Medium
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.
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
@Suppress("NAME_SHADOWING")
class Solution {
fun findTargetSumWays(nums: IntArray, target: Int): Int {
var target = target
var sum = 0
target = Math.abs(target)
for (num in nums) {
sum += num
}
// Invalid target, just return 0
if (target > sum || (sum + target) % 2 != 0) {
return 0
}
val dp = Array((sum + target) / 2 + 1) { IntArray(nums.size + 1) }
dp[0][0] = 1
// empty knapsack must be processed specially
for (i in nums.indices) {
if (nums[i] == 0) {
dp[0][i + 1] = dp[0][i] * 2
} else {
dp[0][i + 1] = dp[0][i]
}
}
for (i in 1 until dp.size) {
for (j in nums.indices) {
dp[i][j + 1] += dp[i][j]
if (nums[j] <= i) {
dp[i][j + 1] += dp[i - nums[j]][j]
}
}
}
return dp[(sum + target) / 2][nums.size]
}
}