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494.target-sum.cpp
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60 lines (55 loc) · 1.77 KB
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// Tag: Array, Dynamic Programming, Backtracking
// Time: O(N * Sum)
// Space: O(N * Sum)
// Ref: -
// Note: -
// You are given an integer array nums and an integer target.
// You want to build an expression out of nums by adding one of the symbols '+' and '-' before each integer in nums and then concatenate all the integers.
//
// For example, if nums = [2, 1], you can add a '+' before 2 and a '-' before 1 and concatenate them to build the expression "+2-1".
//
// Return the number of different expressions that you can build, which evaluates to target.
//
// Example 1:
//
// Input: nums = [1,1,1,1,1], target = 3
// Output: 5
// Explanation: There are 5 ways to assign symbols to make the sum of nums be target 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
// +1 + 1 + 1 + 1 - 1 = 3
//
// Example 2:
//
// Input: nums = [1], target = 1
// Output: 1
//
//
// Constraints:
//
// 1 <= nums.length <= 20
// 0 <= nums[i] <= 1000
// 0 <= sum(nums[i]) <= 1000
// -1000 <= target <= 1000
//
//
class Solution {
public:
int findTargetSumWays(vector<int>& nums, int target) {
unordered_map<int, unordered_map<int, int>> cache;
return helper(nums, target, 0, cache);
}
int helper(vector<int>& nums, int target, int index, unordered_map<int, unordered_map<int, int>> &cache) {
if (index == nums.size()) {
return target == 0 ? 1 : 0;
}
if (cache.count(index) && cache[index].count(target)) {
return cache[index][target];
}
int res = helper(nums, target + nums[index], index + 1, cache) + helper(nums, target - nums[index], index + 1, cache);
cache[index][target] = res;
return res;
}
};