add treap

code/Treap.cpp

@@ -0,0 +1,111 @@
+// Cartesian tree (treap)
+// Compute sum (here) of a range, and can reverse a range
+// COMPLEXITY on average : construction O(nlog n)?, operations O(log n), lazy reversal
+// all ranges are 1-based
+struct Node {
+  int y, sz;
+  long long v, sm;
+  bool rev;
+  struct Node *l, *r;
+  Node(long long v) : v(v) {
+    y = rand();
+    sm = v;
+    rev = false;
+    sz = 1;
+    l = r = NULL;
+  }
+};
+typedef struct Node Node;
+int size(Node *n) {
+  return n != NULL ? n->sz : 0;
+}
+long long sum(Node *n) {
+  return n != NULL ? n->sm : 0;
+}
+void update(Node *n) {
+  if(n != NULL) {
+    n->sm = n->v + sum(n->l) + sum(n->r);
+    n->sz = 1 + size(n->l) + size(n->r);
+  }
+}
+void push(Node *n) { // push reverse flag
+  if(n != NULL && n->rev) {
+    swap(n->l, n->r);
+    n->rev = false;
+    if(n->l != NULL)
+      n->l->rev ^= true;
+    if(n->r != NULL)
+      n->r->rev ^= true;
+  }
+}
+void merge(Node* &n, Node *l, Node *r) {
+  push(l); push(r);
+  if(l == NULL) {
+    n = r; return;
+  }
+  if(r == NULL) {
+    n = l; return;
+  }
+  if(l->y > r->y) {
+    merge(l->r, l->r, r);
+    n = l;
+  }
+  else {
+    merge(r->l, l, r->l);
+    n = r;
+  }
+  update(n);
+}
+// x stays in r
+void split(Node *n, Node* &l, Node* &r, int x, int add = 0) {
+  push(n);
+  if(n == NULL) {
+    l = r = NULL; return;
+  }
+  int key = size(n->l) + 1 + add;
+  if(x <= key) {
+    split(n->l, l, n->l, x, add);
+    r = n;
+  }
+  else {
+    split(n->r, n->r, r, x, key);
+    l = n;
+  }
+  update(n);
+}
+// reverse [l, r] (1-based)
+void reverse(Node* &n, int l, int r) {
+  Node *a, *b;
+  split(n, n, a, l, 0);
+  split(a, a, b, r - l + 2, 0);
+  a->rev ^= true;
+  merge(n, n, a);
+  merge(n, n, b);
+}
+// query sum of [l, r] (1-based)
+long long query(Node* &n, int l, int r) {
+  long long ans;
+  Node *a, *b;
+  split(n, n, a, l, 0);
+  split(a, a, b, r - l + 2, 0);
+  ans = sum(a);
+  merge(n, n, a);
+  merge(n, n, b);
+  return ans;
+}
+// insert value v at position p (if p <= size, at the end if p > size)
+void insert(Node* &n, int p, long long v) {
+  Node *a;
+  split(n, n, a, p);
+  merge(n, n, new Node(v));
+  merge(n, n, a);
+}
+// delete element at position p (if any)
+void del(Node* &n, int p) {
+  Node *a, *b;
+  split(n, n, a, p);
+  split(a, a, b, 2);
+  merge(n, n, b);
+  if(a)
+    delete a;
+}

code/Treap_test.cpp

@@ -0,0 +1,53 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+#include "Treap.cpp"
+
+int main() {
+  int values[] = {6,5,4,1,2,3}, n = sizeof(values)/sizeof(int);
+  Node *r = NULL;
+  for(int i = 0; i < n; i++)
+    merge(r, r, new Node(values[i]));
+  assert(query(r, 1, 6) == 21);
+  assert(query(r, 1, 3) == 15);
+  assert(query(r, 3, 4) == 5);
+  reverse(r, 1, 3); // 4 5 6 1 2 3
+  assert(query(r, 1, 3) == 15);
+  assert(query(r, 3, 4) == 7);
+  reverse(r, 1, 6); // 3 2 1 6 5 4
+  assert(query(r, 1, 6) == 21);
+  assert(query(r, 5, 6) == 9);
+  insert(r, 2, 8); // 3 8 2 1 6 5 4
+  assert(query(r, 2, 2) == 8);
+  assert(query(r, 1, 3) == 13);
+  insert(r, 3, 2); // 3 8 2 2 1 6 5 4
+  assert(query(r, 1, 4) == 15);
+  del(r, 3); // 3 8 2 1 6 5 4
+  assert(query(r, 2, 2) == 8);
+  assert(query(r, 1, 3) == 13);
+  del(r, 1); // 8 2 1 6 5 4
+  assert(query(r, 2, 5) == 14);
+  del(r, 2);
+  del(r, 3);
+  del(r, 2);
+  del(r, 2);
+  del(r, 1);
+  del(r, 1); //
+  assert(query(r, 1, 5) == 0);
+
+  r = NULL;
+  insert(r, 1, 10); // 10
+  insert(r, 1, 2); // 2 10
+  assert(query(r, 1, 1) == 2);
+  assert(query(r, 1, 2) == 12);
+  del(r, 2);
+  del(r, 1); //
+
+  r = NULL;
+  insert(r, 1, 3); // 3
+  assert(query(r, 1, 1) == 3);
+  insert(r, 2, 2); // 3 2
+  assert(query(r, 1, 2) == 5);
+  assert(query(r, 2, 2) == 2);
+  return 0;
+}

main.tex

@@ -150,7 +150,10 @@ Temps de cuisson : $O(n)$
 {\scriptsize\lstinputlisting{code/KDTree.cc}}
 
 \subsection{Segment Tree}
-{\scriptsize\lstinputlisting{code/SegmentTree.cpp}}
+{\scriptsize\lstinputlisting{code/SegmentTree.cpp}} % OK
+
+\subsection{Treap}
+{\scriptsize\lstinputlisting{code/Treap.cpp}} % OK
 
 \subsection{Bits Sets}
 {\scriptsize\lstinputlisting{code/BitSet.cpp}} % OK