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Jump Game V in C++
Suppose we have an array of integers called arr and an integer d. In one step we can jump from index i to −
i + x where: i + x < n and x in range 1 to d.
i - x where: i - x >= 0 and x in range 1 to d.
Here n is the size of array. In addition, we can only jump from index i to index j when arr[i] > arr[j] and arr[i] > arr[k] for all indices k between i and j. We can choose any index of the array and start the jumping. We have to find the maximum number of indices we can visit.
So, if the input is like d = 2 and heights are like
then the output will be 4, we can start at index 10. we can jump from index 10 --> 8 --> 6 --> 7 as shown. So if we start at index 6 we can only jump to index 7. We cannot jump to index 5 because 13 > 9. We cannot jump to index 4 because index 5 is between index 4 and 6 and 13 > 9. And also, we cannot jump from index 3 to index 2 or index 1.
To solve this, we will follow these steps −
Define an array dp
Define a function solve(), this will take an array arr, idx, d,
if dp[idx] is not equal to -1, then −
return dp[idx]
ret := 1
n := size of arr
for initialize i := idx + 1, when i < n, update (increase i by 1), do −
if i > idx + d, then −
Come out from the loop
if arr[i] >= arr[idx], then −
Come out from the loop
ret := maximum of ret and 1 + solve(arr, i, d)
for initialize i := idx - 1, when i >= 0, update (decrease i by 1), do −
if i < idx - d, then −
Come out from the loop
if arr[i] >= arr[idx], then −
Come out from the loop
ret := maximum of ret and 1 + solve(arr, i, d)
dp[idx] := ret
return ret
From the main method do the following −
n := size of arr
dp := Define an array of size n and fill this with -1
ret := 1
for initialize i := 0, when i < n, update (increase i by 1), do −
ret := maximum of ret and solve(arr, i, d)
return ret
Let us see the following implementation to get better understanding −
Example
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
vector<int> dp;
int solve(vector <int>& arr, int idx, int d){
if (dp[idx] != -1)
return dp[idx];
int ret = 1;
int n = arr.size();
for (int i = idx + 1; i < n; i++) {
if (i > idx + d)
break;
if (arr[i] >= arr[idx])
break;
ret = max(ret, 1 + solve(arr, i, d));
}
for (int i = idx - 1; i >= 0; i--) {
if (i < idx - d)
break;
if (arr[i] >= arr[idx])
break;
ret = max(ret, 1 + solve(arr, i, d));
}
return dp[idx] = ret;
}
int maxJumps(vector<int>& arr, int d) {
int n = arr.size();
dp = vector<int>(n, -1);
int ret = 1;
for (int i = 0; i < n; i++) {
ret = max(ret, solve(arr, i, d));
}
return ret;
}
};
main(){
Solution ob;
vector<int> v = {6,4,14,6,8,13,9,7,10,6,12};
cout << (ob.maxJumps(v, 2));
}Input
{6,4,14,6,8,13,9,7,10,6,12}, 2Output
4
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