Create digit-operations-to-make-two-integers-equal.py

Author: kamyu104

Python/digit-operations-to-make-two-integers-equal.py

@@ -0,0 +1,53 @@
+# Time:  O(nlogn)
+# Space: O(n)
+
+import heapq
+
+
+# number theory, dijkstra's algorithm
+class Solution(object):
+    def minOperations(self, n, m):
+        """
+        :type n: int
+        :type m: int
+        :rtype: int
+        """
+        def linear_sieve_of_eratosthenes(n):  # Time: O(n), Space: O(n)
+            primes = []
+            spf = [-1]*(n+1)  # the smallest prime factor
+            for i in xrange(2, n+1):
+                if spf[i] == -1:
+                    spf[i] = i
+                    primes.append(i)
+                for p in primes:
+                    if i*p > n or p > spf[i]:
+                        break
+                    spf[i*p] = p
+            return spf
+            
+        def dijkstra(start, target):
+            if spf[start] == start:
+                return -1
+            lookup = set()
+            min_heap = [(start, start)]
+            while min_heap:
+                curr, i = heapq.heappop(min_heap)
+                if i in lookup:
+                    continue
+                lookup.add(i)
+                if i == target:
+                    return curr
+                base = 1
+                while base <= i:
+                    x = i//base
+                    for d in (-1, 1):
+                        if (1 if x <= 9 else 0) <= x%10+d <= 9 and spf[i+d*base] != i+d*base and i+d*base not in lookup:
+                            heapq.heappush(min_heap, (curr+(i+d*base), i+d*base))
+                    base *= 10
+            return -1
+        
+        base = 1
+        while base < max(n, m):
+            base *= 10
+        spf = linear_sieve_of_eratosthenes(base)
+        return dijkstra(n, m)