花花酱 LeetCode 494. Target Sum

zxi — Wed, 10 Jan 2018 06:13:49 +0000

题目大意：给你一串数字，你可以在每个数字前放置+或-，问有多少种方法可以使得表达式的值等于target。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.

Idea: DP

Solution 1: DP

Time complexity: O(n*sum)

Space complexity: O(n*sum)

C++

// Author: Huahua
// Running time: 16 ms
class Solution {
public:
    int findTargetSumWays(vector& nums, int S) {
      const int n = nums.size();
      const int sum = std::accumulate(nums.begin(), nums.end(), 0);
      if (sum < S) return 0;
      const int offset = sum;
      // ways[i][j] means total ways to sum up to (j - offset) using nums[0] ~ nums[i - 1].
      vector> ways(n + 1, vector(sum + offset + 1, 0));
      ways[0][offset] = 1;
      for (int i = 0; i < n; ++i) {
        for (int j = nums[i]; j < 2 * sum + 1 - nums[i]; ++j)
          if (ways[i][j]) {
            ways[i + 1][j + nums[i]] += ways[i][j];
            ways[i + 1][j - nums[i]] += ways[i][j];
          }        
      }
      
      return ways.back()[S + offset];
    }
};

C++ SC O(n)

// Author: Huahua
// Running time: 12 ms
class Solution {
public:
    int findTargetSumWays(vector& nums, int S) {
      const int n = nums.size();
      const int sum = std::accumulate(nums.begin(), nums.end(), 0);
      if (sum < std::abs(S)) return 0;
      const int kOffset = sum;
      const int kMaxN = sum * 2 + 1;
      vector ways(kMaxN, 0);      
      ways[kOffset] = 1;
      for (int num : nums) {
        vector tmp(kMaxN, 0);
        for (int i = num; i < kMaxN - num; ++i)
          if (ways[i]) {
            tmp[i + num] += ways[i];
            tmp[i - num] += ways[i];
          }
        std::swap(ways, tmp);
      }      
      return ways[S + kOffset];
    }
};

Java

// Author: Huahua
// Running time: 28 ms
class Solution {
  public int findTargetSumWays(int[] nums, int S) {
    int sum = 0;
    for (final int num : nums)
      sum += num;
    if (sum < S) return 0;
    final int kOffset = sum;
    final int kMaxN = sum * 2 + 1;
    int[] ways = new int[kMaxN];
    ways[kOffset] = 1;
    for (final int num : nums) {      
      int[] tmp = new int[kMaxN];      
      for (int i = num; i < kMaxN - num; ++i) {
        tmp[i + num] += ways[i];
        tmp[i - num] += ways[i];
      }
      ways = tmp;
    }
    return ways[S + kOffset];
  }
}

C++ / V2

// Author: Huahua
// Running time: 17 ms
class Solution {
public:
    int findTargetSumWays(vector& nums, int S) {
      const int n = nums.size();
      const int sum = std::accumulate(nums.begin(), nums.end(), 0);
      if (sum < std::abs(S)) return 0;
      const int kOffset = sum;
      const int kMaxN = sum * 2 + 1;
      vector ways(kMaxN, 0);      
      ways[kOffset] = 1;
      for (int num : nums) {
        vector tmp(kMaxN, 0);
        for (int i = 0; i < kMaxN; ++i) {
          if (i + num < kMaxN) tmp[i] += ways[i + num];
          if (i - num >= 0)    tmp[i] += ways[i - num];
        }
        std::swap(ways, tmp);
      }
      return ways[S + kOffset];
    }
};

Solution 2: DFS

Time complexity: O(2^n)

Space complexity: O(n)

C++

// Author: Huahua
// Running time: 422 ms
class Solution {
public:
  int findTargetSumWays(vector& nums, int S) {
    const int sum = std::accumulate(nums.begin(), nums.end(), 0);
    if (sum < std::abs(S)) return 0;
    int ans = 0;
    dfs(nums, 0, S, ans);
    return ans;
  }
private:
  void dfs(const vector& nums, int d, int S, int& ans) {
    if (d == nums.size()) {
      if (S == 0) ++ans;
      return;
    }    
    dfs(nums, d + 1, S - nums[d], ans);
    dfs(nums, d + 1, S + nums[d], ans);
  }
};

Java

// Author: Huahua
// Running time: 615 ms
class Solution {
  private int ans;
  public int findTargetSumWays(int[] nums, int S) {
    int sum = 0;
    for (final int num : nums)
      sum += num;
    if (sum < Math.abs(S)) return 0;
    ans = 0;
    dfs(nums, 0, S);
    return ans;
  }
  
  private void dfs(int[] nums, int d, int S) {
    if (d == nums.length) {
      if (S == 0) ++ans;
      return;
    }
    dfs(nums, d + 1, S - nums[d]);
    dfs(nums, d + 1, S + nums[d]);
  }
}

Solution 3: Subset sum

Time complexity: O(n*sum)

Space complexity: O(sum)

C++ w/ copy

// Author: Huahua
// Running time: 7 ms
class Solution {
public:
    int findTargetSumWays(vector& nums, int S) {
      S = std::abs(S);      
      const int sum = std::accumulate(nums.begin(), nums.end(), 0);
      if (sum < S || (S + sum) % 2 != 0) return 0;
      const int target = (S + sum) / 2;
      vector dp(target + 1, 0);
      dp[0] = 1;
      for (int num : nums) {
        vector tmp(dp);
        for (int j = 0; j <= target - num; ++j)
          tmp[j + num] += dp[j];
        std::swap(dp, tmp);
      }
      
      return dp[target];
    }
};

C++ w/o copy

// Author: Huahua
// Running time: 6 ms
class Solution {
public:
    int findTargetSumWays(vector& nums, int S) {
      S = std::abs(S);
      const int n = nums.size();
      const int sum = std::accumulate(nums.begin(), nums.end(), 0);
      if (sum < S || (S + sum) % 2 != 0) return 0;
      const int target = (S + sum) / 2;
      vector dp(target + 1, 0);
      dp[0] = 1;
      for (int num : nums)
        for (int j = target; j >= num; --j)
          dp[j] += dp[j - num];
      
      return dp[target];
    }
};

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花花酱 LeetCode 494. Target Sum

Idea: DP

Solution 1: DP

C++

C++ SC O(n)

Java

C++ / V2

Solution 2: DFS

C++

Java

Solution 3: Subset sum

C++ w/ copy

C++ w/o copy