i - 1][j - 1] + 1; 7 } 8 else { 9 if (dp[i - 1][j] > dp[i][j - 1]) { 10 del[i][j] = 1; 11 dp[i][j] = dp[i - 1][j]; 12 } 13 else { 14 del[i][j] = 2; 15 dp[i][j] = dp[i][j - 1]; 16 } 17 } 18 } 19 }
$O(n*m)$。
https://github.com/Big-Kelly/Algorithm
1 //#include<bits/stdc++.h> 2 #include <set> 3 #include <map> 4 #include <stack> 5 #include <cmath> 6 #include <queue> 7 #include <cstdio> 8 #include <string> 9 #include <vector> 10 #include <cstring> 11 #include <iostream> 12 #include <algorithm> 13 14 #define ll long long 15 #define pll pair<ll,ll> 16 #define pii pair<int,int> 17 #define bug printf("*********\n") 18 #define FIN freopen("input.txt","r",stdin); 19 #define FON freopen("output.txt","w+",stdout); 20 #define IO ios::sync_with_stdio(false),cin.tie(0) 21 #define ls root<<1 22 #define rs root<<1|1 23 #define pb push_back 24 25 using namespace std; 26 const int inf = 2e9 + 7; 27 const ll Inf = 1e18 + 7; 28 const int maxn = 5e3 + 5; 29 const ll mod = 998244353; 30 31 string x, y, ans; 32 int len1, len2; 33 int dp[maxn][maxn], del[maxn][maxn]; 34 35 int main() { 36 cin >> x >> y; 37 len1 = x.length(), len2 = y.length(); 38 x = " " + x, y = " " + y; 39 for (int i = 0; i <= len1; ++i) dp[i][0] = 0; 40 for (int i = 0; i <= len2; ++i) dp[0][i] = 0; 41 for (int i = 1; i <= len1; ++i) { 42 for (int j = 1; j <= len2; ++j) { 43 if (x[i] == y[j]) { 44 dp[i][j] = dp[i - 1][j - 1] + 1; 45 } 46 else { 47 if (dp[i - 1][j] > dp[i][j - 1]) { 48 del[i][j] = 1; 49 dp[i][j] = dp[i - 1][j]; 50 } 51 else { 52 del[i][j] = 2; 53 dp[i][j] = dp[i][j - 1]; 54 } 55 } 56 } 57 } 58 int i = len1, j = len2; 59 ans = ""; 60 while (i && j) { 61 if (!del[i][j]) { 62 ans = x[i] + ans; 63 i--, j--; 64 } 65 else if (del[i][j] == 1) { 66 i--; 67 } 68 else { 69 j--; 70 } 71 } 72 cout << "LCS长度:" << dp[len1][len2] << endl; 73 cout << "LCS:" << ans << endl; 74 }
标签：output iostream string closed cli stdout play display bsp
原文地址：https://www.cnblogs.com/zhang-Kelly/p/12797623.html
