feat: solve No.377

Author: BaffinLee

301-400/377. Combination Sum IV.md

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+# 377. Combination Sum IV
+
+- Difficulty: Medium.
+- Related Topics: Array, Dynamic Programming.
+- Similar Questions: Combination Sum, Ways to Express an Integer as Sum of Powers.
+
+## Problem
+
+Given an array of **distinct** integers `nums` and a target integer `target`, return **the number of possible combinations that add up to** `target`.
+
+The test cases are generated so that the answer can fit in a **32-bit** integer.
+
+ 
+Example 1:
+
+```
+Input: nums = [1,2,3], target = 4
+Output: 7
+Explanation:
+The possible combination ways are:
+(1, 1, 1, 1)
+(1, 1, 2)
+(1, 2, 1)
+(1, 3)
+(2, 1, 1)
+(2, 2)
+(3, 1)
+Note that different sequences are counted as different combinations.
+```
+
+Example 2:
+
+```
+Input: nums = [9], target = 3
+Output: 0
+```
+
+ 
+**Constraints:**
+
+
+	
+- `1 <= nums.length <= 200`
+	
+- `1 <= nums[i] <= 1000`
+	
+- All the elements of `nums` are **unique**.
+	
+- `1 <= target <= 1000`
+
+
+ 
+**Follow up:** What if negative numbers are allowed in the given array? How does it change the problem? What limitation we need to add to the question to allow negative numbers?
+
+
+## Solution
+
+```javascript
+/**
+ * @param {number[]} nums
+ * @param {number} target
+ * @return {number}
+ */
+var combinationSum4 = function(nums, target, map = {}) {
+    if (target === 0) return 1;
+    if (map[target] !== undefined) return map[target];
+    var res = 0;
+    for (var i = 0; i < nums.length; i++) {
+        if (nums[i] > target) continue;
+        res += combinationSum4(nums, target - nums[i], map);
+    }
+    map[target] = res;
+    return res;
+};
+```
+
+**Explain:**
+
+Top-down dynamic programming.
+
+**Complexity:**
+
+* Time complexity : O(target).
+* Space complexity : O(target * n).