# # 1064 Fixed Point (有圖)

[LeetCode](https://leetcode.com/problems/fixed-point/)

```
Given an array A of distinct integers sorted in ascending order, 
return the smallest index i that satisfies A[i] == i.  
Return -1 if no such i exists.
給一個裡面都包含不同數字的陣列 A，排序已經由小到大排好了。請找出符合 A[i] = i 的值
```

```
Example 1:

Input: [-10,-5,0,3,7]
Output: 3
Explanation: 
For the given array, A[0] = -10, A[1] = -5, A[2] = 0, A[3] = 3, thus the output is 3.
Example 2:

Input: [0,2,5,8,17]
Output: 0
Explanation: 
A[0] = 0, thus the output is 0.
Example 3:

Input: [-10,-5,3,4,7,9]
Output: -1
Explanation: 
There is no such i that A[i] = i, thus the output is -1.

/**
 * @param {number[]} A
 * @return {number}
 */
var fixedPoint = function(A) {
    
};
```

### Edge Case

* 可能會有兩種以上答案，例如這種 \[-10, -5, -2, 0, 4, 5, 6, 7, 8, 9, 10]，題目說選最小的為 output 

### 哪種資料結構解

有順序姓而且明顯是在搜尋，所以會用 Array，而且 input 有順序而且又是找東西，所以會用 Binary Search

### 怎麼解

這題比較特別的是有可能會有一種以上答案，所以會先定義 minIndex 存最小的值。

```
let minIndex = Number.MAX_SAFE_INTEGER;
```

其他部分單純用 Binary Search 解

![](https://1787585077-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LqirD3iAZIDk4oDCfwS%2F-LqtRIy64UwWRHZYoDMr%2F-LqtUPZcFBo6znA3tdSt%2Fb1.jpg?alt=media\&token=e9dc0750-aac6-4a9b-8df4-0dd611c3a659)

```
mid = Math.floor((start + end) / 2); // 從中間開始找
if (mid < A[mid]) { // 2 < 0
    // 往左找      
    end = mid - 1;
} else if (mid > A[mid]) { // 2 > 0
    // 往右找
    start = mid + 1 // start = 3
} else {
    minIndex = Math.min(minIndex, mid);
    end = mid - 1;
};
```

![](https://1787585077-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-LqirD3iAZIDk4oDCfwS%2F-LqtRIy64UwWRHZYoDMr%2F-LqtUV8U_EyFjxBi_Rjr%2Fb2.jpg?alt=media\&token=524529c3-b74a-43f9-8c56-b99503c35a47)

```
var fixedPoint = function (A) {
    const len = A.length;
    let minIndex = Number.MAX_SAFE_INTEGER;
    if (len < 1) return -1;

    // 這邊都以 index 為單位
    let start = 0;
    let end = len - 1;

    //  從中間開始切
    let mid;

    while (start <= end) {
        mid = Math.floor((start + end) / 2);
        console.log('mid: ' + mid)
        if (mid < A[mid]) { 
            // 往左找      
            end = mid - 1;
        } else if (mid > A[mid]) { 
            // 往右找
            start = mid + 1 
        } else {
            minIndex = Math.min(minIndex, mid);
            end = mid - 1;
        };
    }
    // 如果上面都不符合代表找不到
    return (minIndex == Number.MAX_SAFE_INTEGER) ? -1 : minIndex;

};


console.log(fixedPoint([-10, -5, -2, 0, 4, 5, 6, 7, 8, 9, 10]))
```