题目

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.

答案

巨短的dfs答案

class Solution {
    public int findTargetSumWays(int[] nums, int S) {
        return dfs(nums, 0, 0, S);
    }
    
    public int dfs(int[] nums, int index, int curr_sum, int S) {
        if(index == nums.length) return (curr_sum == S)?1:0;
        int ways = dfs(nums, index + 1, curr_sum + nums[index], S) + dfs(nums, index + 1, curr_sum - nums[index], S);
        return ways;
    }
}

下面用dp 优化下时间
这道题要改成dp有点tricky
我本来的想法是在dfs递归计算的同时记录 dp[当前的sum][当前的index]的值
但是这样做有个问题，就是curr_sum是有可能小于0的，这样就会引发异常

所以我想偷懒用HashMap来替代dp数组，代码如下

class Solution {
    class Pair {
        int curr_sum;
        int index;
        public Pair(int sum, int i) { curr_sum = sum; index = i;}
    }

    public int findTargetSumWays(int[] nums, int S) {
        Map<Pair, Integer> dfs_memory = new HashMap<Pair, Integer>();
        return dfs(nums, dfs_memory, 0, 0, S);
    }

    public int dfs(int[] nums, Map<Pair, Integer> dfs_memory, int index, int curr_sum, int S) {
        if(index == nums.length) {
            return (curr_sum == S)?1:0;
        }
        Pair key = new Pair(curr_sum, index);
        Integer memorized = dfs_memory.get(key);
        if(memorized == null) {
            int ways = dfs(nums, dfs_memory, index + 1, curr_sum + nums[index], S);
            ways += dfs(nums, dfs_memory, index + 1, curr_sum - nums[index], S);
            dfs_memory.put(key, ways);
            return ways;
        }
        return memorized;
    }
}

大概Hashmap有点慢，竟然超时了

最后调整了一下dp数组的细节就过了，代码如下

class Solution {
    public int findTargetSumWays(int[] nums, int S) {
        int[][] dfs_memory = new int[2001][nums.length];
        for(int i = 0; i < dfs_memory.length; i++) Arrays.fill(dfs_memory[i], -1);
        return dfs(nums, dfs_memory, 0, 0, S);
    }

    public int dfs(int[] nums, int[][] dfs_memory, int index, int curr_sum, int S) {
        if(index == nums.length) {
            return (curr_sum == S)?1:0;
        }
        int adjusted_currsum = curr_sum + 1000;
        if(dfs_memory[adjusted_currsum][index] == -1) {
            dfs_memory[adjusted_currsum][index] = dfs(nums, dfs_memory, index + 1, curr_sum + nums[index], S);
            dfs_memory[adjusted_currsum][index] += dfs(nums, dfs_memory, index + 1, curr_sum - nums[index], S);
        }
        return dfs_memory[adjusted_currsum][index];
    }
}