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diff --git a/pintos-progos/lib/kernel/hash.h b/pintos-progos/lib/kernel/hash.h
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+++ b/pintos-progos/lib/kernel/hash.h
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+#ifndef __LIB_KERNEL_HASH_H
+#define __LIB_KERNEL_HASH_H
+
+/* Hash table.
+
+   This data structure is thoroughly documented in the Tour of
+   Pintos for Project 3.
+
+   This is a standard hash table with chaining.  To locate an
+   element in the table, we compute a hash function over the
+   element's data and use that as an index into an array of
+   doubly linked lists, then linearly search the list.
+
+   The chain lists do not use dynamic allocation.  Instead, each
+   structure that can potentially be in a hash must embed a
+   struct hash_elem member.  All of the hash functions operate on
+   these `struct hash_elem's.  The hash_entry macro allows
+   conversion from a struct hash_elem back to a structure object
+   that contains it.  This is the same technique used in the
+   linked list implementation.  Refer to lib/kernel/list.h for a
+   detailed explanation. */
+
+#include <stdbool.h>
+#include <stddef.h>
+#include <stdint.h>
+#include "list.h"
+
+/* Hash element. */
+struct hash_elem 
+  {
+    struct list_elem list_elem;
+  };
+
+/* Converts pointer to hash element HASH_ELEM into a pointer to
+   the structure that HASH_ELEM is embedded inside.  Supply the
+   name of the outer structure STRUCT and the member name MEMBER
+   of the hash element.  See the big comment at the top of the
+   file for an example. */
+#define hash_entry(HASH_ELEM, STRUCT, MEMBER)                   \
+        ((STRUCT *) ((uint8_t *) &(HASH_ELEM)->list_elem        \
+                     - offsetof (STRUCT, MEMBER.list_elem)))
+
+/* Computes and returns the hash value for hash element E, given
+   auxiliary data AUX. */
+typedef unsigned hash_hash_func (const struct hash_elem *e, void *aux);
+
+/* Compares the value of two hash elements A and B, given
+   auxiliary data AUX.  Returns true if A is less than B, or
+   false if A is greater than or equal to B. */
+typedef bool hash_less_func (const struct hash_elem *a,
+                             const struct hash_elem *b,
+                             void *aux);
+
+/* Performs some operation on hash element E, given auxiliary
+   data AUX. */
+typedef void hash_action_func (struct hash_elem *e, void *aux);
+
+/* Hash table. */
+struct hash 
+  {
+    size_t elem_cnt;            /* Number of elements in table. */
+    size_t bucket_cnt;          /* Number of buckets, a power of 2. */
+    struct list *buckets;       /* Array of `bucket_cnt' lists. */
+    hash_hash_func *hash;       /* Hash function. */
+    hash_less_func *less;       /* Comparison function. */
+    void *aux;                  /* Auxiliary data for `hash' and `less'. */
+  };
+
+/* A hash table iterator. */
+struct hash_iterator 
+  {
+    struct hash *hash;          /* The hash table. */
+    struct list *bucket;        /* Current bucket. */
+    struct hash_elem *elem;     /* Current hash element in current bucket. */
+  };
+
+/* Basic life cycle. */
+bool hash_init (struct hash *, hash_hash_func *, hash_less_func *, void *aux);
+void hash_clear (struct hash *, hash_action_func *);
+void hash_destroy (struct hash *, hash_action_func *);
+
+/* Search, insertion, deletion. */
+struct hash_elem *hash_insert (struct hash *, struct hash_elem *);
+struct hash_elem *hash_replace (struct hash *, struct hash_elem *);
+struct hash_elem *hash_find (struct hash *, struct hash_elem *);
+struct hash_elem *hash_delete (struct hash *, struct hash_elem *);
+
+/* Iteration. */
+void hash_apply (struct hash *, hash_action_func *);
+void hash_first (struct hash_iterator *, struct hash *);
+struct hash_elem *hash_next (struct hash_iterator *);
+struct hash_elem *hash_cur (struct hash_iterator *);
+
+/* Information. */
+size_t hash_size (struct hash *);
+bool hash_empty (struct hash *);
+
+/* Sample hash functions. */
+unsigned hash_bytes (const void *, size_t);
+unsigned hash_string (const char *);
+unsigned hash_int (int);
+
+#endif /* lib/kernel/hash.h */