/*
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.
Find out how many ways to assign symbols to make sum of integers equal to target S.
Example 1:
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.
*/
type pair struct {
x,y int
}
func calc(nums[]int, i int, current_sum int, S int, memo map[pair]int) int {
if count, ok := memo[pair{i,current_sum}]; ok{
return count
}
if i == len(nums) {
if current_sum == S {
return 1
} else {
return 0
}
}
pos := calc(nums, i+1, current_sum+nums[i],S, memo)
neg := calc(nums, i+1, current_sum-nums[i],S, memo)
memo[pair{i,current_sum}] = pos + neg
return memo[pair{i,current_sum}]
}
func findTargetSumWays(nums []int, S int) int {
memo := map[pair]int{}
return calc(nums, 0,0,S, memo)
}