feat: solve combination sum

combination-sum/GangBean.java

@@ -0,0 +1,43 @@
+class Solution {
+    public List<List<Integer>> combinationSum(int[] candidates, int target) {
+        /**
+        1. understanding
+        - find all combinations, which sum to target
+        - can use same number multiple times
+        2. strategy
+        - dp[target]: all combination, which sum to target
+        - dp[n + 1] = dp[n] | dp[1]
+        - [2,3,6,7], target = 7
+            - dp[0] = [[]]
+            - dp[1] = [[]]
+            - dp[2] = [[2]]
+            - dp[3] = [[3]]
+            - dp[4] = dp[2] | dp[2] = [[2,2]]
+            - dp[5] = dp[2] | dp[3] = [[2,3]]
+            - dp[6] = dp[2] | dp[4] , dp[3] | dp[3] = [[2,2,2], [3,3]]
+            - dp[7] = dp[2] | dp[5], dp[3] | dp[4], dp[6] | dp[1], dp[7] = [[2,2,3],]
+        3. complexity
+        - time: O(target * N) where N is length of candidates
+        - space: O(target * N)
+        */
+        List<List<Integer>>[] dp = new List[target + 1];
+        for (int i = 0; i <= target; i++) {
+            dp[i] = new ArrayList<>();
+        }
+
+        dp[0].add(new ArrayList<>());
+
+        for (int candidate : candidates) {
+            for (int i = candidate; i <= target; i++) {
+                for (List<Integer> combination : dp[i - candidate]) {
+                    List<Integer> newCombination = new ArrayList<>(combination);
+                    newCombination.add(candidate);
+                    dp[i].add(newCombination);
+                }
+            }
+        }
+
+        return dp[target];
+    }
+}
+