494. Target Sum

Description

You are given an integer array nums and an integer target.

You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.

• For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1".

Return the number of different expressions that you can build, which evaluates to target.

 

Example 1:

Input: nums = [1,1,1,1,1], target = 3
Output: 5
Explanation: There are 5 ways to assign symbols to make the sum of nums be target 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
+1 + 1 + 1 + 1 - 1 = 3

Example 2:

Input: nums = [1], target = 1
Output: 1

 

Constraints:

• 1 <= nums.length <= 20
• 0 <= nums[i] <= 1000
• 0 <= sum(nums[i]) <= 1000
• -1000 <= target <= 1000

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n*sum(nums))
• Space complexity: O(n+n*sum(nums))

 

JavaScript

/**
 * @param {number[]} nums
 * @param {number} target
 * @return {number}
 */
const findTargetSumWays = function (nums, target) {
  const n = nums.length;
  const memo = new Map();

  const buildExpression = (index, sum) => {
    if (index >= n) return sum === target ? 1 : 0;
    const key = `${index},${sum}`;

    if (memo.has(key)) return memo.get(key);
    const num = nums[index];
    const plus = buildExpression(index + 1, sum + num);
    const minus = buildExpression(index + 1, sum + num * -1);
    const result = plus + minus;

    memo.set(key, result);

    return result;
  };

  return buildExpression(0, 0);
};