add BigInt.cpp

code/BigInt.cpp

@@ -0,0 +1,145 @@
+#define iszero(t) (t.len==1&&t.s[0]==0)
+#define setlen(l,t) t.len=l;while(t.len>1&&t.s[t.len-1]==0) t.len--
+const int maxlen=100;
+struct bigint {
+  int len, s[maxlen];
+  bigint() { *this = 0; }
+  bigint(int a) { *this = a; }
+  bigint(const char *a) { *this = a; }
+  bigint operator=(int);
+  bigint operator=(const char *);
+  bigint operator=(const bigint &); //Optional
+  friend ostream &operator<<(ostream &, const bigint &);
+  bigint operator+(const bigint &);
+  bigint operator-(const bigint &);
+  bigint operator*(const bigint &);
+  bigint operator/(const bigint &); //Require - cmp
+  bigint operator%(const bigint &); //Require - cmp
+  static int cmp(const bigint &, const bigint &);
+  static bigint sqrt(const bigint &); //Require - * cmp
+};
+bigint bigint::operator=(int a) {
+  len = 0;
+  do {
+    s[len++] = a % 10;
+    a /= 10;
+  } while (a > 0);
+  return *this;
+}
+bigint bigint::operator=(const char *a) {
+  len = strlen(a);
+  for (int i = 0; i < len; i++) s[i] = a[len - i - 1] - '0';
+  return *this;
+}
+bigint bigint::operator=(const bigint &a) {
+  len = a.len;
+  memcpy(s, a.s, sizeof(*s) * len);
+  return *this;
+}
+ostream& operator<<(ostream &os,const bigint &a) {
+  for (int i = a.len - 1; i >= 0; i--) os << a.s[i];
+  return os;
+}
+bigint bigint::operator+(const bigint &a) {
+  bigint b;
+  b.s[b.len = max(len, a.len)] = 0;
+  for (int i = 0; i < b.len; i++) b.s[i] = (i < len ? s[i] : 0) + (i < a.len ? a.s[i] : 0);
+  for (int i = 0; i < b.len; i++)
+    if (b.s[i] >= 10) {
+      b.s[i] -= 10;
+      b.s[i + 1]++;
+    }
+  if (b.s[b.len]) b.len++;
+  return b;
+}
+//Make sure *this>=a
+bigint bigint::operator-(const bigint &a) {
+  bigint b;
+  for (int i = 0; i < len; i++) b.s[i] = s[i] - (i < a.len ? a.s[i] : 0);
+  for (int i = 0; i < len; i++)
+    if (b.s[i] < 0) {
+      b.s[i] += 10;
+      b.s[i + 1]--;
+    }
+  setlen(len, b);
+  return b;
+}
+bigint bigint::operator*(const bigint &a) {
+  bigint b;
+  memset(b.s, 0, sizeof(*s) * (len + a.len + 1));
+  for (int i = 0; i < len; i++)
+    for (int j = 0; j < a.len; j++) b.s[i + j] += s[i] * a.s[j];
+  for (int i = 0; i < len + a.len; i++) {
+    b.s[i + 1] += b.s[i] / 10;
+    b.s[i] %= 10;
+  }
+  setlen(len + a.len + 1, b);
+  return b;
+}
+bigint bigint::operator/(const bigint &a) {
+  bigint b, c;
+  for (int i = len - 1; i >= 0; i--) {
+    if (!iszero(b)) {
+      for (int j = b.len; j > 0; j--) b.s[j] = b.s[j - 1];
+      b.len++;
+    }
+    b.s[0] = s[i];
+    c.s[i] = 0;
+    while (cmp(b, a) >= 0) {
+      b = b - a;
+      c.s[i]++;
+    }
+  }
+  setlen(len, c);
+  return c;
+}
+bigint bigint::operator%(const bigint &a) {
+  bigint b;
+  for (int i = len - 1; i >= 0; i--) {
+    if (!iszero(b)) {
+      for (int j = b.len; j > 0; j--) b.s[j] = b.s[j - 1];
+      b.len++;
+    }
+    b.s[0] = s[i];
+    while (cmp(b, a) >= 0) b = b - a;
+  }
+  return b;
+}
+int bigint::cmp(const bigint &a,const bigint &b) {
+  if (a.len < b.len) return -1;
+  else if (a.len > b.len) return 1;
+  for (int i = a.len - 1; i >= 0; i--)
+    if (a.s[i] != b.s[i]) return a.s[i] - b.s[i];
+  return 0;
+}
+bigint bigint::sqrt(const bigint &a) {
+  int n = (a.len - 1) / 2, p;
+  bigint b, d;
+  b.len = n + 1;
+  for (int i = n; i >= 0; i--) {
+    if (!iszero(d)) {
+      for (int j = d.len + 1; j > 1; j--) d.s[j] = d.s[j - 2];
+      d.s[0] = a.s[i * 2];
+      d.s[1] = a.s[i * 2 + 1];
+      d.len += 2;
+    }
+    else d = a.s[i * 2] + (i * 2 + 1 < a.len ? a.s[i * 2 + 1] * 10 : 0);
+    bigint c;
+    c.s[1] = 0;
+    for (int j = 1; j <= n - i; j++) {
+      c.s[j] += b.s[i + j] << 1;
+      if (c.s[j] >= 10) {
+        c.s[j + 1] = 1;
+        c.s[j] -= 10;
+      } else c.s[j + 1] = 0;
+    }
+    c.len = n - i + 1 + c.s[n - i + 1];
+    for (p = 1; ; p++) {
+      c.s[0] = p;
+      if (cmp(d, c * p) < 0) break;
+    }
+    b.s[i] = c.s[0] = p - 1;
+    d = d - c * (p - 1);
+  }
+  return b;
+}

main.tex

@@ -148,6 +148,9 @@ Temps de cuisson : $O(n)$
 \subsection{Binomial coefficient}
 {\scriptsize\lstinputlisting{code/Binom.cpp}}
 
+\subsection{BigInt}
+{\scriptsize\lstinputlisting{code/BigInt.cpp}}
+
 \section{Graphes}
 
 \subsection{Fast Dijkstra's algorithm}