We have an array of numbers, and we start at index 0. At every point, we're...

We have an array of numbers, and we start at index 0.

At every point, we're allowed to jump from index i to i+3, i+4, or stop where we are.

We'd like to find the maximum possible sum of the numbers we visit.

For example, for the array [14, 28, 79, -87, 29, 34, -7, 65, -11, 91, 32, 27, -5], the answer is 140.

(starting at the 14, we jump 4 spots to 29, then 3 spots to 65, another 3 to 32, then stop. 14 + 29 + 65 + 32 = 140)

What's the maximum possible sum we could visit for this array:

[95, 69, 68, 44, 0, 53, 34, -83, -8, 38, -63, -89, 34, -91, 1, 39, -7, -54, 85, -25, -47, 89, -57, -18, -22, -50, -74, -91, -38, 99, 73, 7, 44, -47, -35, -70, 26, -54, -28, 7, -26, -73, -48, -76, -18, 94, -54, 65, -71, -10, 5, 64, 55, 68, 7, 41, -52, 57, -75, 90, -21, -47, -88, -5, -9, 46, -8, 71, 34, 82, 10, -37, 37, 1, 49, 91, 80, 57, -56, 83, -58, 24, -34, 30, -65, 42, -28, -84, -58, -62, 20, 89, -43, -16, 9, 37, -21, -71, -27, 93, 93, 3, 24, 51, 19, -54, -20, 43, 96, 15, -4, -30, -12, -88, 95, -89, 63, 63, 26, 34, 9, 66, 40, 59, -69, -29, -3, -89, -58, 45, 68, 45, 92, -51, 89, -75, 0, 14, 46, -20, -90, -83, 82, 29, -32, 68, 55, 41, -85, 56, 97, -11, -25, -28, 65, 61, 54, -36, -24, 98, 49, 19, 3, -94, -46, 26, 92, -72, -29, 93, 71, 15, 3, -89, -66, -85, -42, 83, 43, 27, 76, 71, 62, 44, 9, 2, 40, 8, 78, -6, -61, -93, 28, -46, -48, 25, -34, -91, 73, 90, 77, -5, 98, 1, -5, -85, 63, -15, 57, 20, 71, -67, -60, -46, -71, -9, 62, 99, 80, -15, 53, 29, 52, -91, -78, -77, -57, 21, -74, 46, -11, 74, -21, -48, -7, -56, 54, 8, -51, -61, -46, 79, 42, 97, 61, 40, -99, -13, 55, -53, -71, 80, 31, -35, 77, 89, -2, 75, 59, -66, 87, 23, 48, 80, -28, 86, 54, 37, -41, 95, -87, 79, -49, 8, -95, 66, 79, -38, 75, 49, -30, 7, -46, -44, 43, -26, -63, 23, 77, -8, 36, 83, 10, 12, -34, 32, -63, -32, 47, -5, 53, 66, 32, 14, 24, 28, 57, -48, -89, -51, -26, -21, -37, -41, -17, -40, 19, 25, 89, -11, 92, -43, -50, 53, -36, 50, -12, 68, -28, 18, 62, -48, -86, 87, -80, 58, 73, -93, 81, -86, 26, 3, 51, 74, 37, 45, 85, 12, 49, 93, -93, -5, 61, -64, -48, -11, 68, -36, -83, -18, 30, -53, -88, 6, 43, -38, 50, -28, 91, 49, 21, 86, -15, -18, 2, 0, 55, -73, 85, -49, -18, -90, 89, 79, -21, 23, 38, 43, 83, 72, 63, 14, -35, 81, -2, -71, 70, 51, -26, -20, 74, 10, -37, 61, -29, -62, 18, -46, 75, 98, 18, -4, 25, 13, 70, -34, 79, 16, -55, -7, -56, -55, 79, 29, 13, -31, -12, -29, -33, 12, 17, -5, -59, -12, 76, -6, -4, -5, -90, -45, -33, -14, -56, 64, -99, -65, -98, -97, 35, -50, -63, 8, -7, -46, 3, -69, 24, -23, -6, 78, -21, 2, -99, -29, 75, 40, -30, -40, 10, -41, -65, -42, -88, -8, -32, -2, -39, -95, -73, 32, 99, -35, -88, 81, -32, -19, 58, 83, -73, -23, 1, -34, -40, -39, 35, -52, -24, 57, -44, 2]

Expert Solution

Answer is 6510

Program Code Screenshot :

Sample Output :

Program Code to Copy

class Main{

    public static int max(int... arr){
        int mx = arr[0];
        for(int a : arr){
            mx = Math.max(mx,a);
        }
        return mx;
    }

    public static void main(String[] args) {
        int arr[] = {95, 69, 68, 44, 0, 53, 34, -83, -8, 38, -63, -89, 34, -91, 1, 39, -7, -54, 85, -25, -47, 89, -57, -18, -22, -50, -74, -91, -38, 99, 73, 7, 44, -47, -35, -70, 26, -54, -28, 7, -26, -73, -48, -76, -18, 94, -54, 65, -71, -10, 5, 64, 55,
                68, 7, 41, -52, 57, -75, 90, -21, -47, -88, -5, -9, 46, -8, 71, 34, 82, 10, -37, 37, 1, 49, 91, 80, 57, -56, 83, -58, 24, -34, 30, -65, 42, -28, -84, -58, -62, 20, 89, -43, -16, 9, 37, -21, -71, -27, 93, 93, 3, 24, 51, 19, -54, -20, 43,
                96, 15, -4, -30, -12, -88, 95, -89, 63, 63, 26, 34, 9, 66, 40, 59, -69, -29, -3, -89, -58, 45, 68, 45, 92, -51, 89, -75, 0, 14, 46, -20, -90, -83, 82, 29, -32, 68, 55, 41, -85, 56, 97, -11, -25, -28, 65, 61, 54, -36, -24, 98, 49, 19,
                3, -94, -46, 26, 92, -72, -29, 93, 71, 15, 3, -89, -66, -85, -42, 83, 43, 27, 76, 71, 62, 44, 9, 2, 40, 8, 78, -6, -61, -93, 28, -46, -48, 25, -34, -91, 73, 90, 77, -5, 98, 1, -5, -85, 63, -15, 57, 20, 71, -67, -60, -46, -71, -9, 62,
                99, 80, -15, 53, 29, 52, -91, -78, -77, -57, 21, -74, 46, -11, 74, -21, -48, -7, -56, 54, 8, -51, -61, -46, 79, 42, 97, 61, 40, -99, -13, 55, -53, -71, 80, 31, -35, 77, 89, -2, 75, 59, -66, 87, 23, 48, 80, -28, 86, 54, 37, -41, 95,
                -87, 79, -49, 8, -95, 66, 79, -38, 75, 49, -30, 7, -46, -44, 43, -26, -63, 23, 77, -8, 36, 83, 10, 12, -34, 32, -63, -32, 47, -5, 53, 66, 32, 14, 24, 28, 57, -48, -89, -51, -26, -21, -37, -41, -17, -40, 19, 25, 89, -11, 92, -43, -50,
                53, -36, 50, -12, 68, -28, 18, 62, -48, -86, 87, -80, 58, 73, -93, 81, -86, 26, 3, 51, 74, 37, 45, 85, 12, 49, 93, -93, -5, 61, -64, -48, -11, 68, -36, -83, -18, 30, -53, -88, 6, 43, -38, 50, -28, 91, 49, 21, 86, -15, -18, 2, 0, 55,
                -73, 85, -49, -18, -90, 89, 79, -21, 23, 38, 43, 83, 72, 63, 14, -35, 81, -2, -71, 70, 51, -26, -20, 74, 10, -37, 61, -29, -62, 18, -46, 75, 98, 18, -4, 25, 13, 70, -34, 79, 16, -55, -7, -56, -55, 79, 29, 13, -31, -12, -29, -33,
                12, 17, -5, -59, -12, 76, -6, -4, -5, -90, -45, -33, -14, -56, 64, -99, -65, -98, -97, 35, -50, -63, 8, -7, -46, 3, -69, 24, -23, -6, 78, -21, 2, -99, -29, 75, 40, -30, -40, 10, -41, -65, -42, -88, -8, -32, -2, -39, -95, -73, 32,
                99, -35, -88, 81, -32, -19, 58, 83, -73, -23, 1, -34, -40, -39, 35, -52, -24, 57, -44, 2};
        //Initialize an array to store dp
        int dp[] = new int[arr.length];
        //Initialize answer for the last element
        dp[arr.length-1] = Math.max(arr[arr.length-1],0);
        for(int i=arr.length-2;i>=0;i--){
            //Build dp array
            dp[i] = max(0,arr[i]+((i+3)<dp.length?dp[i+3]:0),arr[i]+((i+4)<dp.length?dp[i+4]:0));
        }
        //Print first answer
        System.out.println(dp[0]);

    }
}

venereology answered 6 months ago

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