From e131787f61ae157efafb121d362f713ee6b6914b Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sun, 9 Jun 2019 14:03:27 -0300
Subject: [PATCH] Change format for some functions

Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
 algorithms/math/binary_exponentiation.cpp     |  21 +++--
 algorithms/math/euler_totient.cpp             |  24 +++---
 algorithms/math/extended_euclidean.cpp        |  24 +++---
 algorithms/math/karatsuba.cpp                 |  80 +++++++++---------
 algorithms/math/legendre.cpp                  |  18 ++--
 .../math/linear_diophantine_equation.cpp      |   4 +-
 .../math/modular_multiplicative_inverse.cpp   |  27 +++---
 algorithms/math/sieve_of_eratosthenes.cpp     |  37 +++-----
 algorithms/paradigm/edit_distance.cpp         |  32 ++++---
 algorithms/paradigm/kadane.cpp                |  32 ++++---
 algorithms/paradigm/lis.cpp                   |  22 +++--
 .../paradigm/longest_common_subsequence.cpp   |  54 ++++++------
 algorithms/paradigm/ternary_search.cpp        |  43 +++++-----
 algorithms/string/z-function.cpp              |  32 ++++---
 caderno.pdf                                   | Bin 227413 -> 226610 bytes
 15 files changed, 205 insertions(+), 245 deletions(-)

diff --git a/algorithms/math/binary_exponentiation.cpp b/algorithms/math/binary_exponentiation.cpp
index e20f965..7999416 100644
--- a/algorithms/math/binary_exponentiation.cpp
+++ b/algorithms/math/binary_exponentiation.cpp
@@ -3,15 +3,14 @@
 /// Time: O(log n)
 /// Space: O(1)
 
-struct BinExp {
-  ll run(ll x, ll n) {
-    ll ans = 1;
-    while (n) {
-      if (n & 1)
-        ans = ans * x;
-      n >>= 1;
-      x = x * x;
-    }
-    return ans;
+template <typename T>
+T bin_exp(T x, ll n) {
+  T ans = 1;
+  while (n) {
+    if (n & 1)
+      ans = ans * x;
+    n >>= 1;
+    x = x * x;
   }
-};
+  return ans;
+}
diff --git a/algorithms/math/euler_totient.cpp b/algorithms/math/euler_totient.cpp
index 1fbe385..83cf51d 100644
--- a/algorithms/math/euler_totient.cpp
+++ b/algorithms/math/euler_totient.cpp
@@ -3,19 +3,17 @@
 /// Time: O(sqrt{n})
 /// Space: O(1)
 
-struct EulerTotient {
-  int run(int n) {
-    int result = n;
+int phi(int n) {
+  int result = n;
 
-    for (int i = 2; i*i <= n; i++)
-      if (n % i == 0) {
-        while (n % i == 0) n /= i;
-        result -= result / i;
-      }
+  for (int i = 2; i*i <= n; i++)
+    if (n % i == 0) {
+      while (n % i == 0) n /= i;
+      result -= result / i;
+    }
 
-    if (n > 1)
-      result -= (result / n);
+  if (n > 1)
+    result -= (result / n);
 
-    return result;
-  }
-};
+  return result;
+}
diff --git a/algorithms/math/extended_euclidean.cpp b/algorithms/math/extended_euclidean.cpp
index f1422eb..9697789 100644
--- a/algorithms/math/extended_euclidean.cpp
+++ b/algorithms/math/extended_euclidean.cpp
@@ -3,19 +3,17 @@
 /// Time: O(log min(a,b))
 /// Space: O(1)
 
-struct ExtendedEuclidean {
-  int run(int a, int b, int &x, int &y) {
-    if (a == 0) {
-      x = 0, y = 1;
-      return b;
-    }
+int ext_gcd(int a, int b, int &x, int &y) {
+  if (a == 0) {
+    x = 0, y = 1;
+    return b;
+  }
 
-    int x1, y1;
-    int g = run(b % a, a, x1, y1);
+  int x1, y1;
+  int g = ext_gct(b % a, a, x1, y1);
 
-    x = y1 - (b / a) * x1;
-    y = x1;
+  x = y1 - (b / a) * x1;
+  y = x1;
 
-    return g;
-  }
-};
+  return g;
+}
diff --git a/algorithms/math/karatsuba.cpp b/algorithms/math/karatsuba.cpp
index a3c5d10..22f248f 100644
--- a/algorithms/math/karatsuba.cpp
+++ b/algorithms/math/karatsuba.cpp
@@ -3,46 +3,46 @@
 /// Time: O(n^{log(3)})
 /// Space: O(n)
 
-struct Karatsuba {
-  vector<ll> run(const vector<ll> &a, const vector<ll> &b) {
-    int n = a.size();
-    vector<ll> res(n + n);
-
-    if (n <= 32) {
-      for (int i = 0; i < n; i++)
-        for (int j = 0; j < n; j++)
-          res[i + j] += a[i] * b[j];
-
-      return res;
-    }
-
-    int k = n >> 1;
-    vector<ll> a1(a.begin(), a.begin() + k);
-    vector<ll> a2(a.begin() + k, a.end());
-    vector<ll> b1(b.begin(), b.begin() + k);
-    vector<ll> b2(b.begin() + k, b.end());
-
-    vector<ll> a1b1 = run(a1, b1);
-    vector<ll> a2b2 = run(a2, b2);
-
-    for (int i = 0; i < k; i++)
-      a2[i] += a1[i];
-    for (int i = 0; i < k; i++)
-      b2[i] += b1[i];
-
-    vector<ll> r = run(a2, b2);
-    for (int i = 0; i < a1b1.size(); i++) 
-      r[i] -= a1b1[i];
-    for (int i = 0; i < a2b2.size(); i++) 
-      r[i] -= a2b2[i];
-
-    for (int i = 0; i < r.size(); i++) 
-      res[i + k] += r[i];
-    for (int i = 0; i < a1b1.size(); i++) 
-      res[i] += a1b1[i];
-    for (int i = 0; i < a2b2.size(); i++) 
-      res[i + n] += a2b2[i];
+vector<ll> karatsuba(const vector<ll> &a, 
+    const vector<ll> &b) 
+{
+  int n = a.size();
+  vector<ll> res(n + n);
+
+  if (n <= 32) {
+    for (int i = 0; i < n; i++)
+      for (int j = 0; j < n; j++)
+        res[i + j] += a[i] * b[j];
 
     return res;
   }
-};
+
+  int k = n >> 1;
+  vector<ll> a1(a.begin(), a.begin() + k);
+  vector<ll> a2(a.begin() + k, a.end());
+  vector<ll> b1(b.begin(), b.begin() + k);
+  vector<ll> b2(b.begin() + k, b.end());
+
+  vector<ll> a1b1 = karatsuba(a1, b1);
+  vector<ll> a2b2 = karatsuba(a2, b2);
+
+  for (int i = 0; i < k; i++)
+    a2[i] += a1[i];
+  for (int i = 0; i < k; i++)
+    b2[i] += b1[i];
+
+  vector<ll> r = karatsuba(a2, b2);
+  for (int i = 0; i < a1b1.size(); i++) 
+    r[i] -= a1b1[i];
+  for (int i = 0; i < a2b2.size(); i++) 
+    r[i] -= a2b2[i];
+
+  for (int i = 0; i < r.size(); i++) 
+    res[i + k] += r[i];
+  for (int i = 0; i < a1b1.size(); i++) 
+    res[i] += a1b1[i];
+  for (int i = 0; i < a2b2.size(); i++) 
+    res[i + n] += a2b2[i];
+
+  return res;
+}
diff --git a/algorithms/math/legendre.cpp b/algorithms/math/legendre.cpp
index 6d1fb75..d470908 100644
--- a/algorithms/math/legendre.cpp
+++ b/algorithms/math/legendre.cpp
@@ -3,15 +3,13 @@
 /// Time: O(log_p n)
 /// Space: O(1)
 
-struct Legendre {
-  int run(int n, int p) {
-    int x = 0;
+int legendre(int n, int p) {
+  int x = 0;
 
-    while (n) {
-      n /= p;
-      x += n;
-    }
-
-    return x;
+  while (n) {
+    n /= p;
+    x += n;
   }
-};
+
+  return x;
+}
diff --git a/algorithms/math/linear_diophantine_equation.cpp b/algorithms/math/linear_diophantine_equation.cpp
index 7cdee51..c4a8374 100644
--- a/algorithms/math/linear_diophantine_equation.cpp
+++ b/algorithms/math/linear_diophantine_equation.cpp
@@ -24,10 +24,8 @@ struct Diophantine {
   { init(); }
 
   void init() {
-    ExtendedEuclidean ext_gcd;
-
     int w0, z0;
-    d = ext_gcd.run(a, b, w0, z0);
+    d = ext_gcd(a, b, w0, z0);
     if (c % d == 0) {
       x0 = w0 * (c / d);
       y0 = z0 * (c / d);
diff --git a/algorithms/math/modular_multiplicative_inverse.cpp b/algorithms/math/modular_multiplicative_inverse.cpp
index 97a7dcc..6b08aae 100644
--- a/algorithms/math/modular_multiplicative_inverse.cpp
+++ b/algorithms/math/modular_multiplicative_inverse.cpp
@@ -3,20 +3,15 @@
 /// Time: O(log m)
 /// Space: O(1)
 
-struct ModMultInv {
+// Fermat's Little Theorem: Used when m is prime
+int fermat(int a, int m) {
+  return bin_exp(a, m - 2);
+}
 
-  // Fermat's Little Theorem: Used when m is prime
-  int fermat(int a, int m) {
-    BinaryExponentiation bin_exp;
-    return bin_exp.run(a, m - 2);
-  }
-
-  // Extended Euclidean Algorithm: Used when m 
-  // and a are coprime
-  int extended_euclidean(int a, int m) {
-    ExtendedEuclidean ext_gcd;
-    int x, y;
-    int g = ext_gcd.run(a, m, x, y);
-    return (x % m + m) % m;
-  }
-};
+// Extended Euclidean Algorithm: Used when m 
+// and a are coprime
+int extended_euclidean(int a, int m) {
+  int x, y;
+  int g = ext_gcd(a, m, x, y);
+  return (x % m + m) % m;
+}
diff --git a/algorithms/math/sieve_of_eratosthenes.cpp b/algorithms/math/sieve_of_eratosthenes.cpp
index 853de78..07e3c66 100644
--- a/algorithms/math/sieve_of_eratosthenes.cpp
+++ b/algorithms/math/sieve_of_eratosthenes.cpp
@@ -3,31 +3,18 @@
 /// Time: O(n * log log n)
 /// Space: O(n)
 
-struct Sieve {
-  int N;
-  vector<int> is_prime;
+vector<int> sieve(int n) {
+  vector<int> primes;
+  vector<int> is_prime(n + 1, 1);
 
-  Sieve(int N) : 
-    N(N), is_prime(N+1) 
-  { init(); }
+  for (int p = 2; p*p <= n; ++p)
+    if (is_prime[p])
+      for (int i = p*p; i <= n; i += p)
+        is_prime[i] = false;
 
-  void init() {
-    fill(all(is_prime), 1);
-  }
+  for (int p = 2; p <= n; ++p)
+    if (is_prime[p])
+      primes.pb(p);
 
-  vector<int> run() {
-    vector<int> primes;
-    init();
-
-    for (int p = 2; p*p <= N; ++p)
-      if (is_prime[p])
-        for (int i = p*p; i <= N; i += p)
-          is_prime[i] = false;
-
-    for (int p = 2; p <= N; ++p)
-      if (is_prime[p])
-        primes.pb(p);
-
-    return primes;
-  }
-};
+  return primes;
+}
diff --git a/algorithms/paradigm/edit_distance.cpp b/algorithms/paradigm/edit_distance.cpp
index 1704de2..e3517d7 100644
--- a/algorithms/paradigm/edit_distance.cpp
+++ b/algorithms/paradigm/edit_distance.cpp
@@ -5,21 +5,19 @@
 
 int dp[MAX][MAX];
 
-struct EditDistance {
-  int run(string a, string b) {
-    for (int i = 0; i <= a.size(); ++i)
-      for (int j = 0; j <= b.size(); ++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], 
-                              dp[i-1][j], 
-                              dp[i-1][j-1]});
+int edit_distance(string a, string b) {
+  for (int i = 0; i <= a.size(); ++i)
+    for (int j = 0; j <= b.size(); ++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], 
+                            dp[i-1][j], 
+                            dp[i-1][j-1]});
 
-    return dp[a.size()][b.size()];
-  }
-};
+  return dp[a.size()][b.size()];
+}
diff --git a/algorithms/paradigm/kadane.cpp b/algorithms/paradigm/kadane.cpp
index c1458d0..ab38c65 100644
--- a/algorithms/paradigm/kadane.cpp
+++ b/algorithms/paradigm/kadane.cpp
@@ -3,25 +3,23 @@
 /// Time: O(n + m)
 /// Space: O(n + m)
 
-struct Kadane {
-  int run(const vector<int> &v, int &start, int &end) {
-    start = end = 0;
-    int msf = -inf, meh = 0, s = 0;
+int kadane(const vector<int> &v, int &start, int &end) {
+  start = end = 0;
+  int msf = -inf, meh = 0, s = 0;
 
-    for (int i = 0; i < v.size(); ++i) {
-      meh += v[i];
+  for (int i = 0; i < v.size(); ++i) {
+    meh += v[i];
 
-      if (msf < meh) {
-        msf = meh;
-        start = s, end = i;
-      }
-
-      if (meh < 0) {
-        meh = 0;
-        s = i + 1;
-      }
+    if (msf < meh) {
+      msf = meh;
+      start = s, end = i;
     }
 
-    return msf;
+    if (meh < 0) {
+      meh = 0;
+      s = i + 1;
+    }
   }
-};
+
+  return msf;
+}
diff --git a/algorithms/paradigm/lis.cpp b/algorithms/paradigm/lis.cpp
index 281adfc..821903d 100644
--- a/algorithms/paradigm/lis.cpp
+++ b/algorithms/paradigm/lis.cpp
@@ -3,18 +3,16 @@
 /// Time: O(n^2)
 /// Space: O(n)
 
-struct LIS {
-  int run(vector<int> v) {
-    vector<int> lis(v.size()); lis[0] = 1;
+int lis(vector<int> v) {
+  vector<int> lis(v.size()); lis[0] = 1;
 
-    for (int i = 1; i < v.size(); ++i) {
-      lis[i] = 1;
+  for (int i = 1; i < v.size(); ++i) {
+    lis[i] = 1;
 
-      for (int j = 0; j < i; ++j)
-        if (v[i] > v[j] && lis[i] < lis[j] + 1)
-          lis[i] = lis[j] + 1;
-    }
-
-    return *max_element(all(lis));
+    for (int j = 0; j < i; ++j)
+      if (v[i] > v[j] && lis[i] < lis[j] + 1)
+        lis[i] = lis[j] + 1;
   }
-};
+
+  return *max_element(all(lis));
+}
diff --git a/algorithms/paradigm/longest_common_subsequence.cpp b/algorithms/paradigm/longest_common_subsequence.cpp
index 9bcba82..acffd38 100644
--- a/algorithms/paradigm/longest_common_subsequence.cpp
+++ b/algorithms/paradigm/longest_common_subsequence.cpp
@@ -5,36 +5,34 @@
 
 int dp[MAX][MAX];
 
-struct LCS {
-  string run(string a, string b) {
-    for (int i = 0; i <= a.size(); ++i) {
-      for (int j = 0; j <= b.size(); ++j) {
-        if (i == 0 || j == 0)
-          dp[i][j] = 0;
-        else if (a[i - 1] == b[j - 1])
-          dp[i][j] = dp[i - 1][j - 1] + 1;
-        else
-          dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
-      }
+string lcs(string a, string b) {
+  for (int i = 0; i <= a.size(); ++i) {
+    for (int j = 0; j <= b.size(); ++j) {
+      if (i == 0 || j == 0)
+        dp[i][j] = 0;
+      else if (a[i - 1] == b[j - 1])
+        dp[i][j] = dp[i - 1][j - 1] + 1;
+      else
+        dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]);
     }
+  }
 
-    // The size is already at dp[n][m], now the common 
-    // subsequence is retrieved:
-
-    int idx = dp[a.size()][b.size()];
-    string ans(idx, ' ');
+  // The size is already at dp[n][m], now the common 
+  // subsequence is retrieved:
 
-    int i = a.size(), j = b.size();
-    while (i > 0 && j > 0) {
-      if (a[i - 1] == b[ j - 1]) {
-        ans[idx - 1] = a[i - 1];
-        i--, j--, idx--;
-      } else if (dp[i - 1][j] > dp[i][j - 1]) 
-        i--;
-      else 
-        j--;
-    }
+  int idx = dp[a.size()][b.size()];
+  string ans(idx, ' ');
 
-    return ans;
+  int i = a.size(), j = b.size();
+  while (i > 0 && j > 0) {
+    if (a[i - 1] == b[ j - 1]) {
+      ans[idx - 1] = a[i - 1];
+      i--, j--, idx--;
+    } else if (dp[i - 1][j] > dp[i][j - 1]) 
+      i--;
+    else 
+      j--;
   }
-};
+
+  return ans;
+}
diff --git a/algorithms/paradigm/ternary_search.cpp b/algorithms/paradigm/ternary_search.cpp
index 54372a9..a687284 100644
--- a/algorithms/paradigm/ternary_search.cpp
+++ b/algorithms/paradigm/ternary_search.cpp
@@ -3,31 +3,28 @@
 /// Time: O(log n)
 /// Space: O(1)
 
-struct TernarySearch {
+// Unimodal function 
+double f(double x) {
+  return x * x;
+}
 
-  // Unimodal function 
-  double f(double x) {
-    return x * x;
-  }
-
-  double run(double l, double r) {
-    double rt, lt;
+double ternary_search(double l, double r) {
+  double rt, lt;
 
-    for (int i = 0; i < 500; ++i) {
-      if (fabs(r - l) < EPS)
-        return (l + r) / 2.0;
+  for (int i = 0; i < 500; ++i) {
+    if (fabs(r - l) < EPS)
+      return (l + r) / 2.0;
 
-      lt = (r - l) / 3.0 + l;
-      rt = ((r - l) * 2.0) / 3.0 + l;
+    lt = (r - l) / 3.0 + l;
+    rt = ((r - l) * 2.0) / 3.0 + l;
 
-      // '<' for minimum of f,
-      // '>' for maximum of f
-      if (f(lt) < f(rt))
-        l = lt;
-      else
-        r = rt;
-    }
-
-    return (l + r) / 2.0;
+    // '<' for minimum of f,
+    // '>' for maximum of f
+    if (f(lt) < f(rt))
+      l = lt;
+    else
+      r = rt;
   }
-};
+
+  return (l + r) / 2.0;
+}
diff --git a/algorithms/string/z-function.cpp b/algorithms/string/z-function.cpp
index 593c054..c1e6c78 100644
--- a/algorithms/string/z-function.cpp
+++ b/algorithms/string/z-function.cpp
@@ -3,25 +3,23 @@
 /// Time: O(n)
 /// Space: O(n)
 
-struct ZFunction {
-  vector<int> run(string s) {
-    int n = (int) s.length();
-    vector<int> z(n);
+vector<int> z_function(string s) {
+  int n = (int) s.length();
+  vector<int> z(n);
 
-    int l = 0, r = 0;
-    for (int i = 1; i < n; ++i) {
-      if (i <= r)
-        z[i] = min(r - i + 1, z[i - l]);
+  int l = 0, r = 0;
+  for (int i = 1; i < n; ++i) {
+    if (i <= r)
+      z[i] = min(r - i + 1, z[i - l]);
 
-      while (i + z[i] < n && s[z[i]] == s[i + z[i]])
-        z[i]++;
+    while (i + z[i] < n && s[z[i]] == s[i + z[i]])
+      z[i]++;
 
-      if (i + z[i] - 1 > r) {
-        l = i; 
-        r = i + z[i] - 1;
-      }
+    if (i + z[i] - 1 > r) {
+      l = i; 
+      r = i + z[i] - 1;
     }
-
-    return z;
   }
-};
+
+  return z;
+}
diff --git a/caderno.pdf b/caderno.pdf
index f9ce52fea430d4dc1a24f210c59ff867c4b99e5e..36941c4bd14d17f3e797b3d264b95d3873ddb0fa 100644
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