Maximum height when coins are arranged in a triangle | Returns the square root of n . Note that the function ; We are using n itself as initial approximation This can definitely be improved ; e decides the accuracy level ; Method to find maximum height of arrangement of coins ; calculating portion inside the square root ; Driver code to test above method
< ? php function squareRoot ( $ n ) { $ x = $ n ; $ y = 1 ; $ e = 0.000001 ; while ( $ x - $ y > $ e ) { $ x = ( $ x + $ y ) / 2 ; $ y = $ n / $ x ; } return $ x ; } function findMaximumHeight ( $ N ) { $ n = 1 + 8 * $ N ; $ maxH = ( -1 + squareRoot ( $ n ) ) / 2 ; return floor ( $ maxH ) ; } $ N = 12 ; echo findMaximumHeight ( $ N ) ; ? >