Reach a Number | Live Coding with Explanation | Leetcode #754

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[AlgorithmsMadeEasy]

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[vineetkumar]

I like to add more observation that every step has capacity to reduce 2n steps, where n is step count.
let x = (sum - target)/2.
Then if we take x step in backward direction, we are at the target.

[NANUVALAADITHYA]

It's better to explain the intuition instead of simply just telling the algorithm

[sangameshkodge]

Don't we need to ensure k in 2*k is less than step(k<steps). As we can only do this flipping if k < less than step. If we never reached the step we cant negate it.
For example number 42. The progression would be
step1: add 1-> 1
step2: add 2-> 3
step3: add 3-> 6
step4: add 4-> 10
step5: add 5-> 15
step6: add 6-> 21
step7: add 7-> 28
step8: add 8-> 36
step9: add 9-> 45(45-42 is odd)
step10: add 10-> 55(55-42 is odd)
step11: add 11-> 66(66-42=2*12).
=> k=12 or (1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 - 2*12 = 42 )
you need to flip the 12th step in a total of 11 steps?

[mr.computer]

GUYS MY CODE CAN HANDLE ALL NUMBERS
import java.util.Scanner;
public class Main {
public static int reachTarget(int target) {
if (target < 0)
return target * -1 * 2;
else {
int sum = 1;
int moves = 1;
while (sum < target) {
moves++;
sum += moves;
}
if(sum>target){
sum-=moves;
return (moves-1 + (target-sum)*2);}
else{
return moves;
}
}
}

public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
System.out.print("Enter the target: ");
int target = sc.nextInt();
System.out.print("The number of moves are: " + reachTarget(target));
}
}

[AnkitKumar-mbvl]

Do a dry run of example different from the example given in the question. It would help better.

[aayush]

I tried solving using bfs but it gives TLE
class Solution {
public:
int reachNumber(int target) {
queue<int>q;
q.push(0);
int steps=1;

while(!q.empty()){
int n = q.size();

for(int i=0; i<n; i++){
int curr = q.front();
q.pop();

if(curr==target) return steps-1;
//push 2 choices
q.push(curr + steps);
q.push(curr - steps);
}

steps++;

}
return steps-1;
}
};

[adityaparihar]

in case when target ==
2 why we are going to -1