LintCode 125 · Backpack II.java

Backpack with Value array:
function:
dp[i][j] = Math.max(dp[i - 1][j - A[i - 1]] + V[i - 1], dp[i - 1][j]); (when you take that ith item)
or
dp[i][j] += dp[i - 1][j]; (when you don't take that ith item)

	public class Solution {
	/**
	* @param m: An integer m denotes the size of a backpack
	* @param A: Given n items with size A[i]
	* @param V: Given n items with value V[i]
	* @return: The maximum value
	*/
	public int backPackII(int m, int[] A, int[] V) {
	// write your code here
	if (A == null || A.length == 0) {
	return 0;
	}
	int n = A.length;
	// init
	int[][] dp = new int[n+1][m+1];
	dp[0][0] = 0;
	for (int j = 1; j <= m; j++) {
	dp[0][j] = 0;
	}
	// dp: functions
	int maximumJ = Integer.MIN_VALUE;
	for (int i = 1; i <= n; i++) {
	dp[i][0] = 0;
	for (int j = 1; j <= m; j++) {
	if (j - A[i-1] >= 0) {
	dp[i][j] = Math.max(dp[i - 1][j - A[i - 1]] + V[i - 1], dp[i - 1][j]);
	} else {
	dp[i][j] += dp[i - 1][j];
	}
	}
	}
	// dp: answer
	return dp[n][m];
	}
	}

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