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494. 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.
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.
参考资料
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.
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/**
* Runtime: 3 ms, faster than 90.55% of Java online submissions for Target Sum.
* Memory Usage: 38.8 MB, less than 10.00% of Java online submissions for Target Sum.
*
* Copy from: https://leetcode-cn.com/problems/target-sum/solution/dong-tai-gui-hua-ji-bai-liao-98de-javayong-hu-by-r/[动态规划击败了98%的java用户 - 目标和 - 力扣（LeetCode）]
*/
public int findTargetSumWays(int[] nums, int S) {
int sum = 0;
for (int num : nums) {
sum += num;
}
if (sum < S || (sum + S) % 2 == 1) {
return 0;
}
int target = (sum + S) / 2;
int[] dp = new int[target + 1];
dp[0] = 1;
for (int num : nums) {
for (int i = target; i >= num; i--) {
dp[i] += dp[i - num];
}
}
return dp[target];
}
/**
* Runtime: 688 ms, faster than 5.06% of Java online submissions for Target Sum.
* Memory Usage: 39 MB, less than 10.00% of Java online submissions for Target Sum.
*/
private int count = 0;
public int findTargetSumWaysDfs(int[] nums, int S) {
if (Objects.isNull(nums) || nums.length == 0) {
return 0;
}
findTargetSumWays(nums, S, 0, 0);
return count;
}
private void findTargetSumWays(int[] nums, int target, int sum, int index) {
if (index == nums.length) {
if (sum == target) {
count++;
}
} else {
int num = nums[index];
findTargetSumWays(nums, target, sum + num, index + 1);
findTargetSumWays(nums, target, sum - num, index + 1);
}
}