Add power sum problem

backtracking/power_sum.py

@@ -0,0 +1,77 @@
+"""
+Problem source: https://www.hackerrank.com/challenges/the-power-sum/problem
+Find the number of ways that a given integer X, can be expressed as the sum
+of the Nth powers of unique, natural numbers. For example, if X=13 and N=2.
+We have to find all combinations of unique squares adding up to 13.
+The only solution is 2^2+3^2. Constraints: 1<=X<=1000, 2<=N<=10.
+"""
+
+from math import pow
+
+sum_ = count_ = 0
+
+
+def backtrack(x: int, n: int, i: int) -> None:
+    """
+    DO NOT CALL THIS METHOD DIRECTLY, USE solve() INSTEAD.
+
+    >>> backtrack(13, 2, 1) is None
+    True
+    >>> backtrack(1000, 10, 2) is None
+    True
+    """
+    global sum_, count_
+    i_to_n = int(pow(i, n))
+    if sum_ == x:
+        # If the sum of the powers is equal to x, then we have found a solution.
+        count_ += 1
+        return
+    elif sum_ + i_to_n <= x:
+        # If the sum of the powers is less than x, then we can continue adding powers.
+        sum_ += i_to_n
+        backtrack(x, n, i + 1)
+        sum_ -= i_to_n
+    if i_to_n < x:
+        # If the power of i is less than x, then we can try with the next power.
+        backtrack(x, n, i + 1)
+    return
+
+
+def solve(x: int, n: int) -> int:
+    """
+    >>> solve(13, 2)
+    1
+    >>> solve(100, 2)
+    3
+    >>> solve(100, 3)
+    1
+    >>> solve(800, 2)
+    561
+    >>> solve(1000, 10)
+    0
+    >>> solve(400, 2)
+    55
+    >>> solve(50, 1)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid input, x must be between 1 and 1000, n between 2 and 10.
+    >>> solve(-10, 5)
+    Traceback (most recent call last):
+        ...
+    ValueError: Invalid input, x must be between 1 and 1000, n between 2 and 10.
+    """
+    if not (1 <= x <= 1000 and 2 <= n <= 10):
+        raise ValueError(
+            "Invalid input, x must be between 1 and 1000, n between 2 and 10."
+        )
+
+    global sum_, count_
+    sum_, count_ = 0, 0
+    backtrack(x, n, 1)
+    return count_
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()