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ts.go
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ts.go
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package ts
import (
"fmt"
"math"
)
func TargetSum(nums []int, s int) int {
// brute force
return helper(nums, 0, 0, s)
}
func helper(nums []int, i, sum, s int) int {
if i == len(nums) {
if sum == s {
return 1
} else {
return 0
}
}
var count int
count += helper(nums, i+1, sum+nums[i], s)
count += helper(nums, i+1, sum-nums[i], s)
return count
}
func TargetSumWithMemo(nums []int, s int) int {
n := len(nums)
memo := make([][]int, n)
for i := range memo {
memo[i] = make([]int, 2001)
for j := range memo[i] {
memo[i][j] = math.MinInt32
}
}
return helperWithMemo(nums, 0, 0, s, memo)
}
func helperWithMemo(nums []int, i, sum, s int, memo [][]int) int {
if i == len(nums) {
if sum == s {
return 1
}
return 0
}
if memo[i][sum+1000] != math.MinInt32 {
return memo[i][sum+1000]
}
var count int
count += helperWithMemo(nums, i+1, sum+nums[i], s, memo)
count += helperWithMemo(nums, i+1, sum-nums[i], s, memo)
memo[i][sum+1000] = count
return count
}
func TargetSum2(nums []int, s int) int {
var sum int
for i := range nums {
sum += nums[i]
}
if s > sum || (sum-s)%2 == 1 {
return 0
}
target := (sum - s) / 2
dp := make([]int, target+1)
dp[0] = 1
for i := 0; i < len(nums); i++ {
for j := target; j >= nums[i]; j-- {
dp[j] += dp[j-nums[i]]
}
fmt.Println(dp)
}
return dp[target]
}
func TargetSum3(nums []int, s int) int {
// we have to find a subset P and N
// sum(P) - sum(N) = s
// sum(P) + sum(N) + sum(P) - sun(N) = s + sum(P) + sum(N)
// 2 * sum(P) = s + sum(nums)
// sum(P) = (s + sum(nums)) / 2
var sum int
for i := range nums {
sum += nums[i]
}
if s > sum || (sum+s)%2 == 1 {
return 0
}
// then become the 0-1 knapsack problem
target := (sum + s) / 2
dp := make([]int, target+1)
dp[0] = 1
for i := 0; i < len(nums); i++ {
for j := target; j >= nums[i]; j-- {
dp[j] += dp[j-nums[i]]
}
}
return dp[target]
}