From 424f21b5a9cee88f9d8edae85720c9f482ea5993 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Thu, 14 Feb 2019 11:57:14 -0200
Subject: [PATCH] Add Edit Distance and LIS
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
paradigm/edit_distance.cpp | 30 ++++++++++++++++++++++++++++++
paradigm/lis.cpp | 23 +++++++++++++++++++++++
2 files changed, 53 insertions(+)
create mode 100644 paradigm/edit_distance.cpp
create mode 100644 paradigm/lis.cpp
diff --git a/paradigm/edit_distance.cpp b/paradigm/edit_distance.cpp
new file mode 100644
index 0000000..7f9ef11
--- /dev/null
+++ b/paradigm/edit_distance.cpp
@@ -0,0 +1,30 @@
+/**
+ * Edit Distance
+ *
+ * Complexity (Time): O(m*n)
+ * Complexity (Space): O(m*n)
+ */
+
+int edit_distance(string a, string b) {
+ int n = a.size();
+ int m = b.size();
+
+ vector<vector<int>> dp(n+1, vector<int>(m+1));
+
+ for (int i = 0; i <= n; ++i) {
+ for (int j = 0; j <= m; ++j) {
+ if (i == 0)
+ dp[i][j] = j;
+ else if (j == 0)
+ dp[i][j] = i;
+ else if (a[i-1] == b[j-1])
+ dp[i][j] = d[i-1][j-1];
+ else
+ dp[i][j] = 1 + min(dp[i][j-1], // Insert
+ min(dp[i-1][j], // Remove
+ dp[i-1][j-1])); // Replace
+ }
+ }
+
+ return dp[n][m];
+}
diff --git a/paradigm/lis.cpp b/paradigm/lis.cpp
new file mode 100644
index 0000000..48ccd6e
--- /dev/null
+++ b/paradigm/lis.cpp
@@ -0,0 +1,23 @@
+/**
+ * Longest Increasing Subsequence (LIS)
+ *
+ * Complexity (Time): O(n^2)
+ * Complexity (Space): O(n)
+ */
+
+int lis(vector<int> v) {
+ int n = v.size();
+
+ vector<int> lis(n);
+ lis[0] = 1;
+
+ for (int i = 1; i < n; ++i) {
+ lis[i] = 1;
+
+ for (int j = 0; j < i; ++j)
+ if (v[i] > v[j] and lis[i] < lis[j] + 1)
+ lis[i] = lis[j] + 1;
+ }
+
+ return *max_element(all(lis));
+}
--
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