494. Target Sum (Medium)
https://leetcode.com/problems/target-sum/
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.
Note:
- The length of the given array is positive and will not exceed 20.
- The sum of elements in the given array will not exceed 1000.
- Your output answer is guaranteed to be fitted in a 32-bit integer.
Solutions
class Solution {
int ans = 0;
Map<Integer, Integer> maxMap = new HashMap<>();
Map<Integer, Integer> minMap = new HashMap<>();
public int findTargetSumWays(int[] nums, int S) {
if (nums == null || nums.length == 0) {
return 0;
}
int len = nums.length;
maxMap.put(len, 0);
minMap.put(len, 0);
for (int i = len - 1; i >= 0; i--) {
// max sum after i (inclusive)
maxMap.put(i, maxMap.get(i + 1) + nums[i]);
// min sum after i (inclusive)
minMap.put(i, minMap.get(i + 1) - nums[i]);
}
recurse(nums, S, 0, 0);
return ans;
}
private void recurse(int[] nums, int target, int idx, int sum) {
if (idx == nums.length) {
if (target == sum) {
ans++;
}
return;
}
// sum + maxMap.get(idx) < target means even all the rest numbers
// keep positive, still less than target.
if (sum + maxMap.get(idx) >= target) {
// ith number remains positive
recurse(nums, target, idx + 1, sum + nums[idx]);
}
// sum + minMap.get(idx) > target means even all the rest numbers
// turn to be negative, still larger than target.
if (sum + minMap.get(idx) <= target) {
// ith number turns to be negative
recurse(nums, target, idx + 1, sum - nums[idx]);
}
}
}