Finish 0001

Author: Khanh Do

0001_two_sum.py

@@ -0,0 +1,98 @@
+#!/usr/bin/env python
+
+def two_sum1(nums, target):
+    """Find indexes i and j of an array whose values add up to the target.
+    Can assume that each input has exactly one solution.
+
+    Time: O(n^2) -- nested loops to find all combinations of sums
+    Space: O(1) -- loop through the array in place; each sum is O(1)
+    """
+    if len(nums) < 2:
+        return [None, None]
+
+    for i, u in enumerate(nums):
+        for j, v in enumerate(nums):
+            if u + v == target:
+                return [i, j]
+
+    return [None, None]
+
+
+def two_sum2(nums, target):
+    """Find indexes i and j of an array whose values add up to the target.
+    Can assume that each input has exactly one solution.
+
+    Time: O(n) -- loop through the array once; past dict get/set is O(1)
+    Space: O(n) -- might have to store all n elements in past dict
+    """
+    if len(nums) < 2:
+        return [None, None]
+
+    past = {}
+    for i in range(len(nums)):
+        diff = target - nums[i]
+        if diff in past:
+            return [past[diff], i]
+        past[nums[i]] = i
+
+    return [None, None]
+
+
+def two_sum3(nums, target):
+    """Find indexes i and j of an array whose values add up to the target.
+    Can assume that each input has exactly one solution.
+
+    nums *must* be sorted
+
+    Time: O(n) -- might have to traverse to the middle indexes of the array
+    Space: O(1) -- traverse the array in place; each sum is O(1)
+    """
+    if len(nums) < 2:
+        return [None, None]
+
+    l, r = 0, len(nums) - 1
+    while nums[l] < nums[r]:
+        s = nums[l] + nums[r]
+        if s == target:
+            return [l, r]
+        elif s < target:
+            l += 1
+        else:
+            r -= 1
+
+    return [None, None]
+
+
+def main():
+    nums = [2, 7, 11, 15]
+    target = 9
+    ans = [0, 1]
+
+    assert two_sum1(nums, target) == ans
+    assert two_sum2(nums, target) == ans
+    assert two_sum3(list(nums), target) == ans
+
+
+    short_circuit_cases = [
+        ([], 3),   # len(nums) == 0
+        ([1], 8),  # len(nums) == 1
+    ]
+
+    for nums, target in short_circuit_cases:
+        assert two_sum1(nums, target) == [None, None]
+        assert two_sum2(nums, target) == [None, None]
+        assert two_sum3(nums, target) == [None, None]
+
+
+    interesting_cases = [
+        ([2, 7, 11, 15], 99, [None, None]),  # No matches found
+    ]
+
+    for nums, target, ans in interesting_cases:
+        assert two_sum1(nums, target) == ans
+        assert two_sum2(nums, target) == ans
+        assert two_sum3(list(nums), target) == ans
+
+
+if __name__ == '__main__':
+    main()