377. Combination Sum IV, 377 combination

377. Combination Sum IV, 377 combination

Problem

Given an integer array with all positive numbers and no duplicates, find the number of possible combinations that add up to a positive integer target.

Example:

Nums= [1, 2, 3]Target= 4 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. therefore the output is7.

Analysis
According to the question, the subproblem can be expressed as F (I) = F (I) + F (I-nums [j]), where I starts from 1 to target, j is the subscript of the array, from 0 to nums. size (). The calculation result shows that the target is the maximum number of all combinations of [1, target]. The calculation of each target uses the exhaustive traversal of each nums element.

Code

Int combinationSum4 (vector <int> & nums, int target) {vector <int> V (target + 1, 0); int I, j; V [0] = 1; // V [0] is 1 because I-nums [j] = 0 V [I-nums [j] is successful once for (I = 1; I <= target; I ++) {for (j = 0; j <nums. size (); j ++) if (nums [j] <= I) V [I] + = V [I-nums [j];} return V [target];}View Code