Sparse table class and tests added

pydatastructs/miscellaneous_data_structures/__init__.py

@@ -4,7 +4,8 @@
     stack,
     binomial_trees,
     queue,
-    disjoint_set
+    disjoint_set,
+    sparse_table,
 )
 
 from .binomial_trees import (
@@ -27,3 +28,8 @@
     DisjointSetForest,
 )
 __all__.extend(disjoint_set.__all__)
+
+from .sparse_table import(
+    sparseTable,
+)
+__all__.extend(sparse_table.__all__)

pydatastructs/miscellaneous_data_structures/sparse_table.py

@@ -0,0 +1,82 @@
+import math
+
+__all__ = ['sparseTable']
+
+
+class sparseTable:
+    """
+    Represents the sparse table data structure, used to answer range queries efficiently.
+
+    Parameters
+    ==========
+
+    arr: OneDimensionalArray
+        The given OneDimensionalArray on which the range queries have to be performed.
+
+    combine: lambda/function
+        The function whose value is to be computed on the given range. The function must take
+        two parameters.
+
+    isIdempotent: Boolean
+        Indicates whether the function is idempotent or not. If the function is idempotent,
+        range queries can be answered in constant time, whereas for non-idempotent fucntions,
+        these queries take O(logn) time. By default, isIdempotent is set to False.
+
+    Examples
+    ========
+
+    >>> from pydatastructs import sparseTable, OneDimensionalArray as ODA
+    >>> arr1 = ODA(int, [4, 2, 6, 5, 10, 1])
+    >>> spTable = sparseTable(arr1, lambda x, y: x + y)
+    >>> spTable.query(2, 4)
+    21
+
+    >>> gcd = lambda a, b: a if b == 0 else gcd(b, a % b)
+    >>> spTable2 = sparseTable(arr1, gcd, isIdempotent = True)
+    >>> spTable2.query(0, 2)
+    2
+    """
+
+    def __init__(self, arr, combine, isIdempotent=False):
+        n = len(arr)
+        self.isIdempotent = isIdempotent
+        self.log_values = [0]*(n+1)
+        self.log_values[1] = 0
+        self.arr = arr
+        self.combine = combine
+        for i in range(2, n+1):
+            self.log_values[i] = self.log_values[i//2] + 1
+        table = [[0]*(self.log_values[n]+1) for i in range(n)]
+        self.table = table
+        for i in range(n):
+            self.table[i][0] = arr[i]
+        for j in range(1, self.log_values[n]+2):
+            i = 0
+            while i + (1 << j) <= n:
+                self.table[i][j] = self.combine(
+                    self.table[i][j-1], self.table[i + (1 << (j-1))][j-1])
+                i += 1
+
+    def query(self, left, right):
+        """
+        Used to fetch answers to a range query on the given OneDimensionalArray
+
+        Left:
+            Left end of the given range
+
+        Right:
+            Right end of the given range
+
+        Note: The range is inclusive of both ends.
+        """
+        largestPowOf2 = self.log_values[right - left + 1]
+        lenOfInterval = (1 << largestPowOf2)
+        if(self.isIdempotent is True):
+            return self.combine(self.table[left][largestPowOf2], self.table[right-(1 << largestPowOf2)+1][largestPowOf2])
+        else:
+            answer = 0
+            for j in range(lenOfInterval, -1, -1):
+                if left + (1 << j) - 1 <= right:
+                    answer += self.table[left][j]
+                    left += (1 << j)
+            return answer

pydatastructs/miscellaneous_data_structures/tests/test_sparse_table.py

@@ -0,0 +1,38 @@
+from pydatastructs import (
+    sparseTable, OneDimensionalArray)
+from pydatastructs.utils.raises_util import raises
+
+def test_sparseTable():
+    ODA = OneDimensionalArray
+    array = ODA(int, [4, 2, 6, 5, 1, 7, 8])
+
+    spTable = sparseTable(array, lambda x, y: min(x, y), isIdempotent=True)
+
+    rangeQueryResult = spTable.query(0, 2)
+    expected_result = 2
+    assert(rangeQueryResult == expected_result)
+
+    rangeQueryResult = spTable.query(2, 5)
+    expected_result = 1
+    assert(rangeQueryResult == expected_result)
+
+    def gcd(a, b): return a if b == 0 else gcd(b, a % b)
+    spTable2 = sparseTable(array, gcd, isIdempotent=True)
+
+    rangeQueryResult = spTable2.query(0, 2)
+    expected_result = 2
+    assert(rangeQueryResult == expected_result)
+
+    rangeQueryResult = spTable2.query(5, 6)
+    expected_result = 1
+    assert(rangeQueryResult == expected_result)
+
+    spTable3 = sparseTable(array, lambda x, y: x + y)
+
+    rangeQueryResult = spTable3.query(2, 5)
+    expected_result = 19
+    assert(rangeQueryResult == expected_result)
+
+    rangeQueryResult = spTable3.query(1, 4)
+    expected_result = 14
+    assert(rangeQueryResult == expected_result)