• Difficulty: Medium

• Related Topics: Dynamic Programming, Depth-first Search

• Link: https://leetcode.com/problems/target-sum/

Description

You are given a list of non-negative integers, a1, a2, ..., an, and a target, S. Now you have 2 symbols+and-. For each integer, you should choose one from+and-as its new symbol.
給定一個包含非負整數的列表 [a1, a2, ..., an]

Find out how many ways to assign symbols to make sum of integers equal to target S.
找出有多少種賦值的方式，使得賦值過後這些數的和等於 S。

Example

Input: nums is [1, 1, 1, 1, 1], S is 3. 
Output: 5
Explanation: 

-1+1+1+1+1 = 3
+1-1+1+1+1 = 3
+1+1-1+1+1 = 3
+1+1+1-1+1 = 3
+1+1+1+1-1 = 3

There are 5 ways to assign symbols to make the sum of nums be target 3.
 

Constraints

• The length of the given array is positive and will not exceed 20.
  給定的陣列保證非空，且長度不超過 20。
• The sum of elements in the given array will not exceed 1000.
  給定陣列的元素和不超過 1000。
• Your output answer is guaranteed to be fitted in a 32-bit integer.
  你的答案保證在 32 位整數的範圍內。

Solution

由於此題只出現 + 和 -，沒有其它符號，所以簡單的深搜即可完成任務。程式碼如下：

class Solution {
    private var result = 0

    fun findTargetSumWays(nums: IntArray, S: Int): Int {
        backtrack(nums, S, 0, 0)
        return result
    }

    private fun backtrack(nums: IntArray, s: Int, curSum: Int, curIndex: Int) {
        if (curIndex == nums.size ) {
            if (curSum == s) {
                result++
            }
            return
        }
        // 當前數的符號取 +
        backtrack(nums, s, curSum + nums[curIndex], curIndex + 1)
        // 當前數的符號取 -
        backtrack(nums, s, curSum - nums[curIndex], curIndex + 1)
    }
}