Lintcode 89. k Sum

Given n distinct positive integers, integer k (k <= n) and a number target.

Find k numbers where sum is target. Calculate how many solutions there are?

Example

Example 1

Input:
List = [1,2,3,4]
k = 2
target = 5
Output: 2
Explanation: 1 + 4 = 2 + 3 = 5

Example 2

Input:
List = [1,2,3,4,5]
k = 3
target = 6
Output: 1
Explanation: There is only one method. 1 + 2 + 3 = 6

Code (Java):

public class Solution {
    /**
     * @param A: An integer array
     * @param k: A positive integer (k <= length(A))
     * @param target: An integer
     * @return: An integer
     */
    public int kSum(int[] A, int k, int target) {
        if (A == null || A.length == 0 || k <= 0 || target <= 0) {
            return 0;
        }
        
        int[][][] dp = new int[A.length + 1][k + 1][target + 1];
        for (int i = 0; i <= A.length; i++) {
            dp[i][0][0] = 1;
        }
        
        for (int i = 1; i <= A.length; i++) {
            for (int j = 1; j <= Math.min(i, k); j++) {
                for (int t = 1; t <= target; t++) {
                    dp[i][j][t] = dp[i - 1][j][t];
                    if (t - A[i - 1] >= 0) {
                        dp[i][j][t] += dp[i - 1][j - 1][t - A[i - 1]];
                    }
                }
            }
        }
        
        return dp[A.length][k][target];
    }
}