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花花酱 LeetCode 964. Least Operators to Express Number

Given a single positive integer x, we will write an expression of the form x (op1) x (op2) x (op3) x ... where each operator op1op2, etc. is either addition, subtraction, multiplication, or division (+-*, or /).  For example, with x = 3, we might write 3 * 3 / 3 + 3 - 3 which is a value of 3.

When writing such an expression, we adhere to the following conventions:

  1. The division operator (/) returns rational numbers.
  2. There are no parentheses placed anywhere.
  3. We use the usual order of operations: multiplication and division happens before addition and subtraction.
  4. It’s not allowed to use the unary negation operator (-).  For example, “x - x” is a valid expression as it only uses subtraction, but “-x + x” is not because it uses negation.

We would like to write an expression with the least number of operators such that the expression equals the given target.  Return the least number of operators used.

Example 1:

Input: x = 3, target = 19 
Output: 5
Explanation: 3 * 3 + 3 * 3 + 3 / 3. The expression contains 5 operations.

Example 2:

Input: x = 5, target = 501 
Output: 8
Explanation: 5 * 5 * 5 * 5 - 5 * 5 * 5 + 5 / 5. The expression contains 8 operations.

Example 3:

Input: x = 100, target = 100000000 
Output: 3
Explanation: 100 * 100 * 100 * 100. The expression contains 3 operations.

Note:

  • 2 <= x <= 100
  • 1 <= target <= 2 * 10^8

Solution: Dijkstra

Find the shortest path from target to 0 using ops.

Time complexity: O(nlogn)
Space complexity: O(nlogn)
n = x * log(t) / log(x)

C++/set

C++/heap

Solution 2: DFS + Memoization

Time complexity: O(x * log(t)/log(x))
Space complexity: O(x * log(t)/log(x))

C++

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