# 1064 Fixed Point (有圖)
input 有順序而且又是找東西,很有可能就是考 Binary Search
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

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;
};

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]))
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